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Superimposed renewal processes and storage with gradual input

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  • Cohen, J. W.

Abstract

In systems for data handling, buffers are often applied for temporary storage of messages. The storage process at the buffer may be considered as a queueing process with gradual input, being a process which until now has been hardly studied. The present study provides for several models of this type an analytic description, it shows that existing results of queueing theory can be used. The results obtained provide also important information for the determination of the buffer capacity. A number of new and interesting problems originate from the present model and the results so far obtained.

Suggested Citation

  • Cohen, J. W., 1974. "Superimposed renewal processes and storage with gradual input," Stochastic Processes and their Applications, Elsevier, vol. 2(1), pages 31-57, January.
    • Handle: RePEc:eee:spapps:v:2:y:1974:i:1:p:31-57
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    Cited by:

    1. Boxma, O.J. & Cohen, J.W. & Deng, Q., 1998. "Heavy-Traffic Analysis of the M/G/1 Queue With Priority Classes," Other publications TiSEM 7167fcc5-d147-4352-aae3-6, Tilburg University, School of Economics and Management.
    2. Sidney Resnick & Gennady Samorodnitsky, 2000. "A Heavy Traffic Approximation for Workload Processes with Heavy Tailed Service Requirements," Management Science, INFORMS, vol. 46(9), pages 1236-1248, September.
    3. Onno Boxma & Mahmut Parlar & David Perry, 2015. "A make-to-stock mountain-type inventory model," Annals of Operations Research, Springer, vol. 231(1), pages 65-77, August.
    4. A. B. Dieker & M. Mandjes, 2011. "Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 221-267, June.

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