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The Distribution of the Time Required to Reduce to Some Preassigned Level a Single-Channel Queue Characterized by a Time-Dependent Poisson-Distributed Arrival Rate and a General Class of Holding Times

Author

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  • George Luchak

    (Canadian Defence Research Board, Suffield Experimental Station, Ralston, Alberta, Canada)

Abstract

This paper provides the solution to the problem of the distribution of busy periods of the single-channel queue characterized by a time-dependent Poisson-distributed arrival rate and a general class of holding times. The notation is chosen in such a fashion that the main body of computations and mathematical analysis is identical with what was required in the solution of the general queuing equations considered in a previous paper which should be read first [4] . The solution of the problem for which the traffic intensity is constant and the holding time distribution is Pearson type III is derived in closed form in terms of the I n k functions introduced previously.

Suggested Citation

  • George Luchak, 1957. "The Distribution of the Time Required to Reduce to Some Preassigned Level a Single-Channel Queue Characterized by a Time-Dependent Poisson-Distributed Arrival Rate and a General Class of Holding Times," Operations Research, INFORMS, vol. 5(2), pages 205-209, April.
    • Handle: RePEc:inm:oropre:v:5:y:1957:i:2:p:205-209
    DOI: 10.1287/opre.5.2.205
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    Cited by:

    1. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.

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