The conditional distribution of the residual service time in the Mn/G/1 queue

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Abstract

We study a single server queueing system with general service time distribution and memoryless inter-arrival times. The arrival rate is not constant but varies with the number of customers in the system. A recursive formula for the conditional distribution of the remaining service time given the queue length is derived for an arbitrary epoch. It is also shown that this conditional distribution holds for arrival epochs. The recursion for the corresponding Laplace-Stieltjes transforms and expected values is given in a simple formula.

Original languageEnglish
Pages (from-to)364-375
Number of pages12
JournalStochastic Models
Volume24
Issue number3
DOIs
StatePublished - 1 Jul 2008
Externally publishedYes

Keywords

  • Residual service time
  • Single server queue
  • State department arrival process

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