Optimization of queuing system via stochastic control

The problem of access and service rate control in queuing systems as a general optimization problem for controlled Markov process with finite state space is considered. By using the dynamic programming approach we obtain the explicit form of the optimal control in the case of minimizing cost given as a mixture of an average queue length, number of lost jobs, and service resources. The problem is considered on a finite time interval in the case of nonstationary input flow. In this case we suggest the general procedure of the numerical solution which can be applied to a problems with constraints.