Queue lengths and workloads in polling systems

Queue lengths and workloads in polling systems

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Article ID: iaor201111224
Volume: 39
Issue: 6
Start Page Number: 401
End Page Number: 405
Publication Date: Nov 2011
Journal: Operations Research Letters
Authors: , ,
Keywords: polling systems
Abstract:

For a single‐server multi‐station polling system, we focus on the generating function and Laplace–Stieltjes transform of the time‐stationary joint queue length and workload distributions, respectively, under no further assumptions on the service discipline. We express these quantities as expressions involving the generating functions of the joint queue length distribution at visit beginnings and visit completions at the various stations. The latter is known for a broad variety of cases. Finally, we identify a workload decomposition result.

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