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Allocation of flows in closed bipartite queueing networks


  • Brooks, James D.
  • Kar, Koushik
  • Mendonça, David J.


This paper describes a novel method for allocating agents to routes in a closed bipartite queueing network to maximize system throughput using three open network approximations. Results are presented which compare this method with known prior work and optimal solutions to provide an empirical optimality gap. Average empirical optimality gaps of 1.29 percent, 1.13 percent and 1.29 percent are observed for the three approximations considered. Further, because many systems are under the control of rational agents, conditions are derived in order to determine properties of the market context that induce optimal behavior. It is shown that uniform rewards do not yield an efficient rational equilibrium in general. However, for systems with homogeneous servers and travel times or those with travel times that are much larger than queue waiting times, uniform rewarding is optimal.

Suggested Citation

  • Brooks, James D. & Kar, Koushik & Mendonça, David J., 2016. "Allocation of flows in closed bipartite queueing networks," European Journal of Operational Research, Elsevier, vol. 255(2), pages 333-344.
  • Handle: RePEc:eee:ejores:v:255:y:2016:i:2:p:333-344
    DOI: 10.1016/j.ejor.2016.05.017

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    References listed on IDEAS

    1. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    2. A. Hordijk, 2000. "Optimal static customer routing in a closed queuing network," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(2), pages 148-159.
    3. Xia, Li & Shihada, Basem, 2015. "A Jackson network model and threshold policy for joint optimization of energy and delay in multi-hop wireless networks," European Journal of Operational Research, Elsevier, vol. 242(3), pages 778-787.
    4. Ali K. Parlaktürk & Sunil Kumar, 2004. "Self-Interested Routing in Queueing Networks," Management Science, INFORMS, vol. 50(7), pages 949-966, July.
    5. Colin E. Bell & Shaler Stidham, Jr., 1983. "Individual versus Social Optimization in the Allocation of Customers to Alternative Servers," Management Science, INFORMS, vol. 29(7), pages 831-839, July.
    6. Grossman, Thomas A. & Brandeau, Margaret L., 2002. "Optimal pricing for service facilities with self-optimizing customers," European Journal of Operational Research, Elsevier, vol. 141(1), pages 39-57, August.
    7. Morabito, Reinaldo & de Souza, Mauricio C. & Vazquez, Mariana, 2014. "Approximate decomposition methods for the analysis of multicommodity flow routing in generalized queuing networks," European Journal of Operational Research, Elsevier, vol. 232(3), pages 618-629.
    8. Joel M. Calabrese, 1992. "Optimal Workload Allocation in Open Networks of Multiserver Queues," Management Science, INFORMS, vol. 38(12), pages 1792-1802, December.
    9. Parlakturk, Ali & Kumar, Sunil, 2004. "Self-Interested Routing in Queueing Networks," Research Papers 1782r, Stanford University, Graduate School of Business.
    10. Delasay, Mohammad & Kolfal, Bora & Ingolfsson, Armann, 2012. "Maximizing throughput in finite-source parallel queue systems," European Journal of Operational Research, Elsevier, vol. 217(3), pages 554-559.
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