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The most common form is used to calculate the required number of circuits or circuit group size to carry a given traffic volume between two exchanges, under the constraint of having to m

32

Network Trafic

Control

Traffic control is as much art as it is science, and the profits are gratifying The right control

mechanisms and routing algorithms in the right places will determine the overall performance and efficiency of our network What is more, they will give us simpler administration, better manage- ment and lower costs This chapter describes a number of these admirable devices: first the simple methods commonly used for optimizing network routing under typical ‘normal-day loading’

conditions; then we look at recent more powerful and complex techniques, together with some of the practical complications facing telecommunications today Finally we note how several net-

work operators have found ways of interconnecting with the multiple carriers that have emerged

lately as a result of market deregulation

Any metropolitan, international, trunk, transit or corporate network, by virtue of

its nature and sheer size has to include a considerable number of switches (exchanges)

If there are many inter-connections between these switches, any individual call

crossing the network will have plenty of alternative paths open to it It is in fact the

number of path permutations which determines the robustness of the network to

individual link failure and sets the level or grade of service provided (i.e the prob-

ability of successful call connection) It offers the customer what he most wants, an

acceptable chance of making a successful call or information transfer each time

Particular attention must be paid to choosing the call-control mechanisms which are

going to determine the routing of our customers’ individual calls, connections or mes-

sages, bearing in mind that in an ideal network we aim overall to achieve a controlled

flow of traffic throughout the network at reasonable cost and without the penalty of

complicated administration Various methods and preliminary calculations can now be

considered in turn

571

Networks and Telecommunications: Design and Operation, Second Edition.

Martin P Clark Copyright © 1991, 1997 John Wiley & Sons Ltd ISBNs: 0-471-97346-7 (Hardback); 0-470-84158-3 (Electronic)

32.2 SIZING CIRCUIT-SWITCHED NETWORKS

First of all, to find how many circuits a telecommunications network will need to meet traffic demand, a mathematical model is required to predict network performance, and

it will comprise at least two parts

0 a statistical distribution to represent the number of calls in progress at any given time

0 a forecast of the overall volume of traffic

Erlang’s model provides a statistical method for approximating telephone traffic, which

is based on his measurements of practical telephone networks A short reminder follows Erlang devised a method of calculating the probability of any given number of calls

being in progress at any instant in time The probability density function used for the calculation is termed the Erlang distribution The Erlang formula, a related and complex

iterative mathematical formula, can be manipulated into a number of different forms The most common form is used to calculate the required number of circuits (or circuit group size) to carry a given traffic volume between two exchanges, under the constraint

of having to meet a given grade of service The traffic value input into this formula is the

measurement of trafic intensity The intensity of traffic on a route between any two

exchanges in a network is equal to the average number of calls in progress, and is

measured in Erlangs

In Chapter 30 we discussed how, for planning purposes, it was normal to measure the

route traffic intensity during the busiest hour of activity, or so-called route busy hour Using this value and the Erlang formula, the number of circuits required for the route can be calculated according to a given target grade of service

The grade of service ( G O S ) of a telephone route between any two exchanges in a

circuit-switched network is the fractional quantity of calls which cannot be completed due to network congestion The lower the numerical value of GOS, the better the per- formance A typical target value used in many trunk and international networks is 1 %,

or 0.01 (in other words 1 % of calls cannot be completed due to network congestion, the other 99% can) The calling customer, however, probably only perceives an end-to-end grade of service, on a call-by-call basis, of around 5 % (i.e 5% lost calls) This is because most connections comprise a number of links and exchanges, each of which

is likely to be designed to inflict a 1% loss

The common method is to dimension circuit groups within a network using a target grade of service and the Erlang formula; so that

Circuits Required = E(A, GOS)

where E represents the appropriate form of the Erlang formula or function, with inputs

A = route busy hour traffic and GOS = target grade of service

Alternatively, for packet or message-switched networks, we discussed an alternative formula, which sought to model the waiting time distribution of packets, rather than the proportion of lost calls; instead of dimensioning in accordance with grade of service, we can dimension according to waiting time The method was again covered by Chapter 30

HIERARCHICAL NETWORK 573

32.3 HIERARCHICAL NETWORK

The Erlang model is a good predictor of the traffic behaviour of most telecommunica-

tions networks A feature of telephone routes dimensioned using the Erlang method is

that routes comprising a large number of circuits are proportionately more efficient (i.e

require proportionately fewer circuits per carried call) than smaller ones, when designed

to the same grade of service, and are therefore more economic This is apparent from

the general shape of the graph of circuits against traffic-carrying capacity Figure 32.1

illustrates the graph of 1 % loss, or 1 % grade of service Note that the graph is almost

linear for circuit group with circuit numbers above 20 circuits, each extra circuit adding

approximately 0.85 Erlangs of traffic capacity Thus by adding ten circuits to a group of

