Dynamic routing in a distributed parallel many-server service system: The effect of ξ-choice

We consider a queueing system with multiple stations serving a single class of customers. Each station has many servers, and its own dedicated queue. The system manager must decide to which station each new customer is routed. We propose and analyze a minimum-expected-delay faster-server-first with ξ-choice (MED-FSF(ξ)) routing policy, under which an integer ξ, with P{ξ≥2}>0, is randomly generated for each new customer. Then, a subset of ξ stations will be randomly collected, with state information being retrieved. Among these collected stations, the system manager assigns the new customer to: (i) the one with minimum expected delay if all these ξ stations are fully occupied; or (ii) the one with fastest available server. We prove that in the Halfin–Whitt regime this policy is asymptotically equivalent to the MED-FSF policy, which only works when full information of the system state is available. Moreover, we compare the MED-FSF(ξ) policy with the random routing policy, which uses no information and routes each incoming customer to a station in a random manner. Using simulation experiments, we validate the theoretical results, and find that our proposed policy significantly outperforms the random routing policy. This suggests that a slight increase in information at each routing epoch can substantially improve system performance.