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A single server queue with platooned arrivals and phase type services

Authors
Journal
European Journal of Operational Research
0377-2217
Publisher
Elsevier
Publication Date
Volume
8
Issue
4
Identifiers
DOI: 10.1016/0377-2217(81)90008-4
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract A semi-Markovian point process which qualitatively models platooned arrivals is introduced. This process is used as the input to a single server queue in which the service times are independent and have a common distribution of phase type. It is shown that this queue has an embedded Markov chain of a particular block-partitioned type, whose invariant probability vector in the stable case is of matrix-geometric form. Detailed algorithms for the computation of the steady-state features of the queue are obtained and a representative numerical example is discussed.

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