A new formula for the transient behaviour of a non-empty M/M/1/∞ queue

A new formula for the transient behaviour of a non-empty M/M/1/∞ queue

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Article ID: iaor20033011
Country: United States
Volume: 132
Issue: 1
Start Page Number: 1
End Page Number: 10
Publication Date: Oct 2002
Journal: Applied Mathematics and Computation
Authors:
Keywords: M/M/1 queues
Abstract:

This paper studies the most general model of the Markovian queues namely M/M/1/∞ queue with any arbitrary number i of customers being present in the system initially. For this model, a new and simple series form is obtained for the transient state probabilities whence all particular cases concerning the system being empty and steady-state situations can be derived straightaway. The coefficients in this series satisfy iterative recurrence relations which would allow for the rapid and efficient numerical evaluations of the state probabilities. Moreover, a simple algebraic proof to show the equivalence between different formulae of a non-empty M/M/1/∞ and the new formula is established.

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