5i' SECTION 4 DETERMINATION OF THE NUMBER OF CIRCUITS IN AUTOMATIC AND SEMIAUTOMATIC OPERATION Recommendation E.520 NUMBER OF CIRCUITS TO BE PROVIDED IN AUTOMATIC AND/OR SEMIAUTOMATIC OPERATION, WITHOUT OVERFLOW FACILITIES This Recommendation refers to groups of circuits used: - in automatic operation; - in semiautomatic operation; - in both automatic and semiautomatic operations on the same group of circuits. 1 General method 1.1 The CCITT recommends that the number of circuits needed for a group should be read from tables or curves based on the clas- sical Erlang B formula (see Supplements Nos. 1 and 2 at the end of this fascicle which refers to full availability groups). Recom- mended methods for traffic determination are indicated in Recommendation E.500. For semi-automatic operation the loss probability p should be based on 3% during the mean busy hour. For automatic operation the loss probability p should be based on 1% during the mean busy hour. Semiautomatic traffic using the same circuits as automatic traffic is to be added to the automatic traffic and the same param- eter value of p = 1% should be used for the total traffic. The values of 3% and 1% quoted above refer to the Erlang B formula and derived tables and curves. The 3% value should not be considered as determining a grade of service because with semiau- tomatic operation there will be some smoothing of the traffic peaks; it is quoted here only to determine the value of the parameter p (loss probability) to use in the Erlang B tables and curves. 1.2 In order to provide a satisfactory grade of service both for the mean busy-hour traffic and for the traffic on exceptionally busy days, it is recommended that the proposed number of circuits should, if necessary, be increased to ensure that the loss proba- bility shall not exceed 7% during the mean busy hour for the aver- age traffic estimated for the five busiest days as specified in Recommendation E.500. 1.3 For small groups of long intercontinental circuits with automatic operation some relaxation could be made in respect to loss probability. It is envisaged that such circuits would be operated on a both-way basis and that a reasonable minimum for automatic service would be a group of six circuits. A table provid- ing relaxation in Annex A is based on a loss probability of 3% for six circuits, with a smooth progression to 1% for 20 circuits. The general provision for exceptional days remains unchanged. For exceptional circumstances in which very small groups (less than six intercontinental circuits) are used for automatic opera- tion, dimensioning of the group should be based on the loss proba- bility of 3%. 2 Time differences Time differences at the two terminations of intercontinental circuits are likely to be much more pronounced than those on con- tinental circuits. In order to allow for differences on groups con- taining both-way circuits it will be desirable to acquire informa- tion in respect to traffic flow both during the mean busy hour for both directions and during the mean busy hour for each direction. It is possible that in some cases overflow traffic can be accepted without any necessity to increase the number of circuits, in spite of the fact that this overflow traffic is of a peaky nature. Such circumstances may arise if there is no traffic over- flowing from high-usage groups during the mean busy hour of the final group. 3 Both-way circuits 3.1 With the use of both-way circuits there is a danger of simultaneous seizure at both ends; this is particularly the case on circuits with a long propagation time. It is advisable to arrange the sequence of selection at the two ends so that such double seizure can only occur when a single circuit remains free. When all the circuits of a group are operated on a both-way basis, time differences in the directional mean busy hours may result in a total mean busy-hour traffic flow for the group which is not the sum of the mean busy-hour traffic loads in each direc- tion. Furthermore, such differences in directional mean busy hour may vary with seasons of the year. However, the available methods of traffic measurement can determine the traffic flow during mean busy hour for this total traffic. 3.2 Some intercontinental groups may include one-way as well as both-way operated circuits. It is recommended that in all cases the one-way circuits should be used, when free, in preference to the both-way circuits. The number of circuits to be provided will depend upon the one-way and total traffic. The total traffic will need to be determined for: a) each direction of traffic; b) both-way traffic. This determination is to be made for the busy hour or the busy hours corresponding to the two cases a) and b) above. In the cases where the number of one-way circuits is approxi- mately equal for each direction, no special procedure is necessary, and the calculation can be treated as for a simple two-group grad- ing [1]. If the number of one-way circuits is quite different for the two directions, some correction may be needed for the difference in randomness of the flow of calls from the two one-way circuit groups to the both-way circuit group. The general techniques for handling cases of this type are quoted in Recommendation E.521. ANNEX A (to Recommendation E.520) Table A-1/E.520 may be applied to small groups of long inter- continental circuits. The values in column 2 are suitable for a random offered traffic with full availability access. The table is based on 1% loss probability for 20 circuits and increases progressively to a loss probability of 2% at 9 circuits and 3% at 6 circuits (loss probabilities for these three values being based on the Erlang loss formula: see Supplement No. 1). The traffic flow values obtained from a smoothing curve coincide very nearly with those determined by equal marginal utility theory, i.e. an improvement factor of 0.05 Erlang for an additional cir- cuit. For groups requiring more than 20 circuits the table for loss probability of 1%, mentioned in Supplement No. 1, should be used. H.T. [T1.520] TABLE A-1/E.520 ___________________________________________________________________ Traffic flow (in erlangs) Number of circuits Offered Carried Encountering congestion ___________________________________________________________________ (1) (2) (3) (4) ___________________________________________________________________ 6 2.54 2.47 0.08 7 3.13 3.05 0.09 8 3.73 3.65 0.09 9 4.35 4.26 0.09 10 4.99 4.90 0.09 11 5.64 5.55 0.10 12 6.31 6.21 0.10 13 6.99 6.88 0.10 14 7.67 7.57 0.10 15 8.37 8.27 0.11 16 9.08 8.96 0.11 17 9.81 9.69 0.11 18 10.54 10.42 0.11 19 11.28 11.16 0.12 20 12.03 11.91 0.12 ___________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Table A-1/E.520 [T1.520] p.1 Reference [1] TANGE (I.): Optimal use of both-way circuits in cases of unlimited availability, TELE , English Edition, No. 1, 1956. Recommendation E.521 CALCULATION OF THE NUMBER OF CIRCUITS IN A GROUP CARRYING OVERFLOW TRAFFIC A calculation of the number of circuits in a group carrying overflow traffic should be based on this Recommendation and on Recommendation E.522 dealing with high-usage groups. The objective grade of service used is that the average block- ing during the busy-hour of the 30 busiest days of the year will not exceed 1%. To determine the number of circuits in a group carrying over- flow traffic , three traffic parameters are required: the average traffic offered to the group, the weighted peakedness factor , and the level of day-to-day traffic variations. The level of day-to-day traffic variations indicates the degree to which the daily busy-hour traffic deviates from the overall mean traffic, and is determined by the sample variance of the 30 busy-hour traffic. The peakedness factor indicates the degree to which the varia- bility of the traffic deviates from pure chance traffic within a single hour, and in statistical terms is the variance-to-mean ratio of the distribution of simultaneous overflow traffic. 1 Determination of the level of day-to-day traffic varia- tions Let M1, M2, . | | , M3\d0denote the 30 busy-hour loads of the traffic offered to the final group. Determine the mean traffic M of the daily traffic by M = [Formula Deleted] j =1 ~ 0 M j .bp Determine the sample variance Vdof the daily traffic by V d = [Formula Deleted] j =1 ~ 0 (M j - M ) 2 Determine the point (M , Vd) on Figure 1/E.521; M on the hor- izontal axis, and Vdon the vertical axis. i) If the point (M , Vd) is below the bottom curve, the level of variation is Null . ii) If the point is between the lower two curves, the level of variation is Low . iii) If the point is between the upper two curves, the level of variation is Medium . iv) If the point is above the highest curve, the level of variation is High . Default procedures: if the data are not available to compute the variance Vduse the following guidelines: a) If no more than 25 per cent of the traffic offered to the final group is overflow from other groups, assume the level of day-to-day variation is Low. b) Otherwise, assume a Medium level of variation. Figure 1/E.521, p.2 (Recup.) 