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

Authors:
Yutaka Sakuma;Atsushi Inoie;Ken'ichi Kawanishi;Masakiyo Miyazawa
Affiliations:
Tokyo University of Science, Noda-City, Japan;Kanagawa Institute of Technology, Atsugi-City, Japan;Gunma University, Kiryu-City, Japan;Tokyo University of Science, Noda-City, Japan
Venue:
Proceedings of the 5th International Conference on Queueing Theory and Network Applications
Year:
2010

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Abstract

In this paper, we consider an M/M/s queue where customers may abandon waiting for service and renege the system without receiving their services. We assume that impatient time on waiting for each customer is independent and identically distributed non-negative 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 with low numerical complexity.