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

  •  Joshua Patterson    
  •  Andrzej Korzeniowski    


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.

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  • ISSN(Print): 1927-7032
  • ISSN(Online): 1927-7040
  • Started: 2012
  • Frequency: bimonthly

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