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The control policy of an M[x]/G/1 queueing system with server startup and two vacation types

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  • Jau-Chuan Ke

Abstract

This paper studies the optimal control of an M [x] /G/1 queue with two types of generally distributed random vacation: type 1 (long) and type 2 (short) vacations. The server is turned off and takes type 1 vacation whenever the system is empty. If the number of customers waiting in the system at the instant of a vacation completion is less than Q, the server will take a type 1 vacation. If the number of customers in the system is greater than or equal to Q and smaller than N, the server will take a type 2 vacation. If the server returns from a vacation and finds at least N customers in the system, he is immediately turned on and requires a startup time before providing the service until the system is again empty. We analyze the system characteristics for such a model. The total expected cost function per unit time is developed to determine the optimal thresholds of Q and N at a minimum cost. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Jau-Chuan Ke, 2001. "The control policy of an M[x]/G/1 queueing system with server startup and two vacation types," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 471-490, December.
  • Handle: RePEc:spr:mathme:v:54:y:2001:i:3:p:471-490
    DOI: 10.1007/s001860100167
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    Cited by:

    1. R. Suganya & Lewis Nkenyereye & N. Anbazhagan & S. Amutha & M. Kameswari & Srijana Acharya & Gyanendra Prasad Joshi, 2021. "Perishable Inventory System with N-Policy, MAP Arrivals, and Impatient Customers," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    2. Jau-Chuan Ke, 2006. "An M/G/1 queue under hysteretic vacation policy with an early startup and un-reliable server," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 357-369, May.

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