2 Determination of peakedness factor z Peakedness factors depend principally upon the number of high-usage circuits over which random traffic has access. When the number of such high-usage circuits does not exceed 30, the actual peakedness of the traffic overflowing from a high-usage group will be only slightly below the maximum peakedness values , | Table 1/E.521. H.T. [T1.521] TABLE 1/E.521 Maximum peakedness factor z i _________________________ Tables giving: - the exact mean of the overflow traffic, and - the difference between variance and mean of the overflow have been computed and are set out in [1]. Curves giving the exact mean and variance of overflow traffic are given in [2]. See also a more detailed description of the method in [3] and [4]. _____________________________________________________ | { { _____________________________________________________ 1 1.17 16 2.44 2 1.31 17 2.49 3 1.43 18 2.55 4 1.54 19 2.61 5 1.64 20 2.66 6 1.73 21 2.71 7 1.82 22 2.76 8 1.90 23 2.81 9 1.98 24 2.86 10 2.05 25 2.91 11 2.12 26 2.96 12 2.19 27 3.00 13 2.26 28 3.05 14 2.32 29 3.09 15 2.38 30 3.14 _____________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Table 1/E.521 [T1.521] (Recup. + Corr.) p.3 For more than 30 circuits, the peakedness of the traffic over- flowing from a high-usage group i of nicircuits is given by zi= 1 - |i+ fInfIi+ 1 + |fIi(em AfIi _________________________ where Ai is the mean (random) traffic offered to the nicircuits and |i is the traffic overflowing. The overflow traffic |iis found by employing the standard Erlang loss formula E 1, ni (Ai): |i= A i E 1, ni (Ai). The weighted mean peakedness factor z , is then calculated from: z = i =1 ~ fIh |fIi i =1 ~ fIh |fIi _________ for the h parcels of traffic being offered to the final group. Note that for the traffic directly offered to the final group, the peakedness factor is zi = 1. 3 Determination of the mean traffic offered to the final group and the number of circuits required 3.1 For planning future network requirements, the traffic overflowing to a final group should be determined theoretically from forecasts of traffics offered to the high-usage groups. The mean traffic overflowing to the final group from a high-usage group is determined in two steps: i) the "single-hour" overflow traffic |ioverflowing from nicircuits is given as above by |i= A i E i, ni (Ai), when Aiis the forecast of traffic offered to the i th high-usage group; ii) the average overflow traffic | i overflowing from the nicircuits is then determined by adjusting the single-hour traffic |ifor the effect of day-to-day traffic variations. | i= ri|i The adjustment factor riis given in Table 2/E.521; it is a function of: - the offered traffic Ai, - the traffic A i E i, n -1 (Ai) - |icarried by the last trunk i , and - the level of day-to-day variations of the traffic offered to the high-usage group. This level can be determined using the method described in S 1 above, but applying it to measurements of traffic offered to the high-usage group. If such measurements are not available a medium level can be used. The mean traffic offered to the final group is then the sum of all | iover the h parcels of traffic: M = i =1 ~ fIh | i It can be assumed that the level of day-to-day traffic varia- tions on the final group remains constant over the forecast time period. Using the level of day-to-day traffic variation as determined in S 1 above on the final group and the peakedness factor of S 2 above, the appropriate table of Tables 3/E.521 to 6/E.521 is used to derive the number of circuits required. Note 1 - This method of calculation of the mean traffic offered to the final group is valid only if the overflow traffic due to blocking encountered in the exchange in the attempts to con- nect to a high-usage, is negligible. Note 2 - Table 3/E.521 differs slightly from the previous tables published by CCITT, although in Table 3.1/E.521 there is no allowance for day-to-day variations. The new table takes into account a systematic bias in the measurement procedure that is based on a finite period of time (1 hour), instead of an infinite period as was assumed in the previous table [5]. Note 3 - Tables 4/E.521, 5/E.521 and 6/E.521 are based on the calculation of the average blocking from the formula: | = B (m ) f (m )dm , where B (m ) is the single-hour expected blocking and f (m ) is the density distribution of day-to-day traffic (m ), assuming a Pearson Type III distribution: 336.nr 15 408 | |f(m)=/ (M 2/V fId ) M /V)(____fRfIm [(M 2/V fId )- 1] e -M mfR /V fId | | M and Vdare the mean and day-to-day variance of the traffic as cal- culated [5] in S 1 above. H.T. [T2.521] TABLE 2/E.521 Overflow adjustment for high-usage trunk groups Factor r i __________________________________________________________________________________________________________________________________________________________ Last trunk traffic { Low daily variation Medium daily variation High daily variation 0.25 0.3 0.4 0.5 0.6 0.25 0.3 0.4 0.5 0.6 0.25 0.3 __________________________________________________________________________________________________________________________________________________________ 3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 5 1.0 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.0 1.0 1.2 1.2 1.1 1.1 1.0 7 1.0 1.0 1.0 1.0 1.0 1.2 1.2 1.1 1.1 1.0 1.4 1.3 1.2 1.1 1.1 10 1.1 1.1 1.1 1.0 1.0 1.3 1.2 1.2 1.1 1.1 1.5 1.4 1.3 1.2 1.1 15 1.2 1.1 1.1 1.1 1.0 1.5 1.4 1.2 1.2 1.1 1.8 1.6 1.4 1.3 1.1 20 1.2 1.2 1.1 1.1 1.0 1.6 1.5 1.3 1.2 1.1 2.0 1.8 1.5 1.3 1.2 25 1.3 1.2 1.2 1.1 1.1 1.8 1.6 1.4 1.3 1.1 2.3 2.0 1.7 1.4 1.2 30 1.3 1.3 1.2 1.1 1.1 1.8 1.7 1.4 1.3 1.2 2.4 2.1 1.7 1.5 1.3 __________________________________________________________________________________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Table 2/E.521 (Recup. + Corr.) [T2.521], p.4 Blanc H.T. [T3.521] TABLE 3/E.521 Single-hour capacity, in Erlangs, as a function of the number of trunks and of the peakedness factor ___________________________________________________________________________ Parameters: - | lockage 0.01; { - | fINo allowance for day-to-day variation; } { - | eighted mean peakedness factor. } ___________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | _______________________________________________________________________________________________________________________________________________________ Number of trunks required 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.4 3.8 4.0 1 0.06 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 0.22 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3 0.53 0.33 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4 0.94 0.69 0.50 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5 1.42 1.14 0.89 0.67 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6 1.97 1.64 1.36 1.08 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7 2.56 2.19 1.86 1.58 1.31 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8 3.19 2.81 2.44 2.11 1.81 1.53 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9 3.83 3.42 3.03 2.67 2.36 2.03 1.75 1.50 0.0 0.0 0.0 0.0 0.0 0.0 10 4.53 4.08 3.67 3.28 2.92 2.58 2.28 2.00 1.75 0.0 0.0 0.0 0.0 0.0 11 5.22 4.75 4.31 3.89 3.53 3.17 2.83 2.53 2.25 1.97 0.0 0.0 0.0 0.0 12 5.94 5.44 4.97 4.56 4.14 3.78 3.42 3.08 2.78 2.47 2.22 0.0 0.0 0.0 13 6.67 6.14 5.64 5.19 4.81 4.39 4.03 3.67 3.33 3.03 2.72 0.0 0.0 0.0 14 7.42 6.86 6.36 5.89 5.44 5.03 4.67 4.28 3.94 3.61 3.28 2.69 0.0 0.0 15 8.17 7.58 7.06 6.58 6.11 5.69 5.31 4.92 4.56 4.19 3.86 3.22 0.0 0.0 16 8.94 8.33 7.78 7.28 6.81 6.36 5.94 5.56 5.17 4.81 4.44 3.81 3.19 0.0 17 9.72 9.08 8.50 8.00 7.50 7.06 6.61 6.19 5.81 5.42 5.06 4.39 3.75 3.44 18 10.50 9.83 9.25 8.72 8.22 7.75 7.31 6.86 6.44 6.06 5.69 4.97 4.31 4.00 19 11.31 10.61 10.00 9.44 8.92 8.44 7.97 7.53 7.11 6.72 6.33 5.58 4.89 4.58 20 12.08 11.39 10.78 10.19 9.67 9.14 8.67 8.22 7.81 7.39 6.97 6.22 5.50 5.17 21 12.89 12.19 11.53 10.94 10.39 9.86 9.39 8.92 8.47 8.06 7.64 6.86 6.11 5.78 22 13.72 13.00 12.31 11.69 11.14 10.61 10.08 9.61 9.17 8.72 8.31 7.50 6.75 6.39 23 14.53 13.78 13.08 12.47 11.89 11.36 10.81 10.33 9.86 9.42 8.97 8.17 7.39 7.00 24 15.36 14.58 13.89 13.22 12.64 12.08 11.56 11.03 10.56 10.11 9.67 8.83 8.03 7.64 25 16.19 15.39 14.67 14.00 13.39 12.83 12.28 11.78 11.28 10.81 10.36 9.50 8.69 8.31 26 17.03 16.22 15.47 14.81 14.17 13.58 13.03 12.50 12.00 11.53 11.06 10.19 9.36 8.94 27 17.86 17.03 16.28 15.58 14.94 14.33 13.78 13.22 12.72 12.22 11.75 10.86 10.03 9.61 28 18.69 17.86 17.08 16.36 15.72 15.11 14.53 13.97 13.44 12.94 12.47 11.56 10.69 10.28 29 19.56 18.69 17.89 17.17 16.50 15.86 15.28 14.72 14.19 13.67 13.19 12.28 11.39 10.94 30 20.39 19.53 18.72 17.97 17.28 16.64 16.06 15.47 14.92 14.42 13.92 12.97 12.08 11.64 31 21.25 20.36 19.53 18.78 18.08 17.42 16.81 16.22 15.67 15.14 14.64 13.69 12.78 12.33 32 22.11 21.19 20.36 19.58 18.89 18.22 17.58 17.00 16.42 15.89 15.36 14.39 13.47 13.03 33 22.97 22.06 21.19 20.39 19.67 19.00 18.36 17.75 17.19 16.64 16.11 15.11 14.17 13.72 34 23.83 22.89 22.00 21.22 20.47 19.81 19.14 18.53 17.94 17.39 16.86 15.86 14.89 14.42 35 24.69 23.75 22.83 22.03 21.28 20.58 19.92 19.31 18.69 18.14 17.61 16.58 15.61 15.14 36 25.58 24.58 23.69 22.86 22.11 21.39 20.72 20.08 19.47 18.89 18.36 17.31 16.31 15.83 37 26.44 25.44 24.53 23.69 22.92 22.19 21.50 20.86 20.25 19.67 19.11 18.06 17.06 16.56 38 27.31 26.31 25.36 24.53 23.72 23.00 22.31 21.64 21.03 20.44 19.86 18.81 17.78 17.28 39 28.19 27.17 26.22 25.36 24.56 23.81 23.11 22.44 21.81 21.19 20.64 19.53 18.50 18.00 40 29.08 28.03 27.06 26.19 25.39 24.61 23.89 23.22 22.58 21.97 21.39 20.28 19.25 18.72 41 29.94 28.89 27.92 27.03 26.19 25.44 24.69 24.03 23.36 22.75 22.17 21.06 19.97 19.47 42 30.83 29.75 28.78 27.86 27.03 26.25 25.53 24.81 24.17 23.53 22.94 21.81 20.72 20.19 43 31.72 30.64 29.61 28.72 27.86 27.08 26.33 25.61 24.94 24.31 23.69 22.56 21.47 20.94 44 32.61 31.50 30.47 29.56 28.69 27.89 27.14 26.42 25.75 25.11 24.50 23.33 22.22 21.69 45 33.50 32.39 31.33 30.42 29.53 28.72 27.94 27.22 26.56 25.89 25.28 24.08 22.97 22.42 46 34.39 33.25 32.19 31.25 30.39 29.56 28.78 28.03 27.33 26.69 26.06 24.86 23.72 23.17 47 35.28 34.14 33.08 32.11 31.22 30.39 29.58 28.86 28.14 27.47 26.83 25.64 24.47 23.92 48 36.17 35.00 33.94 32.97 32.06 31.22 30.42 29.67 28.94 28.28 27.64 26.42 25.25 24.69 49 37.06 35.89 34.81 33.81 32.92 32.06 31.25 30.47 