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All drawings appearing in this Recommendation have been done in
Autocad.

Recommendation E.501

ESTIMATION OF TRAFFIC OFFERED IN THE INTERNATIONAL
NETWORK

1    Introduction

    For planning the growth of the international network the following
quantities must be estimated from measurements:

ù    traffic offered to international circuit groups,

ù    traffic offered to destinations, on a pointùtoùpoint basis,

ù    traffic offered to international exchanges,

ù    call attempts offered to international exchanges,

ù    traffic offered to signalling links.

    (The term ôtraffic offeredö as used here is different from the ôequivalent
traffic offeredö used in the pure lost call model, which is defined in Annex
B.)

    These quantities are normally estimated from measurements of busyùhour
carried traffic and call attempts, but there are a number of factors which may
need to be taken into account within the measurement and estimation proce-
dures:

a)    Measurements may need to be subdivided, e.g. on a destination
basis, or by call type (for example, calls using different signalling
systems).

b)    It may not be possible to obtain a complete record of traffic carried.
For example, in a network with high usage and final groups it may
not be possible to measure the traffic overflowing from each high
usage group.

c)    Measurements may be affected by congestion. This will generally
result in a decrease in traffic carried, but the decrease may be
affected by customer repeat attempts and by the actions (for exam-
ple, automatic repeat attempts) of other network components.

d)    When high levels of congestion persist for a lengthy period (many
days), some customers may avoid making calls during the con-
gested period of each day. This apparent missing component of
offered traffic is known as suppressed traffic. It should be taken
into account in planning since the offered traffic will increase
when the equipment is augmented. At present, suitable algorithms
for estimating suppressed traffic have not been defined.

    Three situations should be distinguished:

i)    congestion upstream of the measurement point. This is not directly
observable;

ii)    congestion due to the measured equipment. Congestion measure-
ments should be used to detect this;

iii)    congestion downstream of the measurement point. This can often
be detected from measurements of ineffective traffic or completion
ratio. Note that where groups are bothway, congestion elsewhere in
the network may be both upstream and downstream of the mea-
surement point for different parcels of traffic.

    When congestion is due to the measured equipment this must be properly
accounted for in the estimation of traffic offered, which is used for planning
the growth of the measured equipment.

    When congestion arises elsewhere in the network the planner needs to con-
sider whether the congestion will remain throughout the considered plan-
ning period. This may be difficult if he does not have control of the
congested equipment.

    This Recommendation presents estimation procedures for two of the situa-
tions described above. º 2 deals with the estimation of traffic offered to a
fullyùoperative onlyùroute circuit group which may be in significant con-
gestion. º 3 deals with a highùusage and final group arrangement with no
significant congestion. These estimation procedures should be applied to
individual busyùhour measurements. The resulting estimates of traffic
offered in each hour should then be accumulated according to the proce-
dures described in Recommendation E.500.

2        Onlyùroute circuit group

2.1        No significant congestion

    Traffic offered will equal traffic carried measured according to Rec-
ommendation E.500. No estimation is required.

2.2        Significant congestion

    Let Ac be the traffic carried on the circuit group. Then on the assump-
tion that augmentation of the circuit group would have no effect on the mean
holding time of calls carried, or on the completion ratio of calls carried, the
traffic offered to the circuit group may be expressed as

            A = Ac

where B is the present average loss probability for all call attempts to the
considered circuit group, and W is a parameter representing the effect of call
repetitions. Models for W are presented in Annex A.

    To facilitate the quick determination of offered traffic according to the
approximate procedure in Annex A, Table Aù1/E.501 including numerical
values of the factor (1 ù WB)/(1 ù B) was prepared for a wide range of B,
H and r` (for the definition of H and r`, see Annex A). For the use of Table
Aù1/E.501, see Note 2 in Annex A.

    Note 1 ù Annex A gives a derivation of this relationship, and also describes
a more complex model which may be of use when measurements of com-
pletion ratios are available.

    Note 2 ù When measurements of completion ratios are not available a W
value may be selected from the range 0.6ù0.9. It should be noted that a
lower value of W corresponds to a higher estimate of traffic offered. Admin-
istrations are encouraged to exchange the values of W that they propose to
use.

    Note 3 ù Administrations should maintain records of data collected before
and after augmentations of circuit groups. This data will enable a check on
the validity of the above formula, and on the validity of the value of W used.

    Note 4 ù In order to apply this formula it is normally assumed that the cir-
cuit group is in a fully operative condition, or that any faulty circuits have
been taken out of service. If faulty circuits, or faulty transmission or signal-
ling equipment associated with these circuits remain in service, then the for-
mula may give incorrect results.

3    Highùusage/final network arrangement

3.1    Highùusage group with no significant congestion on the final group

3.1.1    Where a relation is served by a highùusage and final group arrange-
ment, it is necessary to take simultaneous measurements on both circuit
groups.

