# The BMAP/G/1 $\to \cdot$/PH/1/M tandem queue with feedback and losses

Kim, Che Soong and Klimenok, Valentina and Tsarenkov, Gennady and Breuer, Lothar (2007) The BMAP/G/1 $\to \cdot$/PH/1/M tandem queue with feedback and losses. Performance Evaluation, 64 (7-8). pp. 802-818. ISSN 0166-5316. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication) Official URLhttp://dx.doi.org/10.1016/j.peva.2007.01.002

## Abstract

Tandem queues are good mathematical models of communication systems and networks, so their investigation is important for theory and applications. In this paper, exact analytical analysis of the tandem queue of the type with customers loss in case when the intermediate buffer is full and with possible feedback is implemented. Possible correlation in the input stream is taken into account by of assuming the Batch Markovian Arrival Process (BMAP). Stability condition for the tandem is derived. Stationary distribution of the system states is derived. Loss probability is calculated. Dependence of the system performance measures on correlation in the input flow, buffer capacity, and feedback probability is numerically illustrated.

Item Type: Article Q Science Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science Lothar Breuer 07 Oct 2008 08:58 07 May 2014 09:00 https://kar.kent.ac.uk/id/eprint/12992 (The current URI for this page, for reference purposes)