Optimal Control for an M/g/1/n + 1 Queue with Two Service Modes

A finite-buffer queueing model is considered with batch Poisson input and controllable service rate. A batch that upon arrival does not fit in the unoccupied places of the buffer is partially rejected. A decision to change the service mode can be made at service completion epochs only and vacation (switch-over) times are involved to prepare for the new mode. During a switch-over time service is disabled. For the control of this model three optimization criteria are considered: the average number of jobs in the buffer, the fraction of lost jobs and the fraction of batches not fully accepted. Using Markov decision theory, the optimal switching policy can be determined for any of these criteria by the value-iteration algorithm. In the calculation of the expected one-step costs and the transition probabilities an essential role is played by the discrete Fast Fourier Transform.