@article{dd29a94fdc3248838bbf06e3952b73d6,

title = "Optimal routing among ·/M/1 queues with partial information",

abstract = "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.",

keywords = "Communication networks, Dynamic routing, Nash equilibrium, Non-cooperative game, Partial information, Performance optimization, Queueing, Stochastic modeling",

author = "E. Altman and T. Jim{\'e}nez and R. N{\'u}{\~n}ez-Queija and U. Yechiali",

note = "Funding Information: Most of this work was done at INRIA during a sabbatical stay of Prof. Yechiali and several visits of Dr. R. N{\'u}{\~n}ez-Queija. The latter was funded by the Netherlands Organization for Scientific Research (NWO) under grants R 61-451 and VGP 61-520.",

year = "2004",

doi = "10.1081/STM-120034126",

language = "אנגלית",

volume = "20",

pages = "149--171",

journal = "Stochastic Models",

issn = "1532-6349",

publisher = "Taylor and Francis Ltd.",

number = "2",

}