This article is cited in 8 papers

Queuing Systems

Multi-server queueing system with a Batch Markovian Arrival Process and negative customers

Kim Che Soong^a, V. I. Klimenok^b, D. S. Orlovskii<sup>b

a</sup> Sangji University, Wonju, Kangwon, Korea
^b Belarussian State University, Minsk, Belarus

Abstract: A multi-server queueing system with a finite buffer, where a Batch Markovian Arrival Process (BMAP) arrives, is studied. The servicing time of a customer has a phase-type (PH) distribution. Customers are admitted to the system in accordance with the disciplines of partial admission, complete admission and complete rejection. Except standard (positive) customers, a MAP flow of negative customers arrives to the system. In a random way, a negative customer removes from the system one of the positive customers that are at the server. A stationary distribution of system state probabilities, the Laplace–Stieltjes transformation of the stationary distribution of waiting time, major characteristics of system performance are found. Numerical examples are given.

PACS: 89.75.-K

Presented by the member of Editorial Board: V. V. Rykov

Received: 12.12.2005

 English version: Automation and Remote Control, 2006, 67:12, 1958–1973

Bibliographic databases:

• 
• 
•