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Transient and steady state results for two parallel queues

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  • Grassmann, WK

Abstract

This paper lists numerical results for a system with two parallel queues in which arriving customers always join the shorter queue. These results enable us to discuss how fast the expected queue length converges toward its equilibrium, provided the arrivals are below the capacity of the service facility. It also shows how fast the expected queue length increases in case the traffic flow is at or above the capacity of the service facility. Finally, it is shown that the system under consideration behaves very similar to a two-server queue.

Suggested Citation

  • Grassmann, WK, 1980. "Transient and steady state results for two parallel queues," Omega, Elsevier, vol. 8(1), pages 105-112.
    • Handle: RePEc:eee:jomega:v:8:y:1980:i:1:p:105-112
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    Cited by:

    1. Chaithanya Bandi & Nikolaos Trichakis & Phebe Vayanos, 2019. "Robust Multiclass Queuing Theory for Wait Time Estimation in Resource Allocation Systems," Management Science, INFORMS, vol. 65(1), pages 152-187, January.
    2. Zhang, Zhongju & Daigle, John, 2012. "Analysis of job assignment with batch arrivals among heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 217(1), pages 149-161.
    3. M. Saxena & I. Dimitriou & S. Kapodistria, 2020. "Analysis of the shortest relay queue policy in a cooperative random access network with collisions," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 39-75, February.
    4. Nur Sunar & Yichen Tu & Serhan Ziya, 2021. "Pooled vs. Dedicated Queues when Customers Are Delay-Sensitive," Management Science, INFORMS, vol. 67(6), pages 3785-3802, June.
    5. B. M. Rao & M. J. M. Posner, 1987. "Algorithmic and approximation analyses of the shorter queue model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 381-398, June.
    6. Chaithanya Bandi & Dimitris Bertsimas & Nataly Youssef, 2018. "Robust transient analysis of multi-server queueing systems and feed-forward networks," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 351-413, August.
    7. Boronico, Jess S. & Siegel, Philip H., 1998. "Capacity planning for toll roadways incorporating consumer wait time costs," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(4), pages 297-310, May.

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