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Pull-based load distribution among heterogeneous parallel servers: the case of multiple routers

Author

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  • Alexander L. Stolyar

    (Lehigh University)

Abstract

The model is a service system, consisting of several large server pools. A server’s processing speed and buffer size (which may be finite or infinite) depend on the pool. The input flow of customers is split equally among a fixed number of routers, which must assign customers to the servers immediately upon arrival. We consider an asymptotic regime in which the total customer arrival rate and pool sizes scale to infinity simultaneously, in proportion to a scaling parameter n, while the number of routers remains fixed. We define and study a multi-router generalization of the pull-based customer assignment (routing) algorithm PULL, introduced in Stolyar (Queueing Syst 80(4): 341–361, 2015) for the single-router model. Under the PULL algorithm, when a server becomes idle it sends a “pull-message” to a randomly uniformly selected router; each router operates independently—it assigns an arriving customer to a server according to a randomly uniformly chosen available (at this router) pull-message, if there is any, or to a randomly uniformly selected server in the entire system otherwise. Under Markov assumptions (Poisson arrival process and independent exponentially distributed service requirements), and under subcritical system load, we prove asymptotic optimality of PULL: as $$n\rightarrow \infty $$ n → ∞ , the steady-state probability of an arriving customer experiencing blocking or waiting vanishes. Furthermore, PULL has an extremely low router–server message exchange rate of one message per customer. These results generalize some of the single-router results in Stolyar (2015).

Suggested Citation

  • Alexander L. Stolyar, 2017. "Pull-based load distribution among heterogeneous parallel servers: the case of multiple routers," Queueing Systems: Theory and Applications, Springer, vol. 85(1), pages 31-65, February.
    • Handle: RePEc:spr:queues:v:85:y:2017:i:1:d:10.1007_s11134-016-9508-8
    DOI: 10.1007/s11134-016-9508-8
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    Citations

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    Cited by:

    1. Jazeem Abdul Jaleel & Sherwin Doroudi & Kristen Gardner & Alexander Wickeham, 2022. "A general “power-of-d” dispatching framework for heterogeneous systems," Queueing Systems: Theory and Applications, Springer, vol. 102(3), pages 431-480, December.
    2. Daniela Hurtado-Lange & Siva Theja Maguluri, 2022. "A load balancing system in the many-server heavy-traffic asymptotics," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 353-391, August.
    3. Kuang Xu & Yuan Zhong, 2020. "Information and Memory in Dynamic Resource Allocation," Operations Research, INFORMS, vol. 68(6), pages 1698-1715, November.
    4. Debankur Mukherjee & Sem C. Borst & Johan S. H. van Leeuwaarden & Philip A. Whiting, 2020. "Asymptotic Optimality of Power-of- d Load Balancing in Large-Scale Systems," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1535-1571, November.
    5. Seva Shneer & Alexander L. Stolyar, 2021. "Large-scale parallel server system with multi-component jobs," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 21-48, June.
    6. James Cruise & Matthieu Jonckheere & Seva Shneer, 2020. "Stability of JSQ in queues with general server-job class compatibilities," Queueing Systems: Theory and Applications, Springer, vol. 95(3), pages 271-279, August.

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