Numerical Analysis of Optimal Control Policies for Queueing Systems with Heterogeneous Servers

The problem of optimal jobs assignment to heterogeneous servers arises in many applications. The problem of optimal jobs assignment for two heterogeneous servers with respect to minimization of long run average mean number jobs in the system was considered in [1], where it was shown that the policy, which minimizes the number of customers in the system, has a threshold property and consists in using the fastest server if necessary. For the multi-server system, these properties of an optimal policy were generalized in [2]. In the talk, an algorithm is proposed which gives the possibility to find optimal threshold levels for different values of system parameters and investigate their behavior. Some numerical examples are also included.