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Fascicle II.3 _ Rec. E.522 11
All drawings appearing in this Recommendation have been done in
Autocad.
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 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 - CCITT 48090
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 overflow traffic is
routed over a transit exchange T (route 1_T_2, see Figure 1/E.522).
Fn(A) = A {E1, n(A) _ E1, (n + 1) (A)} = M x
A is the traffic flow offered, for the relation "1_2", in the
Erlang loss formula for a full availability group full availability
group. The expression Fn(A) gives the marginal occupancy1)
(improvement function) for the high_usage group, if one more
circuit were added.
M is the marginal utilization factor2) for the final route
"1_T_2" (which has nothing to do with cost ratio), if one
additional circuit were provided. The annual charges are marginal
charges for adding one additional circuit to route "1_2" and
likewise 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
investment costs.
2 Recommended practical method
2.1 Field of application
It must be recognized that the conditions applying to
alternative 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
relations in question, for both the busy hour 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 components with widely
differing busy hours.
2.3 Basis of the recommended method
The method is based on a simplification of the economic
dimensioning 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
circuit group sizes;
Size of group (number Value of M
of circuits)
For less than 0.6
10....................
.....................
For 10 or 0.8
more..................
......................
...
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
individual 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 =
The "annual charge of one additional circuit on the
alternative 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 minute3). This
may be done as follows:
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
calculated using the standard traffic profiles of Table 1/E.523,
may be used.
TABLE 1/E.522
Offere Overflo Time difference
d w
traffi probabi
c lity
(erlan (%)
gs) 0 1 2 3 4 5 6 7 8 9 10 11 12
1 2. 3. 3. 3. 2. 2. 2. 1. 3. 2. 2. 2. 2.
6 2 7 8 7 3 3 7 2 4 2 0 7
10 3. 4. 4. 4. 3. 3. 3. 2. 4. 3. 2. 2. 3.
7 5 8 7 5 1 0 5 1 2 9 8 6
20 4. 5. 5. 5. 4. 3. 3. 3. 4. 3. 3. 3. 4.
5 2 4 3 0 7 5 1 7 8 4 4 2
5 30 5. 5. 6. 5. 4. 4. 4. 3. 5. 4. 3. 4. 4.
1 8 0 8 6 2 0 7 1 3 9 0 8
40 5. 6. 6. 6. 5. 4. 4. 4. 5. 4. 4. 4. 5.
7 4 5 3 1 7 5 2 6 8 4 6 3
50 6. 6. 7. 6. 5. 5. 5. 4. 6. 5. 5. 5. 5.
3 9 0 8 6 2 0 7 0 3 0 1 8
1 2. 2. 3. 3. 2. 2. 2. 1. 2. 2. 2. 1. 2.
1 6 3 5 5 1 1 4 8 0 0 8 4
10 3. 4. 4. 4. 3. 2. 2. 2. 3. 2. 2. 2. 3.
2 0 4 3 1 7 6 1 8 8 6 4 2
20 4. 4. 5. 4. 3. 3. 3. 2. 4. 3. 3. 3. 3.
0 8 1 9 6 3 1 7 3 4 0 0 8
10 30 4. 5. 5. 5. 4. 3. 3. 3. 4. 3. 3. 3. 4.
7 4 6 4 2 8 6 3 8 9 4 6 4
40 5. 6. 6. 5. 4. 4. 4. 3. 5. 4. 4. 4. 4.
3 0 1 9 7 4 2 8 3 4 0 2 9
50 5. 6. 6. 6. 5. 4. 4. 4. 5. 5. 4. 4. 5.
9 6 7 4 3 9 7 4 7 0 6 8 5
1 1. 2. 2. 3. 2. 1. 2. 1. 2. 1. 1. 1. 2.
6 0 8 1 2 8 0 2 4 7 8 6 1
10 2. 3. 3. 3. 2. 2. 2. 1. 3. 2. 2. 2. 2.
