Analysis of State Dependent Vacation Queues with Threshold Gated Service Policy

Analysis of State Dependent Vacation Queues with Threshold Gated Service Policy

Yew Sing (University of Illinois at Chicago, USA)
DOI: 10.4018/joris.2010040103

Abstract

In this article, the authors introduce a simple approach for modeling and analyzing a queue where the server may take repeated vacations. When a busy period ends, the server takes a vacation of random duration. At the end of each vacation, the server may either start a new vacation or resume service. If a queue is found of less than customers, the server will always take a new vacation. If there are at least customers in queue, the server provides services to those customers after a brief set-up time. The authors obtain several performance measures of the system, including the mean and second moment of the cycle time, the number of customers in a cycle of service, and the expected delay experienced by a customer.
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Introduction

Queueing models with server repeated vacations have found applications in many areas such as computer science, telecommunication engineering, production and inventory networks. Server vacations are useful for the system in which the server wants to utilize his idle time for alternative purposes. For comprehensive and excellent surveys on queueing systems with server vacations, we refer the readers to Doshi (1986,1990) and the books by Takagi (1991). It is usually assumed that the server becoming available, or unavailable, completely depends on the number of the customers in the system. For exhaustive service policy, the server is assumes to goes on vacation whenever the system is empty. The instance at which the server comes back from a vacation and finds at least N (predetermined threshold) customers in the system he begins serving immediately and exhaustively. This type of control policy is commonly known as N policy queueing systems with vacations. We refer the readers to Kella (1989) and Lee and Srinivasan (1989) for detail discussions concerning n policy and queueing systems with vacations, respectively. One can also find some applications of N Policy queueing system in these two papers. For other types of nonexhaustive service policy we again refer the readers to Doshi (1986,1990) and the books by Takagi (1990, 1991).

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