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Some Simple Bounds and Approximations in Queueing,
GEORGE WASHINGTON UNIV WASHINGTON D C INST FOR MANAGEMENT SCIENCE AND ENGINEERING
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The paper surveys the current state of the art of finding bounds and approximations in queueing theory. It then proceeds to offer a new lower bound on the limiting expectation of the line wait for the GIG1 case and follows through with the implications of this lower bound for the multiserver case and for the case of tandem queues. The effect on waiting times of priority disciplines is also discussed. Secondly, the study turns to an approximation for the mean wait in queue which is a function solely of the first two moments of the interarrival and service-time distributions. The approximation is shown to be exact in the case of exponential interarrivals and to perform well in other situations. Finally, a novel method of approximating the GIG1 queue by a modified E sub kE sub l1 queue is presented. The presentation includes both the theory of the method and detailed listings of the algorithms to facilitate their use on computers with FORTRAN compilers. Author
APPROVED FOR PUBLIC RELEASE