Analysis of State Dependent Vacation Queues with Threshold Gated Service Policy

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).