nks within a route are statistically independent. In (5.22) order to describe this approximation consider a simple situation of B(A,C,r) = a network of nodes fully connected by links each of capacity C and with independent Poisson arrival streams of traffic offered between the pairs of nodes each of rate a K=1.5 K=2.0 K=2.5 K=3.0 Capacity, C Figure 5.4 Secondary criterion Network models 5/7 The fully connected network architecture has been the focus of with probability B, on its direct route will attempt an alternative much attention in recent years in relation to studies of dynamic route through two links, but may be blocked at either of these links. routeing strategies for national trunk networks. Section 5.4 con- The transition rates correspond to the acceptance by a link of direct siders in some depth the various strategies that have so far been traffic and overflow traffic (at rates a and o respectively) in states proposed. In this section a simple strategy for symmetric fully {0, ...,C-r-1} and of direct traffic only (at rate 2) in states {C - connected networks is considered, that will suffice to illustrate r, ..., C-1}. many of the modelling aspects. In practice, networks are not sym- If L is the probability that a call offered to the network is lost then metric, and in particular traffics may not be well matched to capac- Equation 5.28 may be obtained. ity. Nevertheless, one can learn much about the behaviour of routeing schemes from a consideration of the symmetric case (see Gibbens 1990 for further discussion on dynamic routeing 1-L = (1-B,)+B,(1-B,) (5.28) strategies). This simple strategy is called random routeing and operates as Since calls are first offered to the direct links and are accepted follows: a call arriving at the network from the source destination with probability (1-B,) and with probability B1 they overflow to a pair (i,j) is routed along link (i, j) if there is at least one free circuit randomly chosen two-link alternative path on each link of which on this link; otherwise an interme