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Summary: Tandem Queues with Subexponential Service Times
and Finite Buffers
Jung-Kyung Kim and Hayriye Ayhan
H. Milton Stewart School of Industrial and Systems Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0205, U.S.A.
May 29, 2009
Abstract
We focus on tandem queues with subexponential service time distributions. We assume that
number of customers in front of the first station is infinite and there is infinite room for fin-
ished customers after the last station but the size of the buffer between two consecutive stations
is finite. Using (max,+) linear recursions, we investigate the tail asymptotics of transient re-
sponse times and waiting times under both communication blocking and manufacturing blocking
schemes. We also discuss under which conditions these results can be generalized to the tail
asymptotics of stationary response times and waiting times. Finally, we provide numerical ex-
amples to investigate the convergence of the tail probabilities of transient response times and
waiting times to their asymptotic counter parts.
Keywords: subexponential distribution, tail asymptotics, communication blocking, manufacturing
blocking, response time, waiting time
1 Introduction
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