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Multilevel Bulk Service Queues

Author

Listed:
  • Emil Bahary

    (Western Electric Company, Princeton, New Jersey)

  • Peter Kolesar

    (Columbia University, New York, New York)

Abstract

This paper uses the imbedded-Markov-chain method to study bulk service queuing systems in which the server chooses the capacity and service mechanism depending on the number of customers waiting in line at the start of the service. It derives conditions under which the systems studied are ergodic and obtains the stationary state probability generating functions. A bilevel hysteretic bulk service system is studied in detail using numerical methods. A concept of system “scale” is introduced that permits the calculation of operating characteristics of large systems from those of small systems. This property is important because the computations for large systems are much more difficult, if not impossible, to perform. The characteristics studied are the expectation and variance of the queue size, the proportion of time each service level is used, and the transition rate between service levels.

Suggested Citation

  • Emil Bahary & Peter Kolesar, 1972. "Multilevel Bulk Service Queues," Operations Research, INFORMS, vol. 20(2), pages 406-420, April.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:2:p:406-420
    DOI: 10.1287/opre.20.2.406
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    Cited by:

    1. Fátima Ferreira & António Pacheco & Helena Ribeiro, 2017. "Moments of losses during busy-periods of regular and nonpreemptive oscillating $$M^X/G/1/n$$ M X / G / 1 / n systems," Annals of Operations Research, Springer, vol. 252(1), pages 191-211, May.
    2. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    3. António Pacheco & Helena Ribeiro, 2008. "Consecutive customer losses in oscillating GI X /M//n systems with state dependent services rates," Annals of Operations Research, Springer, vol. 162(1), pages 143-158, September.

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