QUEUEING NETWORKS WITH STRING TRANSITIONS OF MIXED VECTOR ADDITIONS AND VECTOR REMOVALS

1 IntroductionProduct form queueing networks have regained considerable interest over the last coupleof years. In particular, extensions beyOnd the wellknown JaCkson, BCMP and KellyWhittletyPe networks (e.g., I1--5]) have been establlshed. Extensions include networks with batchmovements (such as 6--10]), networks with negative customers and signalling (11--17l, amongothers), and assemblytransfer networks (18, 19]). Transitions ill product form netWOrs nowgeneral1y include multiPle sta…

QUEUEING NETWORKS WITH STRING TRANSITIONS OF MIXED VECTOR ADDITIONS AND VECTOR REMOVALS

Product form queueing networks with string transitions have been studied in the literature as a model incorporating several features of the existing networks. That model includes state-dependent transition rates at the cost of a restrictive form of the string transitions: First a sequence of nonnegative vectors is removed, and then a sequence of nonnegative vectors is added to the network state. Such a transition structure excludes, for example, networks with positive and negative signals recently studied in the literature. This paper extends the string transition networks to allow transitions of mixed vector additions and vector removals, and it includes assembly-transfer networks as well as networks with negative and positive signals as special cases. Assuming that the transition rates are independent of the network state except at the boundaries, we obtain general modifications for the string transition network under which it possesses a product form equilibrium distribution. The network is shown to satisfy a class of local balance as expressed by a set of traffic equations.