Dynamized routing policies for minimizing expected waiting time in a multi-class multi-server system

Minimizing queue waiting time in multi-class multi-server systems, where the service time depends both on the job type and the server type, has wide applications in transportation systems such as emergency networks and taxi networks, service systems such as call centers, and distributed computing platforms. However, the optimal dynamic policy for this problem is not known and remains a hard open problem. In our approach, we develop a math program to model a static variant of this routing problem and use the solution from this math program to construct several novel dynamic policies. In three categories, namely, (i) policies that do not block jobs, (ii) policies that block jobs statically (i.e., blocking jobs using a predetermined blocking probability), and (ii) policies that block jobs dynamically (i.e., blocking jobs when all feasible servers are busy), we compare the performance of our policies with Fastest-Server-First (FSF), a well-known routing policy for such problems in practice and in the literature. Our experiments show that our proposed overflow dynamic routing policies outperform FSF and its extensions, FSFStaticBlock and FSFDynamicBlock. Moreover, to showcase our methodology, we apply our proposed policies to the problem of assigning fire incidents in Irvine, CA, to fire stations.