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Asymptotics of Closed Fork and Join Queues with Subexponential Service Times1
 

Summary: Asymptotics of Closed Fork and Join Queues with
Subexponential Service Times1
Hayriye Ayhan
School of Industrial and Systems Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0205 U.S.A
May 23, 2005
Abstract
We consider a closed fork and join queueing network where several lines feed a single assembly
station. Under the assumption that at least one service time distribution is subexponential, we
obtain the tail asymptotics of transient cycle times and waiting times. We also discuss under
which conditions these results can be generalized to the tail asymptotics of stationary cycle
times and waiting times.
Keywords: cycle time, waiting time, subexponential asymptotics
1 Introduction
Recent research has shown that in many queueing networks service times have subexponential
distributions. For example in telecommunications setting, Fowler [15] argue that FTP (File Trans-
fer Protocol) transfers have session sizes and session durations with subexponential distributions.
Similar observations are made for the TELNET sessions in Paxson and Floyd [20] even though
TELNET is an application qualitatively quite different from FTP. Feldmann, Gilbert, Willinger

  

Source: Ayhan, Hayriye - School of Industrial and Systems Engineering, Georgia Institute of Technology

 

Collections: Engineering