On Optimal control policy of MAP(t)/M/2 queueing system with heterogeneous servers and periodic arrival process

In this paper we consider an optimal control problem for the MAP(t)/M/2 queueing system with heterogeneous servers is introduced. The Markov arrival process (MAP) has time-dependent and periodic rates for phase transitions. We built a continuous time finite-horizon Markov decision process (MDP) with the aim to minimize a cost function. We solve a Bellman equation as a system of ordinary differential equations with time-dependent coefficients. We show that the optimal policy is of threshold type with threshold levels depending on the phases of arrival process. Moreover, the periodic variation of arrival attributes makes a threshold control policy piecewise constant time-dependent and periodic. We study numerically the speed of convergence of the policy to a periodic pattern. For the fixed control policy we calculate a transient solution. and provide a sensitivity analysis to determine how sensitive the performance measures are to changes in parameter values and in inter-arrival time correlation.