The Queueing Model MAP/PH/1/N with Feedback Operating in a Markovian Random Environment

Dudin, A. and Kazimirsky, A. and Klimenok, V.I. and Breuer, U. (2005) The Queueing Model MAP/PH/1/N with Feedback Operating in a Markovian Random Environment. Austrian Journal of Statistics, 34 (2). pp. 101-110. ISSN 1026-597X. (The full text of this publication is not available from this repository)

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Abstract

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.

Item Type: Article
Additional information: Special Issue on the Seventh International Conference Computer Data Analysis and Modeling Proceedings of CDAM’2004 in Minsk, Belarus, September 6–10, 2004
Uncontrolled keywords: Feedback Queue, Batch Markovian Arrival Process, BMAP, Phase- Type Service, PH, Little’s Law.
Subjects: Q Science
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Lothar Breuer
Date Deposited: 16 Apr 2009 12:25
Last Modified: 30 Jul 2012 10:37
Resource URI: http://kar.kent.ac.uk/id/eprint/17841 (The current URI for this page, for reference purposes)
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