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Transient and asymptotic behavior of synchronization processes in assembly-like queues

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  • David Alexander
  • I. Premachandra
  • Toshikazu Kimura

Abstract

This paper analyzes the synchronization process of an assembly-like queueing system in which two distinct types of items/customers arrive at separate buffers, according to independent Poisson processes, so as to be synchronized into pairs at a synchronization node. Once a pair is synchronized it then queues up for service from a single server on a first-in-first-out basis as pairs. It is assumed that the service times of pairs are exponentially distributed and that the system has infinite capacity. Despite their practical significance, such queueing systems have not been adequately treated in the literature due to their transience or null recurrence. We first investigate the transient and asymptotic properties of the synchronization process’ first two moments, both analytically and numerically. Motivated by the observed asymptotic behavior, we then propose an M/M/1 approximation to describe the behavior of such assembly-like queueing systems. Finally, a numerical study of the proposed approximation reveals that it performs sufficiently well for practical applications. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • David Alexander & I. Premachandra & Toshikazu Kimura, 2010. "Transient and asymptotic behavior of synchronization processes in assembly-like queues," Annals of Operations Research, Springer, vol. 181(1), pages 641-659, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:641-659:10.1007/s10479-010-0796-9
    DOI: 10.1007/s10479-010-0796-9
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    References listed on IDEAS

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    1. Paul J. Burke, 1956. "The Output of a Queuing System," Operations Research, INFORMS, vol. 4(6), pages 699-704, December.
    2. Maurice W. Sasieni, 1961. "Double Queues and Impatient Customers with an Application to Inventory Theory," Operations Research, INFORMS, vol. 9(6), pages 771-781, December.
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    Cited by:

    1. Thiago Cantos Lopes & Celso Gustavo Stall Sikora & Adalberto Sato Michels & Leandro Magatão, 2020. "Mixed-model assembly lines balancing with given buffers and product sequence: model, formulation comparisons, and case study," Annals of Operations Research, Springer, vol. 286(1), pages 475-500, March.

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