On the Assignment of Customers to Parallel Queues

Abstract

This paper considers routing to parallel queues in which each queue has its own single server and service times are exponential with nonidentical parameters. We give conditions on the cost function such that the optimal policy assigns customers to a faster queue when that server has a shorter queue. The queues may have finite buffers, and the arrival process can be controlled and can depend on the state and routing policy. Hence our results on the structure of the optimal policy are also true when the assigning control is in the “last” node of a network of service centers. Using dynamic programming we show that our optimality results are true in distribution.

Optimal repairman assignment in two symmetric maintenance models

“…Observe that in the current model there is no equation relating states like i + ej and i, like in the standard routing model with one server for each queue (e.g., Eq. (4.4) in Hordijk and Koole [4]). We do not need such an equation here: the total number of functioning components remains stochastically the same under each policy, due to the structure of the model and the fact that idleness is not allowed (unless all components are functioning).…”

Dynamic Auctions for On-Demand Services

“…Since an incoming customer can only be rejected if all the buffers are busy, a systemwide efficient routing policy is one that maximizes the expected number of customers served over an unbounded horizon. Hordijk and Koole [4] have shown that any systemwide efficient policy has the following structure: an arriving customer should be assigned to a faster server when that server has a shorter queue. They refer to this type of policy as the "Shorter Queue Faster Server Policy, SQFSP."…”

“…They refer to this type of policy as the "Shorter Queue Faster Server Policy, SQFSP." As it is pointed out in [4], this characterization is incomplete in general but sufficient whenever the servers have identical service-time distributions. In this case, the optimal policy follows a simple "Shortest Queue" rule, incoming customers should be routed to the shortest queue.…”

Optimal Routing of Fixed Size Jobs to Two Parallel Servers

“…Since then the optimality of JSQ has been shown in many other similar settings, e.g., Weber (1978) considered arbitrary arrivals together with service times having a non-decreasing failure rate, while Johri (1989) considered state-dependent exponential service times, having a multi-server queues as a special case. Hordijk and Koole (1992) considered non-identical exponential servers and showed that jobs should always…”