29.75 29.08 28.42 27.19 26.00 25.44 50 37.97 36.78 35.67 34.67 33.75 32.89 32.08 31.31 30.58 29.89 29.22 27.97 26.78 26.19 _______________________________________________________________________________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Table 3/E.521 (Recup.) [T3.521], p.5 H.T. [T4.521] TABLE 4/E.521 Single-hour capacity, in Erlangs, as a function of the number of trunks and of the peakedness factor ___________________________________________________________________________ Parameters: - | lockage 0.01; { - | fILow day-to-day variation allowance; } { - | eighted mean peakedness factor. } ___________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | _______________________________________________________________________________________________________________________________________________________ Number of trunks required 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.4 3.8 4.0 1 0.06 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 0.22 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3 0.53 0.33 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4 0.94 0.69 0.50 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5 1.39 1.14 0.89 0.67 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6 1.89 1.64 1.36 1.08 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7 2.44 2.14 1.86 1.58 1.31 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8 3.03 2.69 2.42 2.11 1.81 1.53 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9 3.64 3.28 2.97 2.67 2.36 2.03 1.75 1.50 0.0 0.0 0.0 0.0 0.0 0.0 10 4.25 3.89 3.56 3.22 2.92 2.58 2.28 2.00 1.75 0.0 0.0 0.0 0.0 0.0 11 4.92 4.53 4.17 3.83 3.50 3.17 2.83 2.53 2.25 1.97 0.0 0.0 0.0 0.0 12 5.58 5.17 4.78 4.44 4.08 3.78 3.42 3.08 2.78 2.47 2.22 0.0 0.0 0.0 13 6.25 5.81 5.42 5.06 4.69 4.36 4.03 3.67 3.33 3.03 2.72 0.0 0.0 0.0 14 6.94 6.50 6.08 5.69 5.33 4.97 4.64 4.28 3.94 3.61 3.28 2.69 0.0 0.0 15 7.64 7.17 6.75 6.33 5.97 5.61 5.25 4.92 4.56 4.19 3.86 3.22 0.0 0.0 16 8.33 7.86 7.42 7.00 6.61 6.25 5.89 5.53 5.17 4.81 4.44 3.81 3.19 0.0 17 9.06 8.56 8.11 7.67 7.28 6.89 6.53 6.17 5.81 5.42 5.06 4.39 3.75 3.44 18 9.81 9.28 8.81 8.36 7.94 7.56 7.17 6.81 6.44 6.06 5.69 4.97 4.31 4.00 19 10.53 10.00 9.50 9.06 8.61 8.22 7.83 7.44 7.08 6.72 6.33 5.58 4.89 4.58 20 11.28 10.72 10.22 9.75 9.31 8.89 8.50 8.11 7.72 7.36 6.97 6.22 5.50 5.17 21 12.03 11.44 10.94 10.44 10.00 9.56 9.17 8.78 8.39 8.03 7.64 6.86 6.11 5.78 22 12.78 12.19 11.67 11.17 10.69 10.25 9.83 9.44 9.06 8.67 8.31 7.56 6.75 6.39 23 13.53 12.94 12.39 11.89 11.42 10.94 10.53 10.11 9.72 9.33 8.94 8.19 7.39 7.00 24 14.31 13.69 13.14 12.61 12.11 11.67 11.22 10.81 10.39 10.00 9.61 8.86 8.03 7.64 25 15.08 14.44 13.86 13.33 12.83 12.36 11.92 11.50 11.08 10.67 10.28 9.50 8.67 8.31 26 15.86 15.22 14.61 14.08 13.56 13.08 12.61 12.19 11.75 11.36 10.94 10.17 9.33 8.94 27 16.64 15.97 15.36 14.81 14.28 13.81 13.33 12.89 12.44 12.03 11.64 10.83 10.00 9.61 28 17.42 16.75 16.14 15.56 15.03 14.53 14.06 13.58 13.14 12.72 12.31 11.50 10.67 10.28 29 18.22 17.53 16.89 16.31 15.78 15.25 14.78 14.31 13.86 13.42 13.00 12.19 11.36 10.94 30 19.00 18.31 17.67 17.06 16.50 16.00 15.50 15.03 14.56 14.11 13.69 12.86 12.06 11.64 31 19.81 19.08 18.44 17.83 17.25 16.72 16.22 15.72 15.28 14.83 14.39 13.56 12.75 12.33 32 20.61 19.89 19.19 18.58 18.00 17.47 16.94 16.47 16.00 15.53 15.11 14.25 13.44 13.03 33 21.39 20.67 19.97 19.36 18.78 18.22 17.69 17.19 16.72 16.25 15.81 14.94 14.14 13.72 34 22.22 21.47 20.75 20.11 19.53 18.97 18.42 17.92 17.44 16.97 16.53 15.67 14.83 14.42 35 23.03 22.25 21.56 20.89 20.28 19.72 19.17 18.67 18.17 17.69 17.22 16.36 15.56 15.11 36 23.83 23.06 22.33 21.67 21.06 20.47 19.92 19.39 18.89 18.42 17.94 17.08 16.25 15.81 37 24.64 23.86 23.14 22.44 21.83 21.25 20.67 20.14 19.64 19.14 18.67 17.78 16.94 16.50 38 25.47 24.67 23.92 23.25 22.61 22.00 21.44 20.89 20.36 19.89 19.42 18.50 17.64 17.19 39 26.28 25.47 24.72 24.03 23.39 22.78 22.19 21.64 21.11 20.61 20.14 19.22 18.33 17.89 40 27.11 26.28 25.53 24.81 24.17 23.53 22.94 22.39 21.86 21.36 20.86 19.94 19.06 18.61 41 27.92 27.08 26.31 25.61 24.94 24.31 23.72 23.14 22.61 22.11 21.61 20.67 19.78 19.31 42 28.75 27.92 27.11 26.39 25.72 25.08 24.47 23.92 23.36 22.83 22.33 21.39 20.47 20.03 43 29.58 28.72 27.92 27.19 26.50 25.86 25.25 24.67 24.11 23.58 23.08 22.11 21.19 20.75 44 30.42 29.56 28.75 28.00 27.31 26.64 26.03 25.44 24.89 24.33 23.83 22.86 21.92 21.44 45 31.25 30.36 29.56 28.81 28.08 27.44 26.81 26.22 25.64 25.11 24.58 23.58 22.64 22.17 46 32.08 31.19 30.36 29.61 28.89 28.22 27.58 26.97 26.42 25.86 25.33 24.33 23.36 22.89 47 32.92 32.03 31.17 30.42 29.69 29.00 28.36 27.75 27.17 26.61 26.08 25.06 24.11 23.64 48 33.75 32.83 32.00 31.22 30.47 29.81 29.14 28.53 27.94 27.39 26.83 25.81 24.83 24.36 49 34.58 33.67 32.81 32.03 31.28 30.58 29.94 29.31 28.72 28.14 27.58 26.56 25.56 25.08 50 35.44 34.50 33.64 32.83 32.08 31.39 30.72 30.08 29.50 28.92 28.36 27.31 26.31 25.83 _______________________________________________________________________________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Table 4/E.521 (Recup.) [T4.521], p.6 H.T. [T5.521] TABLE 5/E.521 Single-hour capacity, in Erlangs, as a function of the number of trunks and of the peakedness factor ___________________________________________________________________________ Parameters: - | lockage 0.01; { - | fIMedium day-to-day variation allowance; } { - | eighted mean peakedness factor. } ___________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | _______________________________________________________________________________________________________________________________________________________ Number of trunks required 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.4 3.8 4.0 1 0.06 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 0.22 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3 0.53 0.33 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4 0.94 0.69 0.50 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5 1.39 1.14 0.89 0.67 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6 1.86 1.61 1.36 1.08 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7 2.39 2.11 1.83 1.58 1.31 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8 2.94 2.64 2.36 2.08 1.81 1.53 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9 3.53 3.19 2.89 2.61 2.33 2.03 1.75 1.50 0.0 0.0 0.0 0.0 0.0 0.0 10 4.11 3.78 3.47 3.17 2.86 2.58 2.28 2.00 1.75 0.0 0.0 0.0 0.0 0.0 11 4.72 4.39 4.03 3.72 3.42 3.14 2.83 2.53 2.25 1.97 0.0 0.0 0.0 0.0 12 5.36 4.97 4.64 4.31 4.00 3.69 3.39 3.08 2.78 2.47 2.22 0.0 0.0 0.0 13 6.00 5.61 5.25 4.89 4.56 4.25 3.94 3.67 3.33 3.03 2.72 0.0 0.0 0.0 14 6.64 6.22 5.86 5.50 5.17 4.83 4.53 4.22 3.92 3.61 3.28 2.69 0.0 0.0 15 7.31 6.89 6.47 6.11 5.78 5.42 5.11 4.78 4.47 4.19 3.86 3.22 0.0 0.0 16 7.97 7.53 7.11 6.75 6.39 6.03 5.69 5.39 5.06 4.75 4.44 3.81 3.19 0.0 17 8.64 8.19 7.78 7.36 7.00 6.64 6.31 5.97 5.64 5.33 5.03 4.39 3.75 3.44 18 9.33 8.86 8.42 8.03 7.64 7.28 6.92 6.58 6.25 5.92 5.61 4.97 4.31 4.00 19 10.03 9.53 9.08 8.67 8.28 7.89 7.53 7.19 6.86 6.53 6.19 5.58 4.89 4.58 20 10.69 10.19 9.75 9.33 8.92 8.53 8.17 7.81 7.47 7.14 6.81 6.17 5.50 5.17 21 11.42 10.89 10.42 9.97 9.56 9.17 8.81 8.44 8.08 7.75 7.42 6.75 6.11 5.78 22 12.11 11.58 11.11 10.64 10.22 9.83 9.44 9.06 8.69 8.36 8.03 7.36 6.72 6.39 23 12.83 12.28 11.78 11.33 10.89 10.47 10.08 9.69 9.33 8.97 8.64 7.97 7.33 7.00 24 13.53 13.00 12.47 12.00 11.56 11.14 10.72 10.36 9.97 9.61 9.25 8.58 7.94 7.61 25 14.25 13.69 13.17 12.69 12.25 11.81 11.39 11.00 10.61 10.25 9.89 9.19 8.56 9.19 26 14.97 14.42 13.86 13.39 12.92 12.47 12.06 11.64 11.28 10.89 10.53 9.83 9.17 8.81 27 15.69 15.11 14.58 14.08 13.61 13.14 12.72 12.31 11.92 11.53 11.17 10.44 9.78 9.42 28 16.44 15.83 15.28 14.78 14.28 13.83 13.39 12.97 12.58 12.19 11.81 11.08 10.39 10.06 29 17.17 16.56 16.00 15.47 14.97 14.53 14.08 13.64 13.25 12.83 12.47 11.72 11.03 10.67 30 17.92 17.28 16.72 16.17 15.67 15.19 14.75 14.31 13.92 13.50 13.11 12.36 11.64 11.31 31 18.64 18.03 17.42 16.89 16.39 15.89 15.44 15.00 14.58 14.17 13.78 13.03 12.28 11.94 32 19.39 18.75 18.14 17.58 17.08 16.58 16.11 15.67 15.25 14.83 14.44 13.67 12.92 12.56 33 20.14 19.47 18.86 18.31 17.78 17.28 16.81 16.36 15.92 15.50 15.11 14.33 13.58 13.19 34 20.89 20.22 19.61 19.03 18.50 18.00 17.50 17.06 16.61 16.17 15.78 14.97 14.22 13.86 35 21.64 20.97 20.33 19.75 19.22 18.69 18.19 17.75 17.28 16.86 16.44 15.64 14.86 14.50 36 22.39 21.69 21.06 20.47 19.92 19.42 18.92 18.44 17.97 17.53 17.11 16.31 15.53 15.14 37 23.14 22.44 21.81 21.19 20.64 20.11 19.61 19.14 18.67 18.22 17.81 16.97 16.19 15.81 38 23.89 23.19 22.53 21.94 21.36 20.83 20.31 19.83 19.36 18.92 18.47 17.64 16.86 16.47 39 24.64 23.94 23.28 22.67 22.08 21.56 21.03 20.53 20.06 19.61 19.17 18.33 17.53 17.11 40 25.42 24.69 24.03 23.39 22.81 22.25 21.75 21.25 20.75 20.31 19.86 19.00 18.19 17.78 41 26.17 25.44 24.78 24.14 23.56 22.97 22.44 21.94 21.47 21.00 20.56 19.69 18.86 18.44 42 26.94 26.19 25.50 24.86 24.28 23.72 23.17 22.67 22.17 21.69 21.25 20.36 19.53 19.11 43 27.72 26.97 26.25 25.61 25.00 24.44 23.89 23.36 22.86 22.39 21.94 21.06 20.19 19.81 44 28.47 27.72 27.00 26.36 25.75 25.17 24.61 24.08 23.58 23.08 22.64 21.75 20.89 20.47 45 29.25 28.47 27.78 27.11 26.47 25.89 25.33 24.81 24.31 23.81 23.33 22.44 21.56 21.14 46 30.03 29.25 28.53 27.86 27.22 26.64 26.06 25.53 25.00 24.50 24.03 23.14 22.25 21.83 47 30.81 30.00 29.28 28.61 27.97 27.36 26.78 26.25 25.72 25.22 24.75 23.83 22.94 22.50 48 31.58 30.78 30.03 29.36 28.72 28.11 27.53 26.97 26.44 25.94 25.44 24.53 23.64 23.19 49 32.36 31.56 30.81 30.11 29.44 28.83 28.25 27.69 27.17 26.64 26.17 25.22 24.33 23.89 50 33.14 32.31 31.56 30.86 30.19 29.58 29.00 28.42 27.89 27.36 26.86 25.92 25.03 24.58 _______________________________________________________________________________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Table 