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Some results on a generalized M/G/1 feedback queue with negative customers

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  • B. Kumar
  • D. Arivudainambi
  • A. Krishnamoorthy

Abstract

This paper deals with a generalized M/G/1 feedback queue in which customers are either “positive" or “negative". We assume that the service time distribution of a positive customer who initiates a busy period is G e (x) and all subsequent positive customers in the same busy period have service time drawn independently from the distribution G b (x). The server is idle until a random number N of positive customers accumulate in the queue. Following the arrival of the N-th positive customer, the server serves exhaustively the positive customers in the queue and then a new idle period commences. This queueing system is a generalization of the conventional N-policy queue with N a constant number. Explicit expressions for the probability generating function and mean of the system size of positive customers are obtained under steady-state condition. Various vacation models are discussed as special cases. The effects of various parameters on the mean system size and the probability that the system is empty are also analysed numerically. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • B. Kumar & D. Arivudainambi & A. Krishnamoorthy, 2006. "Some results on a generalized M/G/1 feedback queue with negative customers," Annals of Operations Research, Springer, vol. 143(1), pages 277-296, March.
    • Handle: RePEc:spr:annopr:v:143:y:2006:i:1:p:277-296:10.1007/s10479-006-7388-8
    DOI: 10.1007/s10479-006-7388-8
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    References listed on IDEAS

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    1. Michel Scholl & Leonard Kleinrock, 1983. "On the M / G /1 Queue with Rest Periods and Certain Service-Independent Queueing Disciplines," Operations Research, INFORMS, vol. 31(4), pages 705-719, August.
    2. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    3. Offer Kella, 1989. "The threshold policy in the M/G/1 queue with server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(1), pages 111-123, February.
    4. Hanoch Levy & Leonard Kleinrock, 1986. "A Queue with Starter and a Queue with Vacations: Delay Analysis by Decomposition," Operations Research, INFORMS, vol. 34(3), pages 426-436, June.
    5. Artalejo, J. R., 2000. "G-networks: A versatile approach for work removal in queueing networks," European Journal of Operational Research, Elsevier, vol. 126(2), pages 233-249, October.
    6. Wei Chang, 1968. "Queues with Feedback for Time-Sharing Computer System Analysis," Operations Research, INFORMS, vol. 16(3), pages 613-627, June.
    7. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    8. Hyo-Seong Lee & Mandyam M. Srinivasan, 1989. "Control Policies for the M X /G/1 Queueing System," Management Science, INFORMS, vol. 35(6), pages 708-721, June.
    9. Teghem, J., 1986. "Control of the service process in a queueing system," European Journal of Operational Research, Elsevier, vol. 23(2), pages 141-158, February.
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