Traffic capacity : l'/ g.0.s Number of

20 circuits we make it suitable for carrying 20.5 Erlangs rather than 12 (an increase

in capacity of 8.5 Erlangs) Notice that an isolated group of 10 circuits is only suitable for 4.5 Erlangs of offered traffic Smaller circuit groups are thus far less efficient, as Figure 32.1 shows

Looking at the graph it is useful to imagine that the first six circuits carry no traffic at all, and that all subsequent circuits have a capacity of 0.85Erlangs each It is almost

as if there were a ‘penalty’ price of six circuits for having a route at all! The line representing this assumption is shown in Figure 32.1 The equation of this line provides

a handy method of estimating the number of circuits required to carry a given offered traffic load, but it is only valid up to about A = Erlangs Above this value, other estimating formulae can be used as follows

HIERARCHICAL NETWORK 575

degree of lncreaslng inferconnection between

( 1 or 2 only)

Trunk exchanges (relatively few)

Local exchange

( many 1

Figure 32.3 Hierarchical network structure

Figures 32.2 and 32.3 In such a structure, a small number of main exchanges are

fully interconnected with one another, and various tiers of less important exchanges

have progressively less direct connections to other exchanges If no direct route is

available from one given exchange to another, then the call is referred to an exchange

in the next higher tier By using such a structure we can reduce the number of circuits

on long-haul routes Under such a hierarchical scheme, routes are combined so that

groups may be dimensioned (or sized) to carry multiple-traffic streams, and so reap

the economic benefits of the larger scale The hierarchial network technique works as

shown in Figure 32.2

Let us assume that the callers on each originating exchange (Al, A2, A3) in Figure 32.2

are generating calls equivalent to a traffic intensity of 25 Erlangs (i.e an average of 25

simultaneous calls in progress) to each terminating exchange (Bl, B2, B3) Let us also

assume that exchanges A l , A2, A3 are quite close together, as are exchanges B1, B2, B3,

but that region A and region B are a long way apart

Without a hierarchical network structure, each A exchange would need a set of long-

haul circuits to connect with each B exchange, as shown in Figure 32.2(a) This would

give a total of nine routes (Al-B1, Al-B2, etc.) Using Erlang’s formula for 1 % GOS,

each of these routes or circuit groups would require 36 circuits, amassing a total

requirement of 9 X 36 = 324 long haul circuits

Alternatively, if the traffic is concentrated through collecting exchanges T1 and T2

(called transit or tandem exchanges) within the originating and terminating regions,

only a single route is required That route has to carry all 225 Erlangs, but only 247

long-haul circuits (again using Erlang’s formula) are needed Figure 32.2(b) illustrates

this alternative network structure Of course, when comparing the cost of the the two

structures we must not overlook the additional switches T1 and T2, as Comparison 1

below indicates

(Traffic between each A-B pair: 25 Erlangs)

All direct routes 324 long haul circuits (9 X 36) (as Figure 32.2(a))

Hierarchical structure 247 long haul circuits (as Figure 32.2(b)) 2 X transit switches (Tl, T2); 225 Erlaags each

324 short haul circuits (A-TI and T2-B)

So then, if 77 long-haul circuits (324-247) costs more than two 225 Erlang switches

( Tl, T2 ) plus the short haul access circuits (A-T1 and T2-B), hierarchical structure (Figure 32.2(b)) is the more cost effective

In individual cases the particular circumstances will decide whether a direct or a hierarchical network structure is cheaper, though the general rule applies that in very- long-haul situations (international networks for example) the hierarchical structure

usually wins Hierarchical structure can also be cost-effective when point-to-point route traffic is very small (as in rural networks) To illustrate this point, in Comparison 2 the

example of Figure 32.2 has been repeated with much lower traffic values (and with circuit numbers re-calculated, again using the Erlang method)

32.3.2 Comparison 2: Direct versus Hierachical Structure: Low Traffic Only

(Traffic between each A-B pair: 3 Erlangs only)

All direct routes 72 long haul circuits (9 X 8)

(8 circuits required for each 3 Erlang route) Hierarchical structure 38 long haul circuits (for 27 Erlangs)

2 transit switches ( Tl, T2); 27 Erlangs each

72 short haul circuits Note how in Comparison 2 the proportion of long-haul circuits saved as the result of a network hierarchy is much greater than it was in Comparison 1 (47% saving as opposed

to 24%) This is because the inefficiency of very small routes is very marked, as we saw

in Figure 32.1 There are therefore greater proportional savings to be made from com- bining very small routes

Hierarchical structure is common in many of the world’s telephone and ISDN

networks, in which a large number of local exchanges (or end offices) route their trunk traffic via a smaller number of trunk (or toll) exchanges At the highest tier in the hierarchy there are probably only one or two international exchanges, each lower tier has a greater number of exchanges, but each with only a restricted degree of long-haul inter-connection Figure 32.3 illustrates a typical national hierarchy

