Administrative Control of Multiple-Channel Queuing Systems with Parallel Input Streams

Abstract

Two stochastic models of general theoretical interest and applicability are presented. Both models consider the introduction of decision and control into parallel channel queuing systems with mixed input streams. In the “rate control” model, arrivals are composed of a random, Poisson distributed input superimposed on selected constant rates of input. In the “adaptive control” model, arrivals are composed of a random, Poisson distributed input superimposed on an input controlled by means of instantaneous information feedback as to the state of the system. For both models steady-state probability distributions are derived, together with expressions for the expected value and system variance. The decision-maker exercises control over the system variance and the expected number in the system through the use of decision rules dealing with the arrival process. The models are generalizable to many situations where one is confronted with a demand for service that has both random and scheduled elements.