Tail asymptotics for waiting time distribution of an M/M/s queue with general impatient time

Pages: 593 - 606, Volume 7, Issue 3, August 2011

doi:10.3934/jimo.2011.7.593       Abstract        References        Full Text (434.0K)       Related Articles

Yutaka Sakuma - Department of Distribution and Information Engineering, Hiroshima National College of Maritime Technology, Osakikamijima-Town, 725-0231, Japan (email)
Atsushi Inoie - Department of Information Network and Communication, Kanagawa Institute of Technology, Atsugi-City, 243-0292, Japan (email)
Ken’ichi Kawanishi - Department of Computer Science, Gunma University, Kiryu-City, 376-8515, Japan (email)
Masakiyo Miyazawa - Department of Information Sciences, Tokyo University of Science, Noda-City, 278-8510, Japan (email)

Abstract: In this paper, we consider an $M/M/s$ queueing model where customers may abandon waiting for service and leave the system without receiving their services. We assume that impatient time on waiting for each customer is an independent and identically distributed nonnegative random variable with a general distribution where the probability distribution is light-tailed and unbounded. The main objective of this paper is to provide an approximation for the waiting time distribution in an analytically tractable form. To this end, we obtain the tail asymptotics of the waiting time distributions of served and impatient customers. By using the tail asymptotics, we show that the fairly good approximations of the waiting time distributions can be obtained in asymptotic region with low numerical complexity.

Keywords:  Queue, general impatient time, waiting time distribution, tail behavior.
Mathematics Subject Classification:  Primary: 60K25, 60K25; Secondary: 60K25.

Received: September 2010;      Revised: May 2011;      Published: June 2011.

 References