Approximations of Queue Dynamics and Their Application to Adaptive Routing in Computer Communication Networks

Various adaptive algorithms have been proposed for routing, flow and congestion control in packet-switched computer communication networks. In most of them, information on queue lengths, or equivalently, time delays, at various points in the network is required for proper adaptation. Since up-to-date information is not always available, these quantities must be estimated based on prior information. This paper presents approximations for the dynamic behavior of the
M/M/1
queue which is used to yield the desired estimates of queue lengths. Based on the assumption of finite (but arbitrarily large) storage, a closed form expression for the evolution in time of the queue length distribution is obtained. From this expression various approximations for estimated queue length are extracted. A simple expression for the "relaxation time" of the queue is also deduced as a function of utilization factor and service time. The approximations are applied to a simple adaptive routing example in which packets are routed along the transmission path having the shortest estimated queue, based on delayed information.