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

我们考虑在两级串联排队系统中将服务器分配给两个服务阶段，此时客户可以从每个服务阶段放弃。新的工作岗位到达这两个车站。到达站 1 的作业可能会经历两个服务阶段，而到达站 2 的作业可能只经历一个服务阶段。产生阶段性持有和一次性放弃成本。开发了连续时间马尔可夫决策过程公式，以最大限度地减少贴现预期成本和长期平均成本。由于统一是不可能的，我们使用连续时间框架和样本路径参数来分析控制策略。我们的主要结果是优先级规则最适合单服务器模型的条件。然后，我们提出并评估在数值研究的两个阶段之间分配一台或多台服务器的阈值策略。当总拥塞超过一定数量时，这些策略会优先考虑一个服务阶段，然后“切换”到另一个阶段。结果提供了关于如何调整切换规则以显着降低特定输入参数的成本以及在服务期间不允许抢占或放弃且服务和放弃时间不是指数级的更一般的多服务器情况下的成本。