Probabilistic selfish routing in parallel batch and single-server queues

A. Wang () and I. Ziedins
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A. Wang: The University of Auckland
I. Ziedins: The University of Auckland

Queueing Systems: Theory and Applications, 2018, vol. 88, issue 3, No 7, 389-407

Abstract: Abstract We consider a network of parallel queues, operating under probabilistic routing, where users can choose to join either a batch service queue, or one of several FIFO single-server queues. Afimeimounga et al. (Queueing Syst 49:321–334, 2005) considered the 2-queue case, which is known to exhibit the Downs–Thomson paradox, where delays may increase as capacity is increased. We show that in larger parallel systems, with multiple single-server queues, the user equilibrium is always unique when the batch size is sufficiently large relative to the number of queues; no more than three equilibria exist; Braess paradox may appear when adding extra queues.

Keywords: Queueing network; User equilibria; Parallel queues; Downs–Thomson paradox; Wardrop’s equilibrium; Braess paradox; 90B15; 60K25; 90B20; 91A25; 91A10; 91A13 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11134-017-9558-6

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