Journal of Applied Mathematics and Stochastic Analysis 
Volume 16 (2003), Issue 4, Pages 349-360
doi:10.1155/S1048953303000273

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

Abstract

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.