Deciding which queue to join: Some counterexamples
Operations Research
Improving Service by Informing Customers About Anticipated Delays
Management Science
Journal of the ACM (JACM)
Structural results for the control of queueing systems using event-based dynamic programming
Queueing Systems: Theory and Applications
Dynamic service sharing with heterogeneous preferences
Queueing Systems: Theory and Applications
Individual Equilibrium and Learning in Processor Sharing Systems
Operations Research
Self-Interested Routing in Queueing Networks
Management Science
The Downs-Thomson Paradox: Existence, Uniqueness and Stability of User Equilibria
Queueing Systems: Theory and Applications
Information And Uncertainty In A Queuing System
Probability in the Engineering and Informational Sciences
Analysis and Comparison of Queues with Different Levels of Delay Information
Management Science
The Impact of Delay Announcements in Many-Server Queues with Abandonment
Operations Research
Equilibrium customers' choice between FCFS and random servers
Queueing Systems: Theory and Applications
Monotonicity properties of user equilibrium policies for parallel batch systems
Queueing Systems: Theory and Applications
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Consider a system of two queues in parallel, one of which is a 驴|M|1 single-server infinite capacity queue, and the other a 驴|G (N)|驴 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 驴|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.