7 3 9 9 7 4 3 7 3 4 3 0 7
20 3. 4. 4. 4. 3. 2. 2. 2. 3. 3. 2. 2. 3.
5 2 6 4 2 8 7 2 9 0 6 5 3
25 30 4. 5. 5. 5. 3. 3. 3. 2. 4. 3. 3. 3. 3.
2 0 2 0 7 4 2 8 4 5 0 1 9
40 4. 5. 5. 5. 4. 3. 3. 3. 4. 4. 3. 3. 4.
8 6 8 5 3 9 8 4 9 0 5 7 5
50 5. 6. 6. 6. 4. 4. 4. 4. 5. 4. 4. 4. 5.
5 2 3 1 9 5 3 0 4 6 1 4 1
1 1. 1. 2. 2. 2. 1. 2. 1. 2. 1. 1. 1. 2.
3 7 4 9 1 6 0 1 1 5 6 4 0
10 2. 2. 3. 3. 2. 2. 2. 1. 3. 2. 2. 1. 2.
3 8 5 6 5 2 1 4 1 2 2 8 4
20 3. 3. 4. 4. 3. 2. 2. 1. 3. 2. 2. 2. 3.
1 9 3 2 0 6 4 9 7 7 5 2 0
50 30 3. 4. 5. 4. 3. 3. 2. 2. 4. 3. 2. 2. 3.
9 7 0 8 4 1 9 5 2 3 8 8 6
40 4. 5. 5. 5. 4. 3. 3. 3. 4. 3. 3. 3. 4.
6 4 6 3 0 7 5 2 7 8 2 5 3
50 5. 6. 6. 5. 4. 4. 4. 3. 5. 4. 3. 4. 4.
3 0 1 9 7 3 2 8 2 3 8 2 9
Note _ Linear interpolation may be used to obtain intermediate
results.
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:
Annual charges ratio: R = 1.5; 2.0; 3.0; 4.0; 5.0; 6.0 and 7.04)
b) Intercontinental working involving long distances, small
traffic and usually two_way operation:
Annual charges ratio: R = 1.1; 1.3; 1.5; 2.0; 3.0; 4.0 and 5.0.4)
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
underlined in a) and b) of 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 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 followed 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 dimensioning 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 additional
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 2 and Recommendation E.521, trunk group
sizes are prepared for the first hourly traffic demand disregarding
other hourly traffic demands.
Table 2/E.552 is in file named "T2-552E.doc", must be printed on
landscape
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
resulting 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 pattern
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 (circuit 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
considerations may also favour an increase in the number of direct
circuits 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
advantage 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 conclusive. This practice may result in direct high_usage
groups 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
circuits 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 - CCITT 69331
A.2 Numerical results
24 hourly traffic demands are processed. The order of
processing 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.
TABLE A_1/E.522
Numerical results
Number of
circuits Number of
Hou Hourly traffic obtained by circuits Number of
r demand single hour obtained circuits
dimensioning considering required to
(disregarding lower bounds meet multiple
lower bounds imposed by the hourly traffic
imposed by the previous demands
previous iterative
iterative stage
stage)
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. 5.0 3.5 17 19 17 17 19 17 17 19 17
50 0 0
7 20. 5.0 3.5 19 20 18 19 20 18 19 20 18
00 0 0
5 2.5 5.0 28. 1 14 41 19 11 39 19 20 39
0 0 00
4 2.5 5.0 35. 1 14 49 19 11 47 19 20 47
0 0 00
8 37. 5.0 3.5 37 23 22 19 38 37 19 38 47
50 0 0
9 40. 5.0 3.5 39 24 23 19 41 40 19 41 47
00 0 0
3 2.5 5.0 45. 1 14 61 19 11 59 19 41 59
0 0 50
18 2.5 50. 3.5 1 66 12 19 64 9 19 64 59
0 00 0
10 50. 5.0 3.5 49 26 25 9 61 59 19 64 59
00 0 0
