Optimal routing among ·/M/1 queues with partial information

E. Altman*, T. Jiménez, R. Núñez-Queija, U. Yechiali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


When routing dynamically randomly arriving messages, the controller of a high-speed communication network very often gets the information on the congestion state of down stream nodes only after a considerable delay, making that information irrelevant at decision epochs. We consider the situation where jobs arrive according to a Poisson process and must be routed to one of two (parallel) queues with exponential service time distributions (possibly with different means), without knowing the congestion state in one of the queues. However, the (conditional) probability distribution of the state of the unobservable queue can be computed by the router. We derive the joint probability distribution of the congestion states in both queues as a function of the routing policy. This allows us to identify optimal routing schemes for two types of frameworks: global optimization, in which the weighted sum of average queue lengths is minimized, and individual optimization, in which the goal is to minimize the expected delay of individual jobs.

Original languageEnglish
Pages (from-to)149-171
Number of pages23
JournalStochastic Models
Issue number2
StatePublished - 2004


FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk OnderzoekR 61-451, VGP 61-520


    • Communication networks
    • Dynamic routing
    • Nash equilibrium
    • Non-cooperative game
    • Partial information
    • Performance optimization
    • Queueing
    • Stochastic modeling


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