5/E.521 (Recup.) [T5.521], p.7 H.T. [T6.521] TABLE 6/E.521 Single-hour capacity, in Erlangs, as a function of the number of trunks and of the peakedness factor ___________________________________________________________________________ Parameters: - | lockage 0.01; { - | fIHigh day-to-day variation allowance; } { - | eighted mean peakedness factor. } ___________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | _______________________________________________________________________________________________________________________________________________________ Number of trunks required 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.4 3.8 4.0 1 0.06 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 0.22 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3 0.53 0.33 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4 0.94 0.69 0.50 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5 1.36 1.14 0.89 0.67 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6 1.86 1.61 1.36 1.08 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7 2.36 2.08 1.83 1.58 1.31 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8 2.89 2.61 2.33 2.06 1.81 1.53 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9 3.44 3.14 2.86 2.58 2.31 2.03 1.75 1.50 0.0 0.0 0.0 0.0 0.0 0.0 10 4.03 3.69 3.39 3.11 2.83 2.56 2.28 2.00 1.75 0.0 0.0 0.0 0.0 0.0 11 4.61 4.25 3.94 3.64 3.36 3.08 2.81 2.53 2.25 1.97 0.0 0.0 0.0 0.0 12 5.19 4.83 4.50 4.19 3.89 3.61 3.33 3.06 2.78 2.47 2.22 0.0 0.0 0.0 13 5.81 5.42 5.08 4.78 4.44 4.17 3.86 3.58 3.31 3.03 2.72 0.0 0.0 0.0 14 6.42 6.03 5.67 5.33 5.03 4.72 4.42 4.14 3.83 3.58 3.28 2.69 0.0 0.0 15 7.03 6.64 6.28 5.92 5.61 5.28 4.97 4.69 4.39 4.11 3.83 3.22 0.0 0.0 16 7.67 7.25 6.86 6.53 6.19 5.86 5.56 5.25 4.94 4.67 4.36 3.81 3.19 0.0 17 8.31 7.86 7.47 7.11 6.78 6.44 6.11 5.81 5.50 5.22 4.92 4.36 3.75 3.44 18 8.94 8.50 8.11 7.72 7.36 7.03 6.69 6.39 6.08 5.78 5.47 4.89 4.31 4.00 19 9.58 9.14 8.72 8.33 7.97 7.64 7.31 6.97 6.64 6.33 6.03 5.44 4.89 4.58 20 10.22 9.78 9.36 8.94 8.58 8.22 7.89 7.56 7.22 6.92 6.61 6.00 5.44 5.14 21 10.89 10.42 9.97 9.58 9.19 8.83 8.50 8.14 7.83 7.50 7.19 6.58 6.00 5.69 22 11.53 11.06 10.61 10.22 9.83 9.44 9.08 8.75 8.42 8.08 7.78 7.17 6.56 6.25 23 12.19 11.72 11.28 10.83 10.44 10.06 9.69 9.36 9.00 8.67 8.36 7.72 7.14 6.83 24 12.86 12.36 11.92 11.47 11.08 10.69 10.31 9.94 9.61 9.28 8.94 8.31 7.69 7.39 25 13.53 13.03 12.56 12.11 11.69 11.31 10.94 10.56 10.22 9.89 9.56 8.92 8.28 7.97 26 14.19 13.69 13.22 12.75 12.33 11.94 11.56 11.19 10.83 10.47 10.14 9.50 8.86 8.56 27 14.89 14.36 13.86 13.42 12.97 12.58 12.19 11.81 11.44 11.08 10.75 10.08 9.44 9.14 28 15.56 15.03 14.53 14.06 13.64 13.22 12.81 12.42 12.06 11.69 11.36 10.69 10.03 9.72 29 16.25 15.69 15.19 14.72 14.28 13.86 13.44 13.06 12.69 12.33 11.97 11.31 10.64 10.31 30 16.92 16.36 15.86 15.36 14.92 14.50 14.08 13.69 13.31 12.94 12.58 11.89 11.22 10.92 31 17.61 17.06 16.53 16.03 15.58 15.14 14.72 14.33 13.94 13.56 13.19 12.50 11.83 11.50 32 18.31 17.72 17.19 16.69 16.22 15.78 15.36 14.94 14.56 14.19 13.83 13.11 12.44 12.11 33 18.97 18.42 17.86 17.36 16.89 16.44 16.00 15.58 15.19 14.81 14.44 13.72 13.06 12.69 34 19.67 19.08 18.53 18.03 17.56 17.08 16.67 16.25 15.83 15.44 15.08 14.36 13.67 13.31 35 20.36 19.78 19.22 18.69 18.22 17.75 17.31 16.89 16.47 16.08 15.69 14.97 14.28 13.92 36 21.06 20.47 19.89 19.36 18.89 18.42 17.97 17.53 17.11 16.72 16.33 15.61 14.89 14.53 37 21.75 21.14 20.58 20.06 19.56 19.08 18.61 18.19 17.78 17.36 16.97 16.22 15.50 15.14 38 22.44 21.83 21.25 20.72 20.22 19.72 19.28 18.83 18.42 18.00 17.61 16.86 16.14 15.78 39 23.17 22.53 21.94 21.39 20.89 20.39 19.94 19.50 19.06 18.64 18.25 17.50 16.75 16.39 40 23.86 23.22 22.64 22.08 21.56 21.06 20.58 20.14 19.72 19.31 18.89 18.11 17.39 17.00 41 24.56 23.92 23.33 22.75 22.22 21.75 21.25 20.81 20.36 19.94 19.53 18.75 18.00 17.64 42 25.28 24.61 24.00 23.44 22.92 22.42 21.92 21.47 21.03 20.58 20.19 19.39 18.64 18.29 43 25.97 25.31 24.69 24.14 23.58 23.08 22.58 22.14 21.67 21.25 20.83 20.03 19.28 18.89 44 26.67 26.03 25.39 24.81 24.28 23.75 23.25 22.78 22.33 21.92 21.47 20.67 19.89 19.53 45 27.39 26.72 26.08 25.50 24.94 24.44 23.94 23.44 23.00 22.56 22.14 21.33 20.53 20.17 46 28.08 27.42 26.78 26.19 25.64 25.11 24.61 24.14 23.67 23.22 22.78 21.97 21.17 20.81 47 28.81 28.14 27.47 26.89 26.33 25.81 25.28 24.81 24.33 23.89 23.44 22.61 21.81 21.44 48 29.53 28.83 28.19 27.58 27.00 26.47 25.97 25.47 25.00 24.56 24.11 23.28 22.47 22.08 49 30.22 29.53 28.89 28.28 27.69 27.17 26.64 26.14 25.67 25.19 24.75 23.92 23.11 22.72 50 30.94 30.25 29.58 28.97 28.39 27.83 27.31 26.81 26.33 25.86 25.42 24.58 23.75 23.36 _______________________________________________________________________________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Table 6/E.521 (Recup.) [T6.521], p.8 3.2 Computer implementation When computer facilities are available, it is possible to automate the use of Tables 3/E.521 to 6/E.521. For that purpose, numerical algorithms have been developed and are described in [5]. 4 Example 4.1 Level of day-to-day traffic variations If the traffics offered to a final group over the 30 busiest days are given (M1 to M3\d0) and if the mean load and variance are calculated to be 10 and 20 respectively, then applying Figure 1/E.521, a high level of day-to-day traffic variations should be used. 4.2 Future traffic offered to the final group and peaked- ness factor If the forecast of future traffics indicates that three par- cels of traffic will be offered to the final group: - the overflow from 6 circuits offered 7.8 Erlangs, - the overflow from 12 circuits offered 10 Erlangs, - 7 Erlangs offered directly, then Table 7/E.521 can be developed. Table 7/E.521 (Recup. + Corr.) T7.521 p.9 Note that the values of riare derived from Table 2/E.521 for medium level of day-to-day traffic variations; if the 30 busiest day traffics for each of the high-usage groups were available, a more appropriate level could be used for each group. Now all the information required is available: using the capa- city Table 6/E.521 for high level of day-to-day traffic variations, the average traffic offered to the final group M = 11.39 and a peakedness factor z = 1.3 (from interpolating between z = 1.2 and z = 1.4), it is calculated that 23 circuits are required. Note that if the measurements used in S 4.1 above were not available, then to determine the level of day-to-day traffic varia- tions it would have been necessary to use the default procedure of S 1 above. Overflow traffic offered to the final group = 4.15 Erlangs. Total traffic offered to the final group = 11.15 Erlangs. The ratio 4.15/11.15 = 0.37 is higher than 0.25 and hence a medium level of day-to-day traffic variations would have been used. References [1] Tabellen fur die Planung von Fernsprecheinrichtungen , Siemens u. Halske, Munchen, 1961. [2] WILKINSON (R. | .): Theories for toll traffic engineer- ing in the USA (Figures 12 and 13), Bell System Technical Journal , Vol. 35, March 1956. [3] WILKINSON (R. | .): Simplified engineering of single stage alternate routing systems, Fourth International Teletraffic Congress , London, 1964. [4] WILKINSON (R. | .): Non-random traffic curves and tables, Bell Telephone Laboratories , 1970. [5] HILL (D. | .) and NEAL (S. | .): The traffic capacity of a probability-engineered trunk group, Bell System Technical Journal , September 1976. Recommendation E.522 NUMBER OF CIRCUITS IN A HIGH-USAGE GROUP 1 Introduction For the economic planning of an alternate routing network the number of circuits in a high-usage group should be determined so that the annual charges for the whole network arrangement are at a minimum. This is done under the constraint that given requirements for the grade of service are fulfilled. In the optimum arrangement, the cost per erlang of carrying a marginal amount of traffic over the high-usage route or over the alternative route is the same. Figure 1/E.522 p.10 The optimum number of high-usage circuits, n , from one exchange (1) to another exchange (2) is therefore obtained from the following expression when the overflow traffic is routed over a transit exchange T (route 1-T-2, see Figure 1/E.522). F n (A ) = A { fIE 1, n (A ) - E 1, (n + 1) (A } = M x nnual charge(1-T-2) ___________________ A is the traffic flow offered, for the relation "1-2", in the Erlang loss formula for a full availability group Fn(A ) gives the marginal occupancy (improvement function) for the high-usage group, if one more circuit were added. M is the marginal utilization factor for the final route "1-T-2" (which has nothing to do with cost ratio), if one addi- tional circuit were provided. The annual charges are marginal charges for adding one additional circuit to route "1-2" and like- wise to route "1-T-2". Planning of an alternate routing network is described in the technical literature (see [1] to [10]). Annual charge as used in this Recommendation refers to invest- ment costs. 2 Recommended practical method 2.1 Field of application It must be recognized that the conditions applying to alterna- tive routing will vary widely between the continental network and the intercontinental network. Significant differences between the two cases apply to the length and cost of circuits, the traffic flow and the different times at which the busy hours occur. The method described attempts to take account of these factors in so far as it is practicable to do so in any simplified procedure. 