Towards the optimal dynamic size-aware dispatching

In this paper, we study dispatching systems that appear in manufacturing, service, healthcare systems, as well as, in various information, communication and computer systems. Such systems comprise a dispatcher and a pool of parallel servers, to which jobs are assigned upon arrival. A common objective is to minimize the mean waiting or response time. In large systems, due to the state-space explosion and scalability reasons, it is impossible to utilize full state information of the system. We therefore consider systems with a small number of servers, and assume that the job sizes become known upon arrival. In such settings, it is plausible to carefully evaluate each server for every new job. First we study a system with a Poisson arrival process, and derive Bellman equations. Then we generalize to the case with general i.i.d. inter-arrival times. The Bellman equations are essentially functional equations that can be solved numerically via value iteration. From their solutions, the optimal dispatching policy and corresponding mean performance can be determined. Our solution framework is illustrated with examples, which show that significant performance gains compared to popular heuristic policies are available in our setting.