An added advantage enjoyed by hierarchical networks lies in their capacity for getting the most out of their circuits at times when the busy hours of various trans- mission routes do not coincide For an example look back again at Figure 32.2(b), and

we can see that if AI-B1 is busy in the morning and A3-B3 in the afternoon, then thanks to hierarchical structure the same circuits can be used for both traffic streams

On the other hand, separate direct circuit groups (as in Figure 32.2(a)) would be inefficient, as one or other of the groups would a l w a p be Idle

A disadvantage of hierarchical n e t w o r k - d e n compared with direct-circuited net- works, is their greater s u s c e p W t y to congestion under network overload There are two causes

0 Fewer overall circuits are available in hierarchical than in equivalent direct-circuited

~~~~~~

networks

OVERFLOW OR 'AUTOMATIC ALTERNATIVE ROUTING' (AAR) 577

0 Congestion between only one pair of exchanges (e.g AI-B1 of Figure 32.2(b)) will

result in congestion on all other routes (e.g A2-B3), because all calls have to

compete for the same circuits (Tl-T2) This can rapidly lead to further congestion,

as customers dial merrily on regardless

32.4 OVERFLOW OR 'AUTOMATIC ALTERNATIVE ROUTING' (AAR)

A simple means of improving purely-hierarchial networks is to apply the technique of

overflow, and for this we require the automatic alternative routing ( A A R ) mechanism

AAR is also known as overflow or alternative routing, and most exchanges are

capable of it It can be understood as a priority listing of the route choices leading to

any given destination Turning back to our example of Figure 32.2(b), let us assume

that we introduce an additional link between exchanges A1 and B1 This might be a first

choice, or high-usage ( H U ) route (as described below) In this case, an AAR table for

traffic from A1 to B1 might be as shown in Figure 32.4

Cost benefits can be gained by judicious application of AAR (as in Figure 32.4)

rather than using the simple hierarchical structure (as in Figure 32.2(b)), particularly if

the route traffic between points A1 and B1 is large The saving is achieved by making

quite sure that the first choice route between A1 and B1 does not have enough circuits

Figure 32.5 The benefit of high-usage working

to carry the whole traffic A remainder is then left which is forced to overflow via T1 Because of the way they are used, the two routes A1-B1 and AI-Tl-T2-B1 are called

high-usage ( H U ) a n d j n a l routes, respectively In fact A1-B1 is a primary high-usage

route, as it is first choice; however, secondary, tertiary, and so on, high-usage routes

(i.e extra route choices between prirnary HU a n d j n a l ) may also be used, and they have

their place in the AAR table

To evaluate the savings of high-usage working, let us assume that we provide high- usage routes of 25 circuits between each pair of exchanges in Figure 32.2(b) (i.e nine H U routes; A1-B1, Al-B2, etc) Then the network adopts the pattern shown in Figure 32.5

To compare the overall circuit requirement with earlier examples, we must dimension the network to the same overall 1% grade of service performance However, the dimensioning of the overflow links (A-T1 and T2-B), as well as of the overflow orfinal route Tl-T2, presents a special problem for which the Erlang formula has to be modified This is because overflow traffic does not have a random nature as the Erlang dimensioning method requires Consequently, in Comparison 3, the more complex Wilkinson-Rapp equivalent random method (explained later in the chapter) has been employed, and the network has been dimensioned so that all customers receive a grade of service equivalent

to or better than 1 Yn By this method, we determine that 4 3 j n a l route circuits are required

on Tl-T2 We thus need (9 X 25) + 43 = 268 circuits in total Comparison 3 below compares this value with the direct and the hierarchical network structures

(Traffic between each A-B pair: 25 Erlangs)

All direct routes: 324 long haul circuits Hierarchical structure: 247 long haul circuits

2 X transit switches (225 Erlangs each)

324 short haul circuits

WILKINSON-RAPP EQUIVALENT RANDOM METHOD 579

Overflow structure: 268 long haul circuits

2 X transit switches (32 Erlangs each)

99 short haul circuits Comparison 3 shows that it is possible (by choosing the optimum size of high-usage (HU) circuit groups) to reduce significantly the size of the transit switches required

(between the hierarchical and overflow structures), without significantly increasing the

long-haul circuit requirement This clearly reduces the cost However, our example is not very realistic In practice, if any of the individual traffic streams are too small, the benefit

of providing high-usage circuits for the corresponding direct route disappears In

practice then, it is often useful to provide high-usage routes only for those traffic streams exceeding a given Erlang threshold value In other words, ‘if more than X Erlangs of

traffic exist between any two nodes, then a direct HU route is justified’ The value of X

will depend upon the relative costs and of lineplant and exchanges equipment and on whether the exchanges are local, trunk, or international ones

A problem facing planners using overflow in practical networks is that the number of

