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

Joshua Patterson and Andrzej Korzeniowski

International Journal of Statistics and Probability, 2020, vol. 9, issue 1, 63

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.

Date: 2020
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