M/G/1 Vacation Queueing Systems with Server Timeout

Oliver C. Ibe

Department of Electrical and Computer Engineering, University of Massachusetts, Lowell, USA.

DOI: 10.4236/ajor.2015.52007                

Abstract

We consider a single-server vacation queueing system that operates in the following manner. When the server returns from a vacation, it observes the following rule. If there is at least one customer in the system, the server commences service and serves exhaustively before taking another vacation. If the server finds the system empty, it waits a fixed time c. At the expiration of this time, the server commences another vacation if no customer has arrived; otherwise, it serves exhaustively before commencing another vacation. Analytical results are derived for the mean waiting time in the system. The timeout scheme is shown to be a generalized scheme of which both the single vacation and multiple vacations schemes are special cases, with c=∞ and c=0, respectively. The model is extended to the N-policy vacation queueing system.

Keywords

Vacation Queueing Systems, Timeout Policies, Performance Analysis, N-Policy with Timeout

Conflicts of Interest

The authors declare no conflicts of interest.

References

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