al trunk network there could well be 60 trunk exchanges (5.68) spread throughout the United Kingdom. 5.4.4 Least busy alternative (LBA) 5.4.3.1 DAR applied to the BT network The least busy alternative routeing strategy is an example of a state Figure 5.10 shows a typical routeing problem similar to those that dependent routeing strategy defined for fully connected networks were faced in the British Telecom national trunk network. A call which operates as follows. A call is first attempted on the direct route and is accepted so long as at least one free circuit is available. Otherwise, the strategy looks at the occupancies of all the available two-link alternative routes and attempts to route the call along the Alternative least busy such route subject to trunk reservation. Specifically, if Mik Destination and mkj give the number of circuits free on the links (i, k) and (k,j) Trunk Current then the alternative chosen is via tandem node k which maximises Tandem Exchange Exchange in{mik,mkj} over all tandem nodes k x i, j. Then trunk reservation with parameter r will mean that the chosen alternative is only used Destination Local if min{mik, mkj} >I. Exchange It is possible to obtain an Erlang fixed point model for the LBA strategy (see Wong, 1990). We present the model in the simpler case of a symmetric network of N nodes with link capacities C and offered traffics at rate a. Let n be the birth and death process representing the utilization of a link then the transition rates are as in Equations 5.69 and 5.70. Origin Destination Trunk Trunk Exchange Exchange (5.69) q(i,i+1) Figure 5.10 DAR in the BT network q(i,i-1)ii1,.,C (5.70) 5/14 Teletraffic theory In this equation o, is a state dependent birth rate given in terms of Ash, G.R., et al. (1991) Real time network routeing in a dynamic the equilibrium distribution {r : i = 0,...,C} for n as in Equation class of service network In Proc. 13th International Teletraffic 5.71 where y is given by Equation 5.72 and Q. by Equation 5.73. Congress, Copenhagen, North Holland,