2.2 Traffic statistics The importance of reliable traffic estimates should be emphasized. Traffic estimates are required for each of the _________________________ Marginal occupancy is often called LTC (last trunk capacity). Marginal utilization factor is often called ATC (addi- tional trunk capacity). relations in question, for both the busy hour of the relation and for the busy hour of each link of the routes to which the traffic overflows. Since this may be affected by the high-usage arrangements finally adopted, it will be necessary to have traffic estimates for each relation covering most of the significant hours of the day. This applies particularly to the intercontinental network where the final routes carry traffic com- ponents with widely differing busy hours. 2.3 Basis of the recommended method The method is based on a simplification of the economic dimen- sioning equations described under 1. Introduction. The simplifying assumptions are: i) the ratios of the alternative high-usage annual charges are grouped in classes and a single ratio selected as representative for each class. This is acceptable because total network costs are known to be relatively insensitive to changes in the annual charges ratio; ii) the marginal utilization factor M applicable to the overflow routes is regarded as constant within a range of cir- cuit group sizes; H.T. [T1.522] ___________________________________ { Size of group (number of circuits) } Value of M ___________________________________ For less than 10 0.6 For 10 or more 0.8 ___________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | Table 1/E.522 (Recup.) [T1.522], p.11 iii) each high-usage group will be dimensioned against the cheapest alternative route to which traffic overflows. (That is, the effect of parallel alternative routes is ignored.) Where greater precision is required in either network or indi- vidual route dimensioning, more sophisticated methods may be employed (see [5] and [7]). 2.4 Determination of cost ratio In continental and intercontinental working, the number of circuits to be provided in high-usage circuit groups depends upon the ratio of the annual charges estimated by the Administrations involved. The annual charge ratio (see Table 1/E.522) is defined as: R = nnual charge of one additional circuit on the high-usage route _______________________________________________________________ The "annual charge of one additional circuit on the alterna- tive route" is calculated by summing: - the annual charge per circuit of each link comprising the alternative route, and - the annual charge of switching one circuit at each intermediate switching centre. When a third Administration is involved, it may be necessary to calculate the annual charge for switching at the intermediate centre from the transit switching charge per holding minute Annual charges for switching = M x 60 x F x 26 x 12 x transit switching charge per holding minute. In the calculation of the conversion factor F from busy hour to day, its dependence on the traffic offered to the high usage route, the overflow probability and the time difference should be taken into account. As a guideline, Table 1/E.522, which is calcu- lated using the standard traffic profiles of Table 1/E.523, may be used. H.T. [T2.522] TABLE 1/E.522 _________________________ It may be necessary to calculate transit switching charge per holding minute from charge per conversation minute (efficiency factor is described in Recommendation E.506). ____________________________________________________________________________________________________________________________________ Time difference Offered traffic (erlangs) Overflow probability (%) 0 1 2 3 4 5 6 7 8 9 10 11 12 ____________________________________________________________________________________________________________________________________ 1 2.6 3.2 3.7 3.8 2.7 2.3 2.3 1.7 3.2 2.4 2.2 2.0 2.7 10 3.7 4.5 4.8 4.7 3.5 3.1 3.0 2.5 4.1 3.2 2.9 2.8 3.6 20 4.5 5.2 5.4 5.3 4.0 3.7 3.5 3.1 4.7 3.8 3.4 3.4 4.2 5 30 5.1 5.8 6.0 5.8 4.6 4.2 4.0 3.7 5.1 4.3 3.9 4.0 4.8 40 5.7 6.4 6.5 6.3 5.1 4.7 4.5 4.2 5.6 4.8 4.4 4.6 5.3 50 6.3 6.9 7.0 6.8 5.6 5.2 5.0 4.7 6.0 5.3 5.0 5.1 5.8 ____________________________________________________________________________________________________________________________________ 1 2.1 2.6 3.3 3.5 2.5 2.1 2.1 1.4 2.8 2.0 2.0 1.8 2.4 10 3.2 4.0 4.4 4.3 3.1 2.7 2.6 2.1 3.8 2.8 2.6 2.4 3.2 20 4.0 4.8 5.1 4.9 3.6 3.3 3.1 2.7 4.3 3.4 3.0 3.0 3.8 10 30 4.7 5.4 5.6 5.4 4.2 3.8 3.6 3.3 4.8 3.9 3.4 3.6 4.4 40 5.3 6.0 6.1 5.9 4.7 4.4 4.2 3.8 5.3 4.4 4.0 4.2 4.9 50 5.9 6.6 6.7 6.4 5.3 4.9 4.7 4.4 5.7 5.0 4.6 4.8 5.5 ____________________________________________________________________________________________________________________________________ 1 1.6 2.0 2.8 3.1 2.2 1.8 2.0 1.2 2.4 1.7 1.8 1.6 2.1 10 2.7 3.3 3.9 3.9 2.7 2.4 2.3 1.7 3.3 2.4 2.3 2.0 2.7 20 3.5 4.2 4.6 4.4 3.2 2.8 2.7 2.2 3.9 3.0 2.6 2.5 3.3 25 30 4.2 5.0 5.2 5.0 3.7 3.4 3.2 2.8 4.4 3.5 3.0 3.1 3.9 40 4.8 5.6 5.8 5.5 4.3 3.9 3.8 3.4 4.9 4.0 3.5 3.7 4.5 50 5.5 6.2 6.3 6.1 4.9 4.5 4.3 4.0 5.4 4.6 4.1 4.4 5.1 ____________________________________________________________________________________________________________________________________ 1 1.3 1.7 2.4 2.9 2.1 1.6 2.0 1.1 2.1 1.5 1.6 1.4 2.0 10 2.3 2.8 3.5 3.6 2.5 2.2 2.1 1.4 3.1 2.2 2.2 1.8 2.4 20 3.1 3.9 4.3 4.2 3.0 2.6 2.4 1.9 3.7 2.7 2.5 2.2 3.0 50 30 3.9 4.7 5.0 4.8 3.4 3.1 2.9 2.5 4.2 3.3 2.8 2.8 3.6 40 4.6 5.4 5.6 5.3 4.0 3.7 3.5 3.2 4.7 3.8 3.2 3.5 4.3 50 5.3 6.0 6.1 5.9 4.7 4.3 4.2 3.8 5.2 4.3 3.8 4.2 4.9 ____________________________________________________________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Note - Linear interpolation may be used to obtain intermediate results. Table 1/E.522 [T2.522], p.12 The value determined for R should then be employed to select in Table 2/E.522 the precise (or next higher) value of annual charges ratio for use in traffic tables. The value of annual charges ratios may be grouped in the following general sets: a) Within a single continent or other smaller closely connected land mass involving distances up to 1000 miles, high traffic and frequently one-way operation: These values are tentative. Ranges and representative values of annual charges ratio require further study. Annual charges ratio: R = 1.5; 2.0 ; 3.0; 4.0; 5.0; 6.0 and 7.0 b) Intercontinental working involving long dis- tances, small traffic and usually two-way operation: Annual charges ratio: R = 1.1; 1.3 ; 1.5; 2.0; 3.0; 4.0 and 5.0. 2.5 Use of method High-usage circuit groups carrying random traffic can be dimensioned from Table 2/E.522. Step 1 - Estimate the annual charges ratio R as described under 2.4 above. (There is little difference between adjacent ratios.) If this ratio is difficult to estimate, the values under- lined in a) and b) of S 2.4 above, should be used. Step 2 - Consult Table 2/E.522 to determine the number of high-usage circuits N . Note - When two values of N are given the right-hand figure applies to alternative routes of more than 10 circuits, the left-hand figure applies to smaller groups. The left-hand figure is omitted when it is no longer possible for the alternative route to be small. 3 24-hour traffic profiles The traffic value used in the method in S 2 should be the value of traffic offered to the high-usage route during the busy hour of the final route. In the case that some of the busy hours of the circuit groups or links forming an alternative route do not coincide with the busy hour of the relation, the ensuing method should be fol- lowed to take 24-hour traffic profiles into account (see [6], [8] and [9]). The method consists of the following three basic steps: i) prepare hourly traffic demands for which dimen- sioning is to be done; ii) size all circuit groups, high usage and final, for one hourly traffic demand; iii) iterate the process in step ii) for each addi- tional hourly matrix. 3.1 Preparation of hourly traffic demands Each Administration gathers historical traffic data on an hourly basis in accordance with Recommendations E.500 and E.523. Using historical data and information contained in Recommendation E.506, hourly traffic demand forecasts are made, resulting in a series of hourly demands for each exchange to every other exchange. 3.2 Sizing circuit groups for one-hourly traffic demand Using the methods in S 2 and Recommendation E.521, trunk group sizes are prepared for the first hourly traffic demand disregarding other hourly traffic demands. H.T. [T3.522] _____________________________________________________ TABLE 2/E.522 { Number of high-usage circuits for different values of offered traffic, annual charges ratios and sizes of overflow groups } _____________________________________________________ | | | | | | | | | | | | | | __________________________________________________________________________________________________________________________________________________ | | | | | | | | | | Annual charges ratios | | | | | | | | | { 1.1 1.3 { 0.545/0.727 0.46/0.615 { { __________________________________________________________________________________________________________________________________________________ 1.5 1/0 1/0 2/1 2/2 3/2 3/3 4/3 4/3 4/4 6 1.75 1/0 2/1 2/1 3/2 3/3 4/3 4/4 4/4 4/4 6 2.0 1/0 2/1 2/2 3/2 4/3 4/4 4/4 5/4 5/5 7 2.25 2/0 2/1 3/2 3/3 4/4 5/4 5/4 5/5 5/5 7 2.5 2/0 3/1 3/2 4/3 5/4 5/5 5/5 6/5 6/5 7 2.75 2/1 3/2 3/2 4/3 5/4 5/5 6/5 6/6 6/6 8 3.0 3/1 3/2 4/3 4/4 5/5 6/5 6/6 6/6 7/6 8 3.5 3/1 4/2 4/3 5/4 6/5 7/6 7/6 7/7 7/7 9 4.0 4/2 4/3 5/4 6/5 7/6 7/7 8/7 8/7 8/8 10 4.5 4/2 5/3 6/4 6/6 7/7 8/7 8/8 9/8 9/8 10 5.0 5/3 6/4 6/5 7/6 8/7 9/8 9/9 9/9 10/9 11 5.5 5/3 6/5 7/5 8/7 9/8 9/9 10/9 10/10 10/10 12 6.0 6/3 7/5 7/6 8/7 9/9 10/9 11/10 11/10 11/11 13 7.0 7/4 8/6 8/7 10/8 11/10 11/11 12/11 12/12 13/12 14 8.0 8/5 9/7 10/8 11/10 12/11 13/12 13/13 14/13 14/13 15 9.0 /6 /8 /9 /11 /12 /13 /14 /14 /15 17 10.0 /7 /9 /10 /12 /14 /15 /15 /16 /16 18 12.0 /9 /11 /12 /14 /16 /17 /18 /18 /19 20 15.0 /12 /14 /16 /18 /20 /21 /21 /22 /22 24 20.0 /16 /19 /21 /23 /25 /27 /28 /28 /29 30 25.0 /21 /24 /26 /29 /31 /33 /33 /34 /35 36 30.0 /26 /29 /31 /34 /37 /38 /39 /40 /41 42 40.0 /36 /39 /42 /45 /48 /50 /51 /52 /52 53 50.0 /45 /49 /52 /55 /59 /61 /62 /63 64 60.0 /55 /60 /62 /66 /70 /72 /73 75 80.0 /74 /80 /83 /87 /92 /94 /95 96 100.0 /94 /100 /103 /108 /113 /116 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 117 120.0 /113 /120 /124 /129 /134 /137 { Direct final circuit groups are } 138 150.0 /143 /150 /154 /160 /166 /169 economical within this area. 170 200.0 /192 /200 /205 /212 /219 221 250.0 /241 /250 /256 /263 /271 273 300.0 /290 /300 /306 /315 /323 324 __________________________________________________________________________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | Table 2/E.522 (Recup. + Corr.) [T3.522], p.13 MONTAGE a l'italienne, reprendre des originaux 3.3 Iterating for each additional hourly traffic matrix In sizing the circuit groups for the second hourly traffic demand, the method is provided with the circuit quantities result- ing from the previous step, and is constrained solely to increasing circuit group sizes; i.e., if the circuit group sizes for the first hourly traffic demand were greater than for the second hourly demand, then the circuit group sizes for the first hourly traffic demand would be retained. All additional hourly traffic demands are processed in the same iterative manner. The resulting circuit group sizes then satisfy the traffic demands for all hours being considered (see Annex A for a computational example). 3.4 Processing sequence Processing may start with the first hour of traffic demand, however, experiments have indicated that efficiencies of the network can be improved if processing starts with the hour with the smallest total traffic demand. It should be noted that this method gives us suboptimal networks, which may be improved by manual refinements. 4 Minimum outlay alternate routing networks The method below allows Administrations to adjust alternate routing networks to take into account existing revenue accounting divisions. The method consists of the following steps: i) Obtain 24-hour traffic profiles in accordance with Recommendations E.500 and E.523; ii) Compute circuit quantities and costs for a no-overflow network in accordance with Recommendation E.520; iii) Compute monthly overflow minutes (holding time) at varying percentages of busy-hour overflow. This is done by applying three conversion factors to the busy hour overflow erlangs: - Ratio of holding minutes to erlangs: a fixed value of 60. - Daily overflow to busy-hour overflow ratio: a value that depends on the 24-hour traffic profile and the degree of overflow. - Monthly overflow to daily overflow ratio (Recommendation E.506): a value that depends on the day-to-day pat- tern within a month and the degree of overflow. iv) Starting with the network calculated in step ii): - reduce the high usage circuits by one circuit, - calculate overflow to final circuit groups, - dimension final circuit groups in accordance with Recommendation E.521, - calculate circuit costs and transit charges; v) Iterate step iv) until the minimum outlay (cir- cuit costs plus transit charges) for terminal administrations is reached (see Annex B for computational example). 5 Service considerations On intercontinental circuits, where both-way operation is employed, a minimum of two circuits may be economical. Service con- siderations may also favour an increase in the number of direct circuits provided, particularly where the annual charges ratio approaches unity. Although the dimensioning of high-usage groups is normally determined by traffic flows and annual charges ratios, it is recognized that such groups form part of a network having service requirements relative to the subscriber. The ability to handle the offered traffic with acceptable traffic efficiency should be tempered by the overall network considerations on quality of service. The quality of service feature, which is of primary importance in a system of high-usage and final circuit groups, is the advan- tage derived from direct circuits versus multi-link connections. A liberal use of direct high-usage circuit groups, taking into account the economic factors, favours a high quality of service to the subscriber. It is recommended that new high-usage groups should be provided whenever the traffic flow and cost ratios are not con- clusive. This practice may result in direct high-usage groups of two circuits or more. The introduction of high-usage groups improves the overall grade of service and provides better opportunities of handling traffic during surges and breakdown conditions. When high-usage links bypass the main final routes the introduction of high-usage routes can assist in avoiding expenses which might otherwise be incurred in keeping below the maximum number of long-distance links in series. In the future, more measurements of traffic flows may be necessary for international accounting purposes and high-usage cir- cuits should make this easier. ANNEX A (to Recommendation E.522) Example of network dimensioning taking into account 24-hour traffic profiles A.1 Assumptions (see also Figure A-1/E.522) Calculations are performed under the following conditions: 1) Time difference: A is 9 hours west of B C is 5 hours west of A B is 10 hours west of C 2) Traffic profiles: 24-hour traffic profiles as per Table 1/E.523 are used. 3) Busy hour traffic: A-B 50 erlangs A-C 100 erlangs C-B 70 erlangs 4) Cost ratio: R = 1.3 Figure A-1/E.522 p.14 A.2 Numerical results 24 hourly traffic demands are processed. The order of process- ing are from the hour with the smallest total traffic demand to the hour with the largest total traffic demand. Computational results are given in Table A-1/E.522. H.T. [T4.522] TABLE A-1/E.522 Numerical results _______________________________________________________________________________________________________________ Hour Hourly traffic demand { Number of circuits obtained by single hour dimensioning (disregarding lower bounds imposed by the previous iterative stage) } { Number of circuits obtained considering lower bounds imposed by the previous iterative stage } { Number of circuits required to meet multiple hourly traffic demands } _______________________________________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ___________________________________________________________________________________ A-B A-C C-B A-B A-C C-B A-B A-C C-B A-B A-C C-B ___________________________________________________________________________________ 6 17.50 5.00 3.50 17 19 17 17 19 17 17 19 17 7 20.00 5.00 3.50 19 20 18 19 20 18 19 20 18 5 2.50 5.00 28.00 1 14 41 19 11 39 19 20 39 4 2.50 5.00 35.00 1 14 49 19 11 47 19 20 47 8 37.50 5.00 3.50 37 23 22 19 38 37 19 38 47 9 40.00 5.00 3.50 39 24 23 19 41 40 19 41 47 3 2.50 5.00 45.50 1 14 61 19 11 59 19 41 59 18 2.50 50.00 3.50 1 66 12 19 64 9 19 64 59 10 50.00 5.00 3.50 49 26 25 9 61 59 19 64 59 19 2.50 60.00 3.50 1 77 12 19 75 9 19 75 59 20 2.50 60.00 3.50 1 77 12 19 75 9 19 75 59 22 12.50 30.00 24.50 12 45 39 12 45 39 19 75 59 2 2.50 5.00 63.00 1 14 80 19 11 78 19 75 78 17 2.50 70.00 3.50 1 87 12 19 85 9 19 85 78 1 2.50 5.00 70.00 1 14 87 19 11 85 19 85 85 23 20.00 20.00 42.00 19 36 60 19 36 60 19 85 85 11 47.50 25.00 17.50 47 46 38 3 85 77 19 85 85 21 12.50 55.00 24.50 12 73 39 12 73 39 19 85 85 12 42.50 30.00 21.00 42 50 41 3 85 76 19 85 85 16 2.50 90.00 3.50 1 109 12 19 107 9 19 107 85 0 20.00 20.00 66.50 19 36 87 19 36 87 19 107 87 13 30.00 65.00 35.00 29 86 54 5 107 76 19 107 87 15 17.50 100.00 28.00 17 121 44 19 120 43 19 120 87 14 27.50 95.00 38.50 27 117 57 19 124 64 19 124 87 ___________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Table A-1/E.522 [T4.522], p.15 This example relates to an intercontinental network where busy hours of the three traffic relations are widely different among each other. The busy hour of the relation A-C, i.e. hour 15, is a low traffic period for the relations A-B and C-B. The busy hour of the relation C-B, i.e. hour 1, is a low traffic period for the relations A-B and A-C. Similarly, the busy hour of the relation A-B, i.e. hour 10, is a low traffic period for the relations A-C and C-B. In this case, the single hour dimensioning method, where traffic data during the busy hour of the final circuit group are used for dimensioning, cannot be applied. If the single hour dimen- sioning method is applied, this results in considerable under-dimensioning. If all the circuit groups are dimensioned as final, the required number of circuits are 64, 117 and 85 for the circuit groups A-B, A-C and C-B, respectively. About 14% of the total number of circuits is saved by the use of alternate routing. ANNEX B (to Recommendation E.522) Example of minimum outlay network dimensioning Figure B-1/E.522 p.16 B.1 Assumptions (see also Figure B-1/E.522) Calculations are performed under the following conditions: 1) Time difference: A is 3 hours west of B A is 3 hours west of C No time difference between B and C 2) Traffic profiles: 24-hour traffic profiles as per Table 1/E.523 are used. 3) Busy hour traffic: A-B 16 erlangs A-C 33 erlangs C-B 33 erlangs 4) Each Administration monthly cost per circuit: A-B 1000 units A-C 1000 units C-B 800 units 5) Transit charge per holding minute to each termi- nal Administration: 1/2 unit 6) Conversion factors: i) Holding minutes/erlangs: 60 ii) Daily overflow/busy hour overflow This conversion factor (F ) is calculated according to the guideline given in S 2.4. iii) Monthly overflow/daily overflow: 26 where medium social contact per Recommendation E.502 is assumed. 