19 2.5 60. 3.5 1 77 12 19 75 9 19 75 59
0 00 0
20 2.5 60. 3.5 1 77 12 19 75 9 19 75 59
0 00 0
22 12. 30. 24. 12 45 39 12 45 39 19 75 59
50 00 50
2 2.5 5.0 63. 1 14 80 19 11 78 19 75 78
0 0 00
17 2.5 70. 3.5 1 87 12 19 85 9 19 85 78
0 00 0
1 2.5 5.0 70. 1 14 87 19 11 85 19 85 85
0 0 00
23 20. 20. 42. 19 36 60 19 36 60 19 85 85
00 00 00
11 47. 25. 17. 47 46 38 3 85 77 19 85 85
50 00 50
21 12. 55. 24. 12 73 39 12 73 39 19 85 85
50 00 50
12 42. 30. 21. 42 50 41 3 85 76 19 85 85
50 00 00
16 2.5 90. 3.5 1 109 12 19 107 9 19 107 85
0 00 0
0 20. 20. 66. 19 36 87 19 36 87 19 107 87
00 00 50
13 30. 65. 35. 29 86 54 5 107 76 19 107 87
00 00 00
15 17. 100 28. 17 121 44 19 120 43 19 120 87
50 .00 00
14 27. 95. 38. 27 117 57 19 124 64 19 124 87
50 00 50
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
dimensioning 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 - CCITT 69321
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 terminal
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 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
profiles matching. The number of high usage circuits A_B in the
minimum outlay network is larger than that in the minimum cost
network. The impact of considering transit charges in dimensionings
is always in the direction of less overflow.
TABLE B_1/E.522
Numerical results
Network results Economic results (x 1000 units/month)
Busy_hou
r Number of Circuit Transit Total outlay
overflow circuits costs charges
probabil
ity
A_B A_C C_B A B C A B C A B C
0.0000 25 45 45 70 61 81 _ _ _ 70. 61. 81.
0 0 0
0.0090 25 45 45 70 61 81 0.3 0.3 (0. 70. 61. 80.
7) 3 3 3
0.0151 24 45 45 69 60 81 0.6 0.6 (1. 69. 60. 79.
3) 6 6 7
0.0221 23 45 45 68 59 81 0.9 0.9 (1. 68. 59. 79.
9) 9 9 1
0.0331 22 46 45 68 58 82 1.4 1.4 (2. 69. 59. 79.
9) 4 4 1
0.0471 21 46 45 67 57 82 2.1 2.1 (4. 69. 59. 77.
2) 1 1 8
0.0641 20 46 45 66 56 82 3.0 3.0 (6. 69. 59. 76.
0) 0 0 0
Minimum
outlay
for A and B
0.0861 19 47 45 66 55 83 4.2 4.2 (8. 70. 59. 74.
4) 2 2 5
0.1121 18 47 45 65 54 83 5.7 5.7 (11 70. 59. 71.
.5) 7 7 5
Minimum cost
network
0.142 17 48 45 65 53 84 7.6 7.6 (15 72. 60. 68.
.1) 6 6 9
0.175 16 49 45 65 52 85 9.7 9.7 (19 74. 61. 65.
.4) 7 7 6
References
[1] WILKINSON (R. I.): Theories for toll traffic engineering in
the USA, Bell Syst. Tech. J., 1956, No. 35, pp. 421_514.
[2] WILKINSON (R. I.): 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. W.) and WERNANDER (M. A.): Modular engineering of
trunk groups for traffic requirements, Fifth International
Teletraffic Congress, New York, 1967.
[5] PRATT (C. W.): 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
systems, Ninth International Teletraffic Congress,
Torremolinos, 1979.
[8] HORN (R. W.): A simple approach to dimensioning a
telecommunication network for many hours of traffic demand,
International Conference on Communications, Denver, 1981.
[9] BESHAI (M. E.): 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.
_______________________________
1) Marginal occupancy is often called LTC (last trunk capacity).
2) Marginal utilization factor is often called ATC (additional
trunk capacity).
3) 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).
4) These values are tentative. Ranges and representative values
of annual charges ratio require further study.
