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Consider a network where two routes are available for users wishing to travel from a source to a destination. On one route (which could be viewed as private transport) service slows as traffic increases. On the other (which could be viewed as public transport) the service frequency increases with demand. The Downs-Thomson paradox occurs when improvements in service produce an overall decline in performance as user equilibria adjust. Using the model proposed by Calvert [10], with a ⋅|M|1 queue corresponding to the private transport route, and a bulk-service infinite server queue modelling the public transport route, we give a complete analysis of this system in the setting of probabilistic routing. We obtain the user equilibria (which are not always unique), and determine their stability.AMS subject classification: 60K30, 90B15, 90B20, 91A10, 91A13This revised version was published online in June 2005 with corrected coverdate 相似文献
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Consider a system of two queues in parallel, one of which is a ⋅|M|1 single-server infinite capacity queue, and the other a ⋅|G
(N)|∞ batch service queue. A stream of general arrivals choose which queue to join, after observing the current state of the
system, and so as to minimize their own expected delay. We show that a unique user equilibrium (user optimal policy) exists
and that it possesses various monotonicity properties, using sample path and coupling arguments. This is a very simplified
model of a transportation network with a choice of private and public modes of transport. Under probabilistic routing (which
is equivalent to the assumption that users have knowledge only of the mean delays on routes), the network may exhibit the
Downs–Thomson paradox observed in transportation networks with expected delay increasing as the capacity of the ⋅|M|1 queue (private transport) is increased. We give examples where state-dependent routing mitigates the Downs–Thomson effect
observed under probabilistic routing, and providing additional information on the state of the system to users reduces delay
considerably. 相似文献
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