elayed. The prob- lem of dimensioning a route is thus to determine from the traffic forecast the number of circuits required to provide the grade of indicate direct connection. Intermediate situations favour automatic service specified by the network operator (Farr, 1982). alternative routing, as shown in Figure 29.14, due to Rapp (1964). It can be shown that, for a circuit-switched route, the grade of Automatic alternative routing is applicable in private networks as service (i.e. the probability of a lost call) is given by (Bear, 1988) well as in PSTNs. A PABX in a private network may be pro- Erlang's equation (Equation 29.1) where A is the traffic offered (in grammed SO that, when all private circuits to another PABX in the erlangs) and N is the number of trunks on the route. network are busy, the traffic then overflows onto the PSTN. Variations of the basic automatic alternative routing scheme have (29.1) been introduced. In dynamic alternative routing (Stacey 1989), if a call is successful on a given routing then that current choice is retained. If instead the call fails on the current choice, then a new choice is selected for the next one. The introduction of common- channel signalling between exchanges, together with exchanges Dimensioning 29/17 For a queuing system, provided that the probability of delay is Specifying a grade of service is, ultimately, a matter of judgement. small, it is approximately given by Equation 29.2. It should be sufficiently large to make the provision of trunks economical, but not SO large as to cause undue customer dissatisfac- E2N(A)=N-A 1.N (A) (29.2) tion. In practice, grades of service may vary between 0.001 for trunks within an exchange to 0.1 for expensive long-distance and international circuits. The assumptions made in deriving the above formulae include full Equations 29.1 and 29.2 and the traffic tables relate to the busy- availability, random (Poisson) call arrivals, and a negative exponen- hour traffic. At other times of the day, the probability of loss will be tial