Analysis of the MAP/G/1 Queue Under the Min(N, D)-Policy

Abstract

In this paper, we consider the queueing system under the MAP (Markovian Arrival process) arrivals and the Min(N, D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service time of the waiting customers exceeds D, whichever occurs first (Min(N, D)-policy). We analyze the queue length, workload, and waiting time. Then, we present numerical examples in which our analytical results are compared with the simulation estimates for verification purposes. We also compare our system with the M/G/1 queue under the same parameter setting and show that a naive Poisson assumption may severely underestimate the mean performance measures.

Keywords:

• MAP/G/1
• Min(N, D)-policy

Mathematics Subject Classification:

• Primary 60K25
• Secondary 68M20

ACKNOWLEDGMENTS

This work was supported by Samsung Research Fund, Sungkyunkwan University (2007). The authors are grateful to anonymous referees for their helpful comments. Their suggestions greatly enhanced the readability of this paper. The authors also thank Dr. Peter Taylor for correcting poor English exposition.