    Let AH be the traffic carried on the highùusage group, and AF the
traffic overflowing from this highùusage group and carried on the final
group. With no significant congestion on the final group, the traffic offered
to the highùusage group is:

            A = AH + AF

3.1.2    Two distinct types of procedure are recommended, each with several
possible approaches. The method given in º 3.1.2.1 a) is preferred because it
is the most accurate, although it may be the most difficult to apply. The
methods of º 3.1.2.2 may be used as additional estimates.

3.1.2.1    Simultaneous measurements are taken of AH and the total traffic car-
ried on the final group. Three methods are given for estimating AF, in
decreasing order of preference:

a)    AF is measured directly. In most circumstances this may be
achieved by measuring traffic carried on the final group on a desti-
nation basis.

b)    The total traffic carried on the final group is broken down by desti-
nation in proportion to the number of effective calls to each desti-
nation.

c)    The traffic carried on the final group is broken down according to
ratios between the bids from the highùusage groups and the total
number of bids to the final group.

3.1.2.2    Two alternative methods are given for estimating the traffic offered to
the highùusage group, which in this circumstance equals the equivalent
traffic offered:

a)    A is estimated from the relationship

            AH = A[1 ù EN(A)]

    Here EN(A) is the Erlang loss formula, N is the number of working
circuits on the highùusage group. The estimation may be made by
an iterative computer program, or manually by the use of tables or
graphs.

    The accuracy of this method may be adversely affected by the nonù
randomness of the offered traffic, intensity variation during the
measurement period, or use of an incorrect value for N.

b)    A is estimated from

A = AH/(1 ù B)

    where B is the measured overflow probability. The accuracy of this
method may be adversely affected by the presence of repeat bids
generated by the exchange if they are included in the circuit group
bid register.

    It is recommended to apply both methods a) and b); any significant discrep-
ancy would then require further investigation. It should be noted however
that both of these methods may become unreliable for highùusage groups
with high overflow probability: in this situation a longer measurement
period may be required for reliable results.

3.2    Highùusage group with significant congestion on the final group

    In this case, estimation of the traffic offered requires a combination of
the methods of ºº 2.2 and 3.1. A proper understanding of the different
parameters, through further study, is required before a detailed procedure
can be recommended.

ANNEX A

(to Recommendation E.501)

A simplified model for the formula presented in º 2.2

    The call attempts arriving at the considered circuit group may be classified
as shown in Figure Aù1/E.501.

    The total call attempt rate at the circuit group is

            N = N0 + NNR + NLR.

    We must consider N0 + NNR which would be the call attempt rate if
there were no congestion on the circuit group.

    Let

    B =  = measured blocking probability on the circuit group.

    W =  = proportion of blocked call attempts that reùattempt.

    We have

    N0 + NNR = N ù NLR = (N ù NLR)  = Nc  = Nc.

FIGURE Aù1/E.501 - CCITT 64230



    Multiplying by the mean holding time of calls carried on the circuit group,
h, gives

            A = Ac,

where

    Ac the traffic carried on the circuit group.

    The above model is actually a simplification since the rate NNR would be
changed by augmentation of the circuit group.

    An alternative procedure is to estimate an equivalent persistence W from the
following formulae:

            W =

            H =

            ▀ =

where r` is the completion ratio for seizures on the considered circuit group
and r is the completion ratio for call attempts to the considered circuit
group.

    These relationships may be derived by considering the situation after aug-
mentation (see Figure Aù2/E.501).

FIGURE Aù2/E.501 - CCITT 64240



    It is required to estimate N`c, the calls to be carried when there is no conges-
tion on the circuit group. This may be done by establishing relationships
between Nc and N0 (before augmentation) and between N`c, and N0 (after
augmentation), since the first attempt rate N0 is assumed to be unchanged.
We introduce the following parameters:

    H = overall subscriber persistence,

    r` = completion ratio for seizures on the circuit group.

    Before augmentation:

            H =

            r` =

    After augmentation:

            H =

            r` =

    It is assumed for simplicity that H and r` are unchanged by the aug-
mentation. The following two relationships may be readily derived:

            N0 =

            N0 = N`c [1 ù H (1 ù r`)].

Hence

            N`c = Nc

    On multiplying by the mean call holding time, h, this provides our
estimate of traffic offered in terms of traffic carried.

    The relationship     H =

is valid both before and after augmentation, as may easily be derived from
the above diagrams.

    Note 1 ù Other Administrations may be able to provide information on the
call completion ratio to the considered destination country.

