Performance of the \((\mathrm{BMAP}_1,\mathrm{BMAP}_2)/(\mathrm{PH}_1,\mathrm{PH}_2)/N\) retrial queueing system with finite buffer. (English) Zbl 1305.60099
Summary: This paper considers the \((\mathrm{BMAP}_1,\mathrm{BMAP}_2)/(\mathrm{PH}_1,\mathrm{PH}_2)/N\) retrial queue with finite-position buffer. The behavior of the system is described in terms of continuous time multi-dimensional Markov chain. Arriving type I calls find all servers busy and join the buffer, if the positions of the buffer are insufficient, they can go to orbit. Arriving type II calls find all servers busy and join the orbit directly. Each server can provide two types of heterogeneous services with Phase-type (PH) time distribution to every arriving call (including type I and II calls), and the arriving calls have an option to choose either type of services. The model is quite general enough to cover most of the systems in communication networks. We derive the ergodicity condition, the stationary distribution and the main performance characteristics of the system. The effects of various parameters on the system performance measures are illustrated numerically.
MSC:
| 60K25 | Queueing theory (aspects of probability theory) |
| 90B22 | Queues and service in operations research |
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