Analysis of BMAP^{(r)}/M^{(r)}/N^{(r)} Type Queueing System Operating in Random Environment

- Journal title : Journal of Korean Institute of Industrial Engineers
- Volume 42, Issue 1, 2016, pp.30-37
- Publisher : Korean Institute of Industrial Engineers
- DOI : 10.7232/JKIIE.2016.42.1.030

Title & Authors

Analysis of BMAP^{(r)}/M^{(r)}/N^{(r)} Type Queueing System Operating in Random Environment

Kim, Chesoong; Dudin, Sergey;

Kim, Chesoong; Dudin, Sergey;

Abstract

A multi-server queueing system with an infinite buffer and impatient customers is analyzed. The system operates in the finite state Markovian random environment. The number of available servers, the parameters of the batch Markovian arrival process, the rate of customers` service, and the impatience intensity depend on the current state of the random environment and immediately change their values at the moments of jumps of the random environment. Dynamics of the system is described by the multi-dimensional asymptotically quasi-Toeplitz Markov chain. The ergodicity condition is derived. The main performance measures of the system are calculated. Numerical results are presented.

Keywords

Multi-Server Queue;Batch Markovian Arrival Process;Random Environment;Stationary Distribution of the System States;

Language

English

Cited by

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