M/G/1 Vacation Queueing Systems with Server Timeout

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 = 0 c , respectively. The model is extended to the N-policy vacation queueing system.

Load Balancing Approaches for Web Servers: A Survey of Recent Trends

“…This kind of system is called vacation queueing system. An expression for mean waiting time of a vacation queueing system is derived in reference [15]. Many models already exist for vacation queueing system but they don't consider server time out.…”

“…Many models already exist for vacation queueing system but they don't consider server time out. Server time out also considered and extended for N-Policy scheme where time out is measured [15].…”

Simulation Models of Modified Multiple Vacation Policy for Multi-Server Queuing Systems

“…Queueing systems with server vacations have attracted the attention of many researchers since the idea was first discussed in the paper of Levy and Yechiali [1]. One can find a comprehensive review of many important analytical results for different vacation queueing models, for example, in [2][3][4].…”

Effects of Reneging, Server Breakdowns and Vacation on a Batch Arrival Single Server Queueing System with Three Fluctuating Modes of Service

“…Enogwe Obviously, during the period of system breakdown, the server may proceed on vacation. By vacation, we mean that the server becomes unavailable for a random period of time from its primary customers to serve elsewhere [13]. Works by [14]- [21] deals extensively on vacation queueing systems.…”