7) Grade-of-service (GOS) on final circuit groups: 0.01 B.2 Numerical results Numerical results are shown in Table B-1/E.522. The number of circuits C-B does not increase because of the 24-hour traffic pro- files matching. The number of high usage circuits A-B in the minimum outlay network is larger than that in the minimum cost net- work. The impact of considering transit charges in dimensionings is always in the direction of less overflow. H.T. [T5.522] TABLE B-1/E.522 Numerical results ______________________________________________________________ Network results { Economic results (x 1000 units/month) } ______________________________________________________________ | | | | | | | | | | | | ______________________________________________________________________________________________________ { Busy-hour overflow probability } Number of circuits Circuit costs Transit charges Total outlay ______________________________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | ________________________________________________________________________________________________________ A-B A-C C-B A B C A B C A B C ________________________________________________________________________________________________________ 0.0000 25 45 45 70 61 81 - - - 70.0 61.0 81.0 0.0090 25 45 45 70 61 81 0.3 0.3 (0.7) 70.3 61.3 80.3 0.0151 24 45 45 69 60 81 0.6 0.6 (1.3) 69.6 60.6 79.7 0.0221 23 45 45 68 59 81 0.9 0.9 (1.9) 68.9 59.9 79.1 0.0331 22 46 45 68 58 82 1.4 1.4 (2.9) 69.4 59.4 79.1 0.0471 21 46 45 67 57 82 2.1 2.1 (4.2) 69.1 59.1 77.8 0.0641 20 46 45 66 56 82 3.0 3.0 (6.0) 69.0 59.0 76.0 Minimum outlay for A and B 0.0861 19 47 45 66 55 83 4.2 4.2 (8.4) 70.2 59.2 74.5 0.1121 18 47 45 65 54 83 5.7 5.7 (11.5) 70.7 59.7 71.5 Minimum cost network 0.142 17 48 45 65 53 84 7.6 7.6 (15.1) 72.6 60.6 68.9 ________________________________________________________________________________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Table B-1/E.522 [T5.522], p.17 References [1] WILKINSON (R. | .): Theories for toll traffic engineer- ing in the USA, Bell Syst. Tech. J. , 1956, No. 35, pp. 421-514. [2] WILKINSON (R. | .): Simplified engineering of single stage alternate routing systems, Fourth International Teletraffic Congress , London, 1964. [3] RAPP (Y.): Planning of junction network in a multi-exchange area. 1. General Principles, Ericsson Tech ; 1964, No. 20, 1, pp. 77-130. [4] LEVINE (S. | .) and WERNANDER (M. | .): Modular engineering of trunk groups for traffic requirements, Fifth Inter- national Teletraffic Congress , New York, 1967. [5] PRATT (C. | .): The concept of marginal overflow in alternate routing, Fifth International Teletraffic Congress , New York, 1967. [6] EISENBERG (M.): Engineering traffic networks for more than one busy hour, Bell System Tech. J. , 1977, Vol. 56, pp. 1-20. [7] AKIMARU (H.) et al. : Derivatives of Wilkinson formula and their application to optimum design of alternative routing sys- tems, Ninth International Teletraffic Congress , Torremoli- nos, 1979. [8] HORN (R. | .): A simple approach to dimensioning a telecommunication network for many hours of traffic demand, Inter- national Conference on Communications , Denver, 1981. [9] BESHAI (M. | .): Traffic data reduction for multiple-hour network dimensioning, Second International Network Planning Symposium , Brighton, 1983. [10] LINDBERGER (K.): Simple approximations of overflow system quantities for additional demands in the optimization, Tenth International Teletraffic Congress , Montreal, 1983. Recommendation E.523 STANDARD TRAFFIC PROFILES FOR INTERNATIONAL TRAFFIC STREAMS The worldwide nature of the international telephone network, spanning as it does all possible time zones , has stimulated stu- dies of the traffic streams between countries in different relative time locations. These studies have led to the development of stand- ardized 24-hour traffic profiles which, theoretically based and verified by measurements, would be useful for engineering purposes. In fact, these concepts can be applied to a variety of network situations: i) variable access satellite working where a large number of traffic streams with possibly differing traffic profiles share the pool of satellite circuits; ii) combining of traffic streams on groups of ter- restrial circuits which may be either high-usage or final choice routes; iii) detour routing of traffic between origin and destination countries to take advantage of prevailing low load con- ditions on the detour path. In developing any such applications, account must be taken of the International Routing Plan (Recommendation E.171 [1]) and of accepted accounting principles (Recommendation D.150 [2]). It must be recognized that the preferred basis for dimension- ing consists of traffic profiles based on real traffic. Neverthe- less, many countries have found the standard profiles presented in this Recommendation very useful where streams are too small to obtain reliable measurements or where no measurements are avail- able. For both-way profiles , two equivalent methods of presentation are given in chart and tabular form. In Figure 1/E.523 hour-by-hour traffic volumes are shown in diagrammatically as percentages of the total daily traffic volume; such percentages are particularly con- venient for tariff studies. In Table 1/E.523, hourly traffics are expressed as percentages of the busy hour traffic , and this is convenient for engineering purposes. Time zone differences are given in whole hours only. Directional profiles are given in Tables 2/E.523 and 3/E.523. Although tables are given for both-way and directional traffic streams, it must be emphasized that at this stage only the both-way profiles can be regarded as soundly supported by measurement. The directional profiles are theoretically based and supported by some measurements, but should be used with caution until adequate verif- ication has been achieved. The theoretical basis for the profiles presented here is con- tained in Annex A. It depends on a convenience function f (t ) which represents the profile of local daily traffic , where of course no time zone difference exists. The function f (t ) used for computation of the standard profile was derived by mathematical manipulation of measurements of the Tokyo-Oakland and Tokyo-Vancouver streams. Although these results have been supported by other measurements, it leaves open the possibility that the con- venience function may vary from one country to another and that, strictly, these should be derived independently and then used to obtain a calculated profile for the international relation. It also seems that the convenience function for the country of destination should be given greater weight than that for the country of origin. These remarks suggest possible refinements, but are not quantified in this Recommendation. Figure 1/E.523 p.18 H.T. [T1.523] TABLE 1/E.523 Standard hourly bothway traffic patterns Local time in the more westerly country _____________________________________ BH { 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 % } _____________________________________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Unable to Convert Table Note 1 - The 24-hour profile of both-way traffic between any two countries is read from left to right from the appropriate row of the table; all time differences can be expressed in the range 0-12 hours. Each entry is expressed as a percentage of the busy hour traffic. Note 2 - The more westerly country of a traffic relation is the one from which we can proceed eastwards to the other through time zones not exceeding 12 hours. Note 3 - For network planning studies, UTC (Universal Coordinated Time) would normally be used so that all traffic streams are pro- cessed time consistently. Clearly if the more westerly country is W hours ahead of UTC (ignoring the international dateline), then the traffic at 0000-0100 UTC is obtained from the row corresponding to the time difference between the two countries at the column headed W ) to (25-W ). Example: For the traffic stream between the U.K. (UTC | | hour) and the central zone of USA (UTC + | 8 hours), the time difference is 7 hours and the USA is regarded as the more westerly country, hence W | | 8. Thus from the table, the traffic during 0000-0100 UTC is 5 | of the busy hour traffic, and the busy hour is 1500-1600 UTC. Note 4 - The column headed "BH %" gives the busy hour traffic volume as a percentage of the daily traffic volume. MONTAGE Time difference (in hours) between two countries Table 1/E.523 [T1.523] p.19 H.T. [T2.523] TABLE 2/E.523 Diurnal distributions of eastbound international telephone traffic Local time in the more westerly country Unable to Convert Table Note - This table is based on p | | .4, q | | .6, i.e. greater weight is given to the convenience function of the called party (see Annex A). MONTAGE Time difference (in hours) between two countries Table 2/E.523 [T2.523] p.20 H.T. [T3.523] TABLE 3/E.523 Diurnal distributions of westbound international telephone traffic Local time in the more westerly country Unable to Convert Table Note - This table is based on p | | .4, q | | .6, i.e. greater weight is given to the convenience function of the called party (see Annex A). MONTAGE Time difference (in hours) between two countries Table 3/E.523 [T2.523] p.21 ANNEX A (to Recommendation E.523) Mathematical expression for the influence of time differences on the traffic flow A telephone call is initiated when a person wishes to call someone else, but both parties have to be on the line before the call is established. It is considered that a telephone call is made at a time which tends to be convenient for both the calling and called parties. The degree of convenience for making a telephone call is considered to be a periodical function of time t , whose period is 24 