Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 4, Pages 349-360

A spectral approach to compute the mean performance measures of the queue with low-order BMAP input

Ho Woo Lee,1 Jong Min Moon,2 Jong Keun Park,3 and Byung Kyu Kim4

1Sung Kyun Kwan University, Dept. of Systems Management Engineering, Su Won 440-746, Korea
2SE Application Prog. , Info Tech. Group Division LG CNS, Good Morning Bldg., Yeo Eui Do, Seoul 150-712, Korea
3I/O System Team, Computer System Department, Computer &Software Research Laboratory, ETRI, Dae Jon 305-350, Korea
4Itsweb, CRM Team, R& D Center 789-4 Young Bldg, Yok Sam Dong Kang Nam, Seoul 135-080, Korea

Received 1 October 2002; Revised 1 May 2003

Copyright © 2003 Ho Woo Lee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper targets engineers and practitioners who want a simple procedure to compute the mean performance measures of the Batch Markovian Arrival process (BMAP/G/1) queueing system when the parameter matrices order is very low. We develop a set of system equations and derive the vector generating function of the queue length. Starting from the generating function, we propose a spectral approach that can be understandable to those who have basic knowledge of M/G/1 queues and eigenvalue algebra.