We consider optimal pricing for a two-station tandem queueing system with finite buffers, communication blocking, and price-sensitive customers whose arrivals form a homogeneous Poisson process. The service provider quotes prices to incoming customers using either a static or dynamic pricing scheme. There may also be a holding cost for each customer in the system. The objective is to maximize either the discounted profit over an infinite planning horizon or the long-run average profit of the provider. We show that there exists an optimal dynamic policy that exhibits a monotone structure, in which the quoted price is non-decreasing in the queue length at either station and is non-increasing if a customer moves from station 1 to 2, for both the discounted and long-run average problems under certain conditions on the holding costs. We then focus on the long-run average problem and show that the optimal static policy performs as well as the optimal dynamic policy when the buffer size at station 1 becomes large, there are no holding costs, and the arrival rate is either small or large. We learn from numerical results that for systems with small arrival rates and no holding cost, the optimal static policy produces a gain quite close to the optimal gain even when the buffer at station 1 is small. On the other hand, for systems with arrival rates that are not small, there are cases where the optimal dynamic policy performs much better than the optimal static policy.

中文翻译：

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具有有限缓冲区的串联队列的最优定价

我们考虑具有有限缓冲区、通信阻塞和价格敏感客户的两站串联排队系统的最优定价，这些客户的到达形成同质泊松过程。服务提供商使用静态或动态定价方案向新客户报价。系统中的每个客户也可能存在持有成本。目标是最大化无限规划范围内的折扣利润或提供商的长期平均利润。我们表明存在一个最优的动态策略，它表现出单调结构，其中报价在任一站点的队列长度中都没有减少，并且如果客户从站点 1 移动到站点 2，则报价不增加。持有成本在一定条件下的长期平均问题。然后我们关注长期平均问题，并表明当站 1 的缓冲区大小变大、没有持有成本、到达率或小或大时，最优静态策略的性能与最优动态策略一样好. 我们从数值结果中了解到，对于到达率小且没有保持成本的系统，即使在站 1 的缓冲区很小时，最优静态策略也会产生非常接近最优增益的增益。另一方面，对于到达率不小的系统，存在最优动态策略比最优静态策略表现更好的情况。到达率或大或小。我们从数值结果中了解到，对于到达率小且没有保持成本的系统，即使在站 1 的缓冲区很小时，最优静态策略也会产生非常接近最优增益的增益。另一方面，对于到达率不小的系统，存在最优动态策略比最优静态策略表现更好的情况。到达率或大或小。我们从数值结果中了解到，对于到达率小且没有保持成本的系统，即使在站 1 的缓冲区很小时，最优静态策略也会产生非常接近最优增益的增益。另一方面，对于到达率不小的系统，存在最优动态策略比最优静态策略表现更好的情况。