Analysis of General Input State Dependent Working Vacation Queue with Changeover Time

Vijaya Laxmi Pikkala,Suchitra Vepada

doi:10.1155/2014/248704

Abstract

We consider a finite buffer GI/M(n)/1 queue with multiple working vacations and changeover time, where the server can keep on working but at a slower speed during the vacation period. Moreover, the amount of service demanded by a customer is conditioned by the queue length at the moment service is begun for that customer. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. Finally, some numerical results of the model are presented to show the parameter effect on various performance measures.

Highlights

Queueing systems with vacations are considered to be effective tools in modeling and analyzing complex computer and communication networks and several other engineering systems where the server can utilize the idle time for different purposes; see Doshi [1] and Tian and Zhang [2]
In multiple working vacations (MWV) policy when a vacation ends and the system is not empty, a service period begins with the normal service rate; otherwise, the server takes another vacation
Using the supplementary variable technique, a recursive algorithm has been explained by Goswami et al [12] for obtaining the system length distributions at prearrival and arbitrary epochs for a finite buffer state dependent GI/M/1 queue with MWV

Summary

Introduction

Queueing systems with vacations are considered to be effective tools in modeling and analyzing complex computer and communication networks and several other engineering systems where the server can utilize the idle time for different purposes; see Doshi [1] and Tian and Zhang [2]. Using the supplementary variable technique, a recursive algorithm has been explained by Goswami et al [12] for obtaining the system length distributions at prearrival and arbitrary epochs for a finite buffer state dependent GI/M/1 queue with MWV. The router, routing at slower speed, state dependent routing, and sleep mode correspond to the server, working vacation, state dependent services, and changeover times, respectively. Motivated by such situations of sleep mode operations, which conserve energy and further reduce the waiting times, this paper aims to focus on finite buffer state dependent queue with MWV and changeover time.

Description of the Model

Steady State Equations and Solution

Computational Algorithm

Performance Measures and Numerical Results

Constant

Conclusions