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


  •  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.



This work is licensed under a Creative Commons Attribution 4.0 License.
  • ISSN(Print): 1927-7032
  • ISSN(Online): 1927-7040
  • Started: 2012
  • Frequency: bimonthly

Journal Metrics

  • h-index (December 2019): 15
  • i10-index (December 2019): 24
  • h5-index (December 2019): N/A
  • h5-median(December 2019): N/A

( The data was calculated based on Google Scholar Citations. Click Here to Learn More. )

Contact