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Decomposition of M/M/1 With Unreliable Service and a Working Vacation

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  • Joshua Patterson
  • Andrzej Korzeniowski

Abstract

We use the stationary distribution for the M/M/1 with Unreliable Service and aWorking Vacation (M/M/1/US/WV) given explicitly in (Patterson & Korzeniowski, 2019) to find a decomposition of the stationary queue length N. By applying the distributional form of Little's Law the Laplace-tieltjes Transform of the stationary customer waiting time W is derived. The closed form of the expected value and variance for both N and W is found and the relationship of the expected stationary waiting time as a function of the service failure rate is determined.

Suggested Citation

  • Joshua Patterson & Andrzej Korzeniowski, 2020. "Decomposition of M/M/1 With Unreliable Service and a Working Vacation," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(1), pages 1-63, January.
    • Handle: RePEc:ibn:ijspjl:v:9:y:2020:i:1:p:63
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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