Evaluatign Cf the Mean In-process Time Fur Queueing Networks with Random

A class of queueing networks with topology, varying with time at random on each cycle of system, is considered. It is also assumed that on each cycle the network failures may occur with non-zero probability. The upper bound for the mean in-process time of networks is constructed by using the idempotent algebra approach. Preliminary remarks. The mathematical apparatus of the idempotent (max, -l-)-algebra is convenient for description of dynamics and analysis of a complex system including queueing networks. In particular, the dynamics of the queueing networks with a customer service synchronization, a topology of which is determined by deterministic acyclic graphs, can be described by means of a generalized linear equation (see, for example, [1-3]) a:(k) = A(k) ® :c(k 1) (1)