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Solutions of M / G /1// N -type Loops with Extensions to M / G /1 and GI / M /1 Queues

Author

Listed:
  • J. L. Carroll

    (San Diego State University, San Diego, California)

  • A. van de Liefvoort

    (University of Kansas, Lawrence, Kansas)

  • Lester Lipsky

    (University of Nebraska, Lincoln, Nebraska)

Abstract

Closed form solutions of the joint equilibrium distribution of queue sizes are derived for a large class of M / G /1// N queues, i.e., any closed loop of two servers in which one is exponential (but possibly load dependent), and the other has a probability density function which has a rational Laplace transform and a queueing discipline that is FCFS. The class of G / M / k // N queues are included as special cases of load-dependent servers. The solutions are presented in terms of vectors and matrices whose size depends only on the distribution of the general server and not on the number of customers in the system. Efficient algorithms are outlined, and expressions for various system measurements are presented. Depending on the relative service rates of the two servers, solutions for both the M / G /1 and GI / M /1 open queues are derived as limiting cases of the M / G /1// N system. All results are contrasted with existing formulas.

Suggested Citation

  • J. L. Carroll & A. van de Liefvoort & Lester Lipsky, 1982. "Solutions of M / G /1// N -type Loops with Extensions to M / G /1 and GI / M /1 Queues," Operations Research, INFORMS, vol. 30(3), pages 490-514, June.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:3:p:490-514
    DOI: 10.1287/opre.30.3.490
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