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.