A General Class of Closed Fork and Join Queues with Subexponential Service Times

Abstract

For a general class of closed feed-forward fork and join queueing networks, we derive the tail asymptotics of transient cycle times and waiting times under the assumption that the service time distribution of at least one station is subexponential. We also argue that under certain conditions, the asymptotic tail distributions remain the same for stationary cycle times and waiting times.

Keywords:

• Cycle time
• Tail asymptotics
• Waiting time

Mathematics Subject Classification:

• Primary 60K25, 90B22
• Secondary 60G10, 90B15

ACKNOWLEDGMENTS

We would like to thank the editor and two anonymous referees for their suggestions which have greatly improved and shortened the paper. Research was supported by the National Science Foundation under Grant DMI-9984352.