The Joint Stationary Multivariate Queue Length Distribution in a Single Server Queueing System with <i>N</i> Queues, Arbitrary Priorities, and a General Probabilistic Inter-Queue Transition Matrix

In modern telephone systems utilizing computers, the realization of a single server feedback queueing system often arises. In this paper, it is assumed that an originating or transferred call to such a system requires a number of different services before leaving the system as a completed or rejected call. A customer may also repeat a portion of his services, omit some services, or leave the system after any service with some assigned probabilities. In this paper, we present a theorem on the joint multi-variate queue length distribution, in a system with N services or queues, arbitrary priorities, and a general probabilistic transition matrix inter-connecting the various queues.

• 저널Management Science · 19(7) · 778–782
• 토픽Advanced Queuing Theory Analysis · Management Information Systems
• DOI10.1287/mnsc.19.7.778
• 저자T. K. Wignall, E. G. Enns