Scheduling servers in a two-stage queue with abandonments and costs

Abstract We consider the assignment of servers to two phases service in a two-stage tandem queueing system when customers can abandon from each stage service. New jobs arrive at both stations. Jobs arriving station 1 may go through and 2 only one phase Stage-dependent holding lump-sum abandonment costs are incurred. Continuous-time Markov decision process formulations developed that minimize discounted expected long-run average costs. Because uniformization is not possible, we use continuous-time framework sample path arguments analyze control policies. Our main results conditions under which priority rules optimal for single-server model. then propose evaluate threshold policies allocating or more between stages numerical study. These prioritize before “switching” other total congestion exceeds certain number. Results provide insight into how adjust switching rule significantly reduce specific input parameters as well general multi-server situations neither preemption abandonments allowed during times exponential.