This paper considers an unobservable two-site tandem queueing system attended by an alternating server. We study the strategic customer behaviour under two threshold-based operating policies, applied by a profit-maximizing server, while customers’ strategic behaviour and server’s switching costs are taken into account. Under the Exact-N policy, in each cycle the server first completes service of N customers in the first stage ( $$Q_1$$ ), then switches to the second stage ( $$Q_2$$ ) and then serves those N customers before switching back to $$Q_1$$ to start a new cycle. This policy leads to a mixture of Follow-the-Crowd and Avoid-the-Crowd customer behaviour. In contrast, under the N-Limited policy, the server switches from $$Q_1$$ to $$Q_2$$ also when the first queue is emptied, making this regime work-conserving and leading only to Avoid-the-Crowd behaviour. Performance measures are obtained using matrix geometric methods for both policies and any threshold N, while for sequential service ( $$N=1$$ ) explicit expressions are derived. It is shown that the system’s stability condition is independent of N, and of the switching policy. Optimal performances in equilibrium, under each of these switching policies, are analysed and compared through a numerical study.

中文翻译：

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具有交替服务器的串联队列中的策略行为

本文考虑了一个由交替服务器参与的不可观察的双站点串联排队系统。我们研究了在利润最大化服务器应用的两种基于阈值的操作策略下的战略客户行为，同时考虑了客户的战略行为和服务器的转换成本。在 Exact-N 策略下，在每个周期中，服务器首先完成第一阶段（ $$Q_1$$ ）对 N 个客户的服务，然后切换到第二阶段（ $$Q_2$$ ），然后为之前的那 N 个客户提供服务切换回 $$Q_1$$ 以开始新的循环。该政策导致“跟随人群”和“避开人群”客户行为的混合。相反，在 N-Limited 策略下，当第一个队列被清空时，服务器也会从 $$Q_1$$ 切换到 $$Q_2$$，使这种制度发挥作用，只会导致避免人群行为。对于策略和任何阈值 N，性能度量都是使用矩阵几何方法获得的，而对于顺序服务 ( $$N=1$$ )，则导出显式表达式。结果表明，系统的稳定性条件与 N 和切换策略无关。通过数值研究，分析和比较了每种切换策略下的最佳平衡性能。