circuits required cannot always be cut to a minimum without adding another control mechanism such as trunk reservation, as explained later in this chapter

Furthermore, the high-usage structure is not as advantageous as the hierarchical when route busy hours of the various traffic streams do not coincide, because the cir- cuits are ‘less available’ for shared use, e.g by one stream in the morning and by another in the afternoon

HU structures do, however, have a better overload performance, in that individual traffic streams are to some extent protected from congestion on other routes (caused for example by very high seasonal or short term demand)

32.5 WILKINSON-RAPP EQUIVALENT RANDOM METHOD

In the previous section when we were attempting to dimension routes carrying overflow

traffic we ran into the difficulty that because the distribution of traffic which is over- flowed from a high usage circuit group is not random, the Erlang formula may not be used directly So, introduce the Wilkinson-Rapp equivalent random method instead This is in fact the Erlang method slightly adapted

Imagine two traffic streams a and b which have high-usage routes of the A and B

circuits available, respectively These two traffic streams overflow amounts of traffic a’

and 6’ onto a common final route of N circuits, which is also the first choice for thejirst-

oflered traffic stream c Figure 32.6 illustrates this schematically The problem is to find

the value of N which will guarantee the appropriate grade of service on all traffic streams

Circuit group N is subjected to overflow traffic a’ + b’ and first-offered traffic c, and

we dimension it by the Wilkinson-Rapp equivalent random method as follows The method assumes that the Ncircuits will behave in the same way as a set of Ncircuits part

way down a larger group of (NEQ + N ) circuits when subjected to an imaginary single

stream of equivalent random trafic, AEQ Figure 32.7 illustrates the set of N circuits and

the imaginary set NEQ The problem is finding the values of NEQ and A E Q so that the

traffic overflowed from the NEQ circuits exactly matches the characteristics of the real

N

c c t s

traffic a' + b' + c The mean M and variance V characterize the traffic a' + b' + c which

we imagine to overflow from the N E Q circuits, and by choosing the values of AEQ and NEQ carefully we can equate the values exactly with the corresponding mean and variance values of the real traffic

By knowing the values A,, and NEQ, the traffic lost by the N circuit group can easily

be determined It is done by using the normal Erlang formula, assuming that an

equivalent random traffic value A,, is offered to a total number of circuits N + NEQ The

grade of service determined by the formula is the overall lost traffic ( L in Figure 32.7) quoted as a proportion of the imaginary original traffic value AEQ

DIMENSIONING ‘FINAL ROUTES’ 581

It is normal to dimension the group of N circuits by first calculating the permissible

traffic loss in Erlangs (i.e the amount of the real traffic which need not be carried, L in

Figure 32.7), and then calculating this as a proportion of &Q This is the imaginary or

equivalent grade of service required when traffic A,, is offered to N + N E Q circuits, and allows us to calculate the value of ( N + NEQ) using the Erlang method as follows

maximum permissible lost traffic = L

L = GOS required X traffic on (a’ + b’ + c) imaginary GOS required on N + NEQ circuits = GOS,Q = L

N + N E Q = E(AEQ, GoSE,), where E represents the Erlang formula

Having determined the value of N + NEQ, the real number of circuits required for the real traffic ( N ) is found by subtracting value NEQ

The values N E Q and AEQ are relatively straightforward to calculate, but the process

requires a number of mathematical steps An appendix at the end of the chapter shows how to calculate these values and gives an example of the whole Wilkinson-Rapp overflow route dimensioning method for those readers who are interested

The Wilkinson-Rapp method is now quite old (1956) and in consequence more complex methods have evolved which seek to improve it As with the alternatives to the basic Erlang method it rests with the user to decide the method which suits his circumstance the best

32.6 DIMENSIONING ‘FINAL ROUTES’

It is normal practice to dimension final routes for only a 1% loss of the mean traffic offered to them This ensures a 1% grade of service for any traffic which i s j r s t offered

to the final route This practice was adopted in the preeding section when mixed overflow and first-offered traffic shared the same circuit group

In instances where there is no first ofSered traffic on the final route, then the circuit numbers may be reduced, commensurate with an overall 1% loss on each of the individual traffic streams Thus if only 10% of traffic overflows from the high usage route (a typical value), only 10% of the original traffic is offered to the final route The caller experiences a net 1 YO grade-of-service even if as much as 10% of the traffic offered

to the final route is lost Thus the grade of service of the final route need only be 10% in this case!

32.7 TRUNK RESERVATION

To some trunk reservation is a relatively new technique, for although it has been around for more than 30 years, only recently has the advent of stored program control (SPC) exchanges made it more widely available It provides a method of priority