The Geo/G/1 Queue with Disasters and Multiple Working Vacations

Abstract

In this paper, we first consider a Geo/G/1 queue with disasters that remove all workloads from the system upon their occurrence. We present the steady-state queue-length distribution of the Geo/G/1 queue with disasters. Using this result, we then analyze the Geo/G/1 queue with multiple working vacations in which the server works at a different rate rather than completely stopping during the vacation period. We also present the steady-state queue-length distribution of the Geo/G/1 queue with multiple working vacations.

Keywords:

• Disasters
• Discrete-time
• Geo/G/1 queue
• Queue-length
• Working vacation

AMS Subject Classification:

• Primary 60K25
• Secondary 68M20

ACKNOWLEDGMENTS

The authors are grateful to the editor and the referees for their valuable comments and suggestions, which have led to considerable improvement of this paper.