Elsevier

Performance Evaluation

Volume 9, Issue 2, April 1989, Pages 93-102
Performance Evaluation

Queueing modeling of a single processor with failures

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Abstract

We analyze a single server queue which models the behavior of a processor in parallel processing environment. Service time distribution is assumed to be a mixture of generalized Erlang distributions and the arrival process is compound Poisson. A failure, upon occurrence, clears the system off of all the present transactions and no tasks arrive during the rollback recovery procedure. Repair times are also assumed to be a mixture of generalized Erlang distributions. A recursive procedure is developed to compute the steady-state probability distribution of the number of transactions in the processor, in which the generating function approach is also utilized to compute the probability of the empty-and-idle state. We also discuss some performance measures.

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Cited by (13)

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    S. Kumar and P. R. Kumar consider machine's failures in manufacturing systems [32], and assign exponential times for times to failure and times to repair. Govil and Fu survey in [33] contributions and applications of queuing theory in the field of discrete part manufacturing, where they reference other works dealing with failures in manufacturing flow lines [34–36]. PMIF was conceived as a common representation for system performance model data that could be used to move models between modeling tools [26].

  • Queueing theory in manufacturing: A survey

    1999, Journal of Manufacturing Systems
  • Two load sharing processors with failures

    1998, Computers and Operations Research
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This research was initiated when the author was visiting the Laboratoire d'Informatique des Systèmes Expérimentaux et leur Modélisation, Université de Paris-Sud, in 1986. The author is thankful for the partial support from the ISEM Laboratory and from the Center for Computer Aids for Industrial Productivity at Rutgers University.

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