Algorithmic analysis of a two‐class multi‐server heterogeneous queueing system with a controllable cross‐connectivity

We analyse algorithmic the queueing system with two paral- lel queues supplied with two heterogeneous group of servers. We assume a controllable cross-connectivity of queues with certain class of customers to different groups of servers. The system is analyzed in steady state. For a given cost structure we formulate the Markov decision problem for an optimal allocation of servers between the queues to minimize the long-run average cost per unit of time. The corresponding dynamic programming equations are derived. We develop algorithms to evaluate different per- formance measures including the mean busy period, the mean number of customers served in a busy period as well as the maximal queue length in a busy period. Some illustrative numerical examples are discussed.