hours. When the time difference between both parties is zero, the degree of convenience is denoted by f (t ), where t is local standard time. The graphic shape of the basic function f (t ) will be determined by the daily pattern of human activities, and will resemble, or fairly closely coincide with, the hour by hour traffic distribution in the national (or local) telephone network. It is assumed that the hourly traffic distribution F\u(*t(t ), when a time difference of ~ hours exists between the originating and called locations, is expressed as the geometric mean of con- venience functions of two locations ~ hours apart: F ~, (t ) = k | | | f(t)x f(t + ~) | | | 1/2 where k = 1/ 24 hours | | | f(t)x f(t + ~) | | | 1/2 dt (A-1) The sign of ~ is positive when the time at the destination is ahead of the reference time, and negative when the time of destination is behind the reference time. The distribution of equation (A-1) represents the sum of the outgoing and incoming traffics. Expressions for the one-way hourly traffic distributions can also be obtained by extending the concept of convenience function as follows. Define convenience functions both for the caller f0(t ) and for the called party fi(t ) .Then the one-way traffic distributions of east-bound and west-bound telephone calls, for the case of ~ hour time-difference, are similarly expressed as follows: F ~, east (t ) = k | | | f 0(t)x f fIi (t + ~) | | | 1/2 k = 1/ 24 hours | | | f 0(t)x f fIi (t + ~) | | | 1/2 dt (A-2) F ~, west (t ) = k | | | f fIi (t)x f 0(t + ~) | | | 1/2 k = 1/ 24 hours | | | f fIi (t)x f 0(t + ~) | | | 1/2 dt (A-3) where t is the local standard time of the west station and ~ is positive. It is natural that a caller makes a call considering the con- venience of the called person, and therefore the convenience func- tion of the called person ficontributes more than the convenience of the caller f0to the directional distribution F. They can be written as follows: f i (t ) = k 1 | | | f(t) | | | $$2x:p _, f 0 (t ) = k 2 | | | f(t) | | | $$2x:q _, (A-4) where p > q and p + q = 2, and where k1and k2are normalizing coefficients to ensure that: 24 hours f i (t ) dt = 1, 24 hours f 0 (t ) dt = 1. As to the values of p and q in equation (A-4), it has been found empirically that the convenience of the called side p is con- siderably larger than that of originating side q , and appropriate values are roughly p = 1.4 and consequently q = 0.6. References [1] CCITT Recommendation International telephone routing plan , Rec. E.171. [2] CCITT Recommendation New system for accounting in international telephony , Rec. D.150. Bibliography CASEY (J. | r.) and SHIMASAKI (N.): Optimal dimensioning of a satellite network using alternate routing concepts, Sixth Interna- tional Teletraffic Convention , Munich, 1970. RAPP (Y.): Planning of a junction network with non-coincident busy hours, Ericsson Technics , No. 1, 1971. CABALLERO (P. | .) and D'AZ (F.): Optimization of networks of hierarchical structure with non-coincident busy hours, Seventh International Teletraffic Convention , Stockholm, 1973. OTHA (T.): Network efficiency and network planning considering telecommunication traffic influenced by time difference, Seventh International Teletraffic Convention , Stockholm, 1973. Recommendation E.524 OVERFLOW APPROXIMATIONS FOR NON-RANDOM INPUTS 1 Introduction This Recommendation introduces approximate methods for the calculation of blocking probabilities for individual traffic streams in a circuit group arrangement. It is based on contribu- tions submitted in the Study Period 1984-1988 and is expected to be amended and expanded in the future (by adding the latest develop- ments of methods). The considered methods are necessary complements to those included in the existing Recommendation E.521 when it is required to take into account concepts such as cluster engineering with ser- vice equalization, service protection and end-to-end grade of ser- vice. Recommendation E.521 is then insufficient as it is concerned with the grade of service for only one non-random traffic stream in a circuit group. Design methods concerning the above-mentioned areas are sub- ject to further study and this Recommendation will serve as a reference when, in the future, Recommendation E.521 is complemented or replaced. In this Recommendation the proposed methods are evaluated in terms of accuracy, processing time, memory requirements and pro- gramming effort. Other criteria may be relevant and added in the future. The proposed methods are described briefly in S 2. Section 3 defines a set of examples of circuit group arrangements with exactly calculated (exact resolution of equations of state) indivi- dual blocking probabilities, to which the result of the methods can be compared. This leads to a table in S 4, where for each method the important criteria are listed. The publications cited in the reference section at the end contain detailed information about the mathematical background of each of the methods. 2 Proposed methods The following methods are considered: a) Interrupted Poisson Process (IPP) method, b) Equivalent Capacity (EC) method, c) Approximative Wilkinson Wallstrom (AWW) method. 2.1 IPP method IPP (Interrupted Poisson Process) is a Poisson process inter- rupted by a random switch. The on-/off-duration of the random switch has a negative exponential distribution. Overflow traffic from a circuit group can be accurately approximated by an IPP, since IPP can represent bulk characteristics of overflow traffic. IPP has three parameters, namely, on-period intensity and mean on-/off-period durations. To approximate overflow traffic by an IPP, those three parameters are determined so that some moments of overflow traffic will coincide with those of IPP. The following two kinds of moment match methods are considered in this Recommendation: - three-moment match method [1] - where IPP parame- ters are determined so that the first three moments of IPP will coincide with those of overflow traffic; - four-moment ratio match method [2] where IPP parameters are determined so that the first moment and the ratios of the 2nd/3rd and 7th/8th binomial moments of IPP will coincide with those of overflow traffic. To analyze a circuit group where multiple Poisson and overflow traffic streams are simultaneously offered, each overflow stream is approximated by an IPP. The IPP method is well suited to computer calculation. State transition equations of the circuit group with IPP inputs can be solved directly and no introduction of equivalent models is necessary. Characteristics of overflow traffic can be obtained from the solution of state transition equations. The main feature of the IPP method is that the individual means and vari- ances of the overflow traffic can be solved. 2.2 EC method The EC (Equivalent Capacity) method [3] does not use the traffic-moments but the transitional behaviour of the primary traffic, by introducing a certain function p"(n ) versus the equivalent capacity (n ) of the partial overflow traffic, as defined by the recurrent process: if n | is a positive integer and approximated by linear interpola- tion, if not. A practical approximation, considering the predominant over- flow congestion states only, leads to the equations: with: Di(n ) = 1 + ai | |pi(n ) -~pfIi(n - 1)| | (2-3) defining the equivalent capacity (ni) of the partial overflow traffic labelled i , and influenced by the mutual dependency between the partial overflow traffic streams. The mean value of the partial second overflow is: Oi= ai~~ p"i(n (2-4) where ~~ is the time congestion of the overflow group. The partial GOS (grade of service) equalization is fulfilled if: p"i(ni) = C (2-5) C | eing a constant to be chosen. 2.3 AWW method The AWW (Approximative Wilkinson Wallstrom) method uses an approximate ERT (Equivalent Random Traffic) model based on an improvement of Rapp's approximation. The total overflow in traffic is split up in the individual parts by a simple expression, see Equations (2-7) and (2-9). To calculate the total overflow traffic, any method can be used. An approximate Erlang formula calculation for which the speed is independent of the size of the calculated circuit group is given in [4]. The following notations are used: M mean of total offered traffic; V variance of total offered traffic; Z V /M ; B mean blocking of the studied group; mi, vi, zi, bi corresponding quantities for an individual traffic stream; ~ is used for overflow quantities. 2.3.1 Blocking of overflow traffic For overflow calculations, an approximate ERT-model is used. By numerical investigations, a considerable improvement has been found to Rapp's classical approximation for the fictitious traffic. The error added by the approximation is small compared to the error of the ERT-model. It is known that ERT underestimates low blockings when mixing traffic of diverse peakedness [2]. The formula, which was given in [4] (although with one printing error), is for Z > 1: A * = V + Z (Z - 1) (2 + /DlF`) where / = (2.36 Z - 2.17) log { + (z - 1)/[M (Z + 1.5) } and | = Z /(1.5M + 2Z -1.3) (2-6) 2.3.2 Wallstrom formula for individual blocking There has been much interest in finding a simple and accurate formula for the individual blocked traffic mi. Already in 1967, Katz [5] proposed a formula of the type mi= miB (1 - w + wzi/Z ) (2-7) with w | eing a suitable expression. Wallstrom proposed a very simple one but with reasonable results [6], [2]: w = 1 - B (2-8) One practical problem is, however, that a small peaked sub- stream could have a blocking bi > 1 with this formula. To avoid such unreasonable results a modification is used in this case. Let zm\da\dxbe the largest individual zi. Then the value used is [Formula Deleted]