    Note 2 ù The procedure of estimating the factor W above is based on the
assumptions that H, r` and h remain unchanged after augmentation. The
elimination of congestion in the group considered leads to a change in H and
in practical cases this causes an underestimation of the factor W and conse-
quently an overestimation of offered traffic in the formula of º 2.2. A rele-
vant study in the period 1985ù88 has shown that the overestimation is
practically negligible if B  0.2 and r`  0.6. For larger B and smaller r` values,
the overestimation may be significant unless other factors, not having been
taken into account by the study, do not counteract. Therefore caution is
required in using TableAù1/E.501 in the indicated range. In the case of
dynamically developing networks the overestimation of offered traffic and
relevant overprovisioning may be tolerated, but this may not be the case for
stable networks.

TABLE Aù1/E.501



Values of



 H =

0.70

0.75

0.80

0.85

0.90

0.95

 B = 0.1

 r` = 0.3

 1.0653

 1.0584

 1.0505

 1.0411

 1.0300

 1.0165

 r` = 0.4

 1.0574

 1.0505

 1.0427

 1.0340

 1.0241

 1.0129

 r` = 0.5

 1.0512

 1.0444

 1.0370

 1.0289

 1.0202

 1.0105

 r` = 0.6

 1.0462

 1.0396

 1.0326

 1.0252

 1.0173

 1.0089

 r` = 0.7

 1.0421

 1.0358

 1.0292

 1.0223

 1.0152

 1.0077

 r` = 0.8

 1.0387

 1.0326

 1.0264

 1.0200

 1.0135

 1.0068

 B = 0.2

 r` = 0.3

 1.1470

 1.1315

 1.1136

 1.0925

 1.0675

 1.0373

 r` = 0.4

 1.1293

 1.1136

 1.0961

 1.0765

 1.0543

 1.0290

 r` = 0.5

 1.1153

 1.1

 1.0833

 1.0652

 1.0454

 1.0238

 r` = 0.6

 1.1041

 1.0892

 1.0735

 1.0568

 1.0390

 1.0201

 r` = 0.7

 1.0949

 1.0806

 1.0657

 1.0503

 1.0342

 1.0174

 r` = 0.8

 1.0872

 1.0735

 1.0595

 1.0451

 1.0304

 1.0154

 B = 0.3

 r` = 0.3

 1.2521

 1.2255

 1.1948

 1.1587

 1.1158

 1.0639

 r` = 0.4

 1.2216

 1.1948

 1.1648

 1.1311

 1.0931

 1.0498

 r` = 0.5

 1.1978

 1.1714

 1.1428

 1.1118

 1.0779

 1.0408

 r` = 0.6

 1.1785

 1.1530

 1.1260

 1.0974

 1.0669

 1.0345

 r` = 0.7

 1.1627

 1.1382

 1.1127

 1.0862

 1.0587

 1.0299

 r` = 0.8

 1.1495

 1.1260

 1.1020

 1.0774

 1.0522

 1.0264

 B = 0.4

 r` = 0.3

 1.3921

 1.3508

 1.3030

 1.2469

 1.1801

 1.0995

 r` = 0.4

 1.3448

 1.3030

 1.2564

 1.2040

 1.1449

 1.0775

 r` = 0.5

 1.3076

 1.2666

 1.2222

 1.1739

 1.1212

 1.0634

 r` = 0.6

 1.2777

 1.2380

 1.1960

 1.1515

 1.1041

 1.0537

 r` = 0.7

 1.2531

 1.2150

 1.1754

 1.1342

 1.0913

 1.0466

 r` = 0.8

 1.2325

 1.1960

 1.1587

 1.1204

 1.0813

 1.0411

 B = 0.5

 r` = 0.3

 1.5882

 1.5263

 1.4545

 1.3703

 1.2702

 1.1492

 r` = 0.4

 1.5172

 1.4545

 1.3846

 1.3061

 1.2173

 1.1162

 r` = 0.5

 1.4615

 1.4

 1.3333

 1.2608

 1.1818

 1.0952

 r` = 0.6

 1.4166

 1.3571

 1.2941

 1.2272

 1.1562

 1.0806

 r` = 0.7

 1.3797

 1.3225

 1.2631

 1.2013

 1.1369

 1.0699



 r` = 0.8

 1.3488

 1.2941

 1.2380

 1.1807

 1.1219

 1.0617

ANNEX B

(to Recommendation E.501)

Equivalent traffic offered

    In the lost call model the equivalent traffic offered corresponds to the traffic
which produces the observed carried traffic in accordance with the relation

            y = A(1 ù B)

where

    y is the carried traffic,

    A is the equivalent traffic offered,

    B is the call congestion through the part of the network considered.

    Note 1 ù This is a purely mathematical concept. Physically it is only possi-
ble to detect bids whose effect on occupancies tells whether these attempts
give rise to very brief seizures or to calls.

    Note 2 ù The equivalent traffic offered, which is greater than the traffic car-
ried and therefore greater than the effective traffic, is greater than the traffic
offered when the subscriber is very persistent.

    Note 3 ù B is evaluated on a purely mathematical basis so that it is possible
to establish a direct relationship between the traffic carried and call conges-
tion B and to dispense with the role of the equivalent traffic offered A.