Bad Luck When Joining the Shortest Queue

A frequent observation in service systems with queues in parallel is that customers in other queues tend to be served faster than those in one’s own queue. This paper quantifies the probability that one’s service would have started earlier if one had joined another queue than the queue that was actually chosen, for exponential multiserver systems with queues in parallel in which customers join one of the shortest queues upon arrival and in which jockeying is not possible.Queueing;Join-the-shortest-queue;Probability of bad luck;Power-series algorithm;Overtaking customers;Dedicated customers

Steady-state analysis of shortest expected delay routing

We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue promising the shortest expected delay, which is a natural and near-optimal policy for systems with non-identical servers. This system can be modeled as an inhomogeneous random walk in the quadrant. By stretching the boundaries of the compensation approach we prove that the equilibrium distribution of this random walk can be expressed as a series of product-forms that can be determined recursively. The resulting series expression is directly amenable for numerical calculations and it also provides insight in the asymptotic behavior of the equilibrium probabilities as one of the state coordinates tends to infinity.Comment: 41 pages, 13 figure

Random queues and risk averse users

We analyse Nash equilibrium in time of use of a congested facility. Users are risk averse with general concave utility. Queues are subject to varying degrees of random sorting, ranging from strict queue priority to a completely random queue. We define the key "no residual queue" property, which holds when there is no queue at the time the last user arrives at the queue, and prove that this property holds in equilibrium under all queueing regimes considered. The no residual queue property leads to simple results concerning the equilibrium utility of users and the timing of the queue

Bad luck when joining the shortest queue

A frequent observation in service systems with queues in parallel is that customers in other queues tend to be served faster than those in one’s own queue. This paper quantifies the probability that one’s service would have started earlier if one had joined another queue than the queue that was actually chosen, for exponential multiserver systems with queues in parallel in which customers join one of the shortest queues upon arrival and in which jockeying is not possible

Bad luck when joining the shortest queue

A frequent observation in service systems with queues in parallel is that customers in other queues tend to be served faster than those in one's own queue. This paper quantifies the probability that one's service would have started earlier if one had joined another queue than the queue that was actually chosen, for exponential multiserver systems with queues in parallel in which customers join one of the shortest queues upon arrival and in which jockeying is not possible.Queueing Join-the-shortest-queue Probability of bad luck Power-series algorithm Overtaking customers Dedicated customers