An \(\mathrm{M}^{[X]}/\mathrm{G}(a,b)/1\) queueing system with breakdown and repair, stand-by server, multiple vacation and control policy on request for re-service. (English) Zbl 1404.60136
Summary: In this paper, we discuss a non-Markovian batch arrival general bulk service single-server queueing system with server breakdown and repair, a stand-by server, multiple vacation and re-service. The main server’s regular service time, re-service time, vacation time and stand-by server’s service time are followed by general distributions and breakdown and repair times of the main server with exponential distributions. There is a stand-by server which is employed during the period in which the regular server remains under repair. The probability generating function of the queue size at an arbitrary time and some performance measures of the system are derived. Extensive numerical results are also illustrated.
MSC:
| 60K25 | Queueing theory (aspects of probability theory) |
| 90B22 | Queues and service in operations research |
| 68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |
Keywords:
non-Markovian queue; general bulk service; multiple vacation; breakdown and repair; stand-by server; re-serviceReferences:
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