IJPAM: Volume 28, No. 1 (2006)

OPTIMAL PERFORMANCE ANALYSIS OF
AN M/M/1/N QUEUE SYSTEM WITH BALKING,
RENEGING AND SERVER VACATION

Dequan Yue$^1$, Yan Zhang$^2$, Wuyi Yue$^3$
$^{1,2}$Department of Statistics
College of Science
Yanshan University
Qinhuangdao, Hebei, 066004, P.R. CHINA
$^1$e-mail: ydq@ysu.edu.cn
$^2$e-mail: helen89@ysu.edu.cn
$^3$Department of Information Science and Systems Engineering
Konan University
8-9-1, Okamoto, Higashinada-ku, Kobe, 658-8501, JAPAN
e-mail: yue@konan-u.ac.jp


Abstract.This paper presents an analysis for an M/M/1/N queueing system with balking, reneging and server vacations. Arriving customers balk with a probability and renege according to a negative exponential distribution. It is assumed that the server has multiple vacations. By using the Markov process method, we first develop the equations of the steady state probabilities. Then, we derive a matrix form solution of the steady-state probabilities. Next, we give some performance measures of the system such as the expected number of the waiting customers, the expected number of the customers in the system, the average rate of customer loss due to impatience and so on. And based on the performance analysis, we formulate a cost model to determine the optimal service rate. Finally, we present some numerical examples to demonstrate how the various parameters influence the behavior of the system.

Received: April 16, 2006

AMS Subject Classification: 60K25

Key Words and Phrases: vacation, balking, reneging, queueing system, optimal performance analysis

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 28
Issue: 1