The Queueing Model MAP|PH|1|N with Feedback Operating in a Markovian Random Environment
Queueing systems with feedback are well suited for the description of message transmission and manufacturing processes where a repeated service is required. In the present paper we investigate a rather general single server queue with a Markovian Arrival Process (MAP), Phase-type (PH) service-time d...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Austrian Statistical Society
2016-04-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | http://www.ajs.or.at/index.php/ajs/article/view/403 |
| Summary: | Queueing systems with feedback are well suited for the description of message transmission and manufacturing processes where a repeated service is required. In the present paper we investigate a rather general single server queue with a Markovian Arrival Process (MAP), Phase-type (PH) service-time distribution, a finite buffer and feedback which operates in a random environment. A finite state Markovian random environment affects the parameters of the input and service processes and the feedback probability. The stationary distribution of the queue and of the sojourn times as well as the loss probability are calculated. Moreover, Little’s law is derived.
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| ISSN: | 1026-597X |