A Functional Equation Arising in a Queue With a Gating Mechanism

David L. Jagerman · Bhaskar Sengupta

11 citations0/0 files storedProbability in the Engineering and Informational Sciences

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

Our primary aim in this paper is to study a functional equation that arises in a problem of queueing. Consider a queue with compound Poisson arrivals and general service times with a gating mechanism. The gating mechanism takes in at most m (≤∞) customers at a time for service and serves these customers according to the processor-sharing discipline. In this paper, we examine various performance characteristics for this queue. The characteristics include waiting-time distribution, queue-length distribution, time spent with the server, and batch-size distribution for service.

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1987Processor-sharing queues: Some progress in analysis 1984The sojourn-time distribution in the M/G/1 queue by processor sharing 1984A new approach to the M / G /1 processor-sharing queue 1974Stochastic Theory of Service Systems 1983Conditional response times in the M/G/1 processor-sharing system 1979The queueing system MX/G/1 and its ramifications 1989A single server queue with gated processor-sharing discipline 1989Response times in gated M/G/1 queues: The processor-sharing case

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