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Pass-and-swap queues

Author

Listed:
  • Céline Comte

    (Eindhoven University of Technology)

  • Jan-Pieter Dorsman

    (University of Amsterdam)

Abstract

Order-independent (OI) queues, introduced by Berezner et al. (Queueing Syst 19(4):345–359, 1995), expanded the family of multi-class queues that are known to have a product-form stationary distribution by allowing for intricate class-dependent service rates. This paper further broadens this family by introducing pass-and-swap (P&S) queues, an extension of OI queues where, upon a service completion, the customer that completes service is not necessarily the one that leaves the system. More precisely, we supplement the OI queue model with an undirected graph on the customer classes, which we call a swapping graph, such that there is an edge between two classes if customers of these classes can be swapped with one another. When a customer completes service, it passes over customers in the remainder of the queue until it finds a customer it can swap positions with, that is, a customer whose class is a neighbor in the graph. In its turn, the customer that is ejected from its position takes the position of the next customer it can be swapped with, and so on. This is repeated until a customer can no longer find another customer to be swapped with; this customer is the one that leaves the queue. After proving that P&S queues have a product-form stationary distribution, we derive a necessary and sufficient stability condition for (open networks of) P&S queues that also applies to OI queues. We then study irreducibility properties of closed networks of P&S queues and derive the corresponding product-form stationary distribution. Lastly, we demonstrate that closed networks of P&S queues can be applied to describe the dynamics of new and existing load-distribution and scheduling protocols in clusters of machines in which jobs have assignment constraints.

Suggested Citation

  • Céline Comte & Jan-Pieter Dorsman, 2021. "Pass-and-swap queues," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 275-331, August.
  • Handle: RePEc:spr:queues:v:98:y:2021:i:3:d:10.1007_s11134-021-09700-3
    DOI: 10.1007/s11134-021-09700-3
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    References listed on IDEAS

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    5. Kristen Gardner & Rhonda Righter, 2020. "Product forms for FCFS queueing models with arbitrary server-job compatibilities: an overview," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 3-51, October.
    6. Xiuli Chao, 2011. "Networks with Customers, Signals, and Product Form Solution," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 0, pages 217-267, Springer.
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