On A Single Server Queue with Two-Stage Heterogeneous Service and Binomial Schedule Server Vacations | ||
| The Egyptian Statistical Journal | ||
| Article 4, Volume 44, Issue 1, June 2000, Pages 39-55 PDF (6.63 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.2000.313822 | ||
| Abstract | ||
| We analyze a single server queue with Poisson arrivals, two stages of heterogeneous service with different general (arbitrary) service time distributions and binomial schedule server vacations with exponential mean vacation time. After first stage service, the server must provide the second stage service. However, after second stage service, he may take a vacation or may decide to stay in the system. For convenience, we designate this model as M/G1,G2,/M/1 queue. We obtain steady state probability generating functions of queue length for various states of the server. Some particular cases of interest such as M/G1,G2,/M/1, M/M1,M1,/M/1, M/E1/M/1, M/Ek/1 and M/G/1 have been discussed and some known results have been derived. | ||
| Keywords | ||
| Poisson arrivals; two-stage heterogeneous service; steady state; probability generating function; binomial schedule sever vacations | ||
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