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Delays for Customers from Different Arrival Streams to a Queue

Author

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  • Susan L. Albin

    (College of Engineering, Rutgers University, Piscataway, New Jersey 08854)

Abstract

In a queue with several different arrival streams, in general, the expected delay for customers from one stream is not equal to the expected delay for customers from the other streams. Two approximations are presented here for the expected delay for customers from a particular arrival stream in an arrival process that is the superposition of independent renewal processes. Both approximations yield errors less than 10 percent, on average, when compared to simulation estimates. One approximation, extended from Holtzman (Holtzman, J. M. 1982. Mean delays of individual streams into a queue: the \Sigma GI i /M/1 queue. Applied Probability-Computer Science: The Interface, I, Proc. Conf. in Boca Raton, 417--430.), yields better results for very sparse arrival streams and the other, empirically derived, is easier to calculate. These approximations are useful in comparing the expected delays for customers from different arrival processes to a single queue and for customers with different routes through a network of queues.

Suggested Citation

  • Susan L. Albin, 1986. "Delays for Customers from Different Arrival Streams to a Queue," Management Science, INFORMS, vol. 32(3), pages 329-340, March.
    • Handle: RePEc:inm:ormnsc:v:32:y:1986:i:3:p:329-340
    DOI: 10.1287/mnsc.32.3.329
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    Cited by:

    1. Chydzinski, Andrzej, 2022. "Per-flow structure of losses in a finite-buffer queue," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    2. Ananth V. Iyer & Apurva Jain, 2003. "The Logistics Impact of a Mixture of Order-Streams in a Manufacturer-Retailer System," Management Science, INFORMS, vol. 49(7), pages 890-906, July.
    3. Kella, Offer & Stadje, Wolfgang, 2006. "Superposition of renewal processes and an application to multi-server queues," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1914-1924, November.
    4. Stadje, Wolfgang, 2012. "Embedded Markov chain analysis of the superposition of renewal processes," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1497-1503.
    5. Bitran, Gabriel R. & Morabito, Reinaldo., 1995. "Manufacturing system design : tradeoff curve analysis," Working papers 3805-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    6. Bitran, Gabriel R. & Morabito, Reinaldo., 1995. "An overview of tradeoff curve analysis in the design of manufacturing systems," Working papers 3806-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. Bitran, Gabriel R. & Sarkar, Debashish., 1990. "Throughput analysis in manufacturing networds [sic]," Working papers 3230-90., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Apurva Jain, 2006. "Priority and dynamic scheduling in a make‐to‐stock queue with hyperexponential demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(5), pages 363-382, August.
    9. Bitran, Gabriel R. & Morabito, Reinaldo., 1994. "Open queueing networks : optimization and performance evaluation models for discrete manufacturing systems," Working papers 3743-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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