Abstract

We study the optimal pricing problem for a tandem queueing system with an arbitrary number of stations, finite buffers, and blocking. The problem is formulated using a Markov decision process model with the objective to maximize the long-run expected time-average revenue or gain of the service provider. Our interest lies in comparing the performances of static and dynamic pricing policies in maximizing the gain. We show that the optimal static pricing policies perform as well as the optimal dynamic pricing policies when the buffer size at station 1 becomes large and the arrival rate is either small or large. More importantly, we propose two specific static pricing policies for systems with small and large arrival rates, respectively, and show that each proposed policy produces a gain converging to the optimal gain with an approximately exponential rate as the buffer size before station 1 becomes large. We learn from numerical results that the proposed static policies perform as well as optimal dynamic policies even for a moderate-sized buffer at station 1. We also learn that there exist cases where optimal static pricing policies are, however, neither optimal nor near-optimal.

摘要

我们研究了具有任意数量的工作站，有限缓冲区和阻塞的串联排队系统的最优定价问题。该问题是使用Markov决策过程模型制定的，其目标是最大化服务提供商的长期预期时间平均收入或收益。我们的兴趣在于比较静态定价策略和动态定价策略在最大化收益方面的表现。我们表明，当站点1的缓冲区大小变大且到达率变小或变大时，最优静态定价策略与最优动态定价策略一样有效。更重要的是，我们针对到达率较小和较大的系统分别提出了两种特定的静态定价策略，并表明，随着站点1之前的缓冲区大小变大，每种提议的策略都将产生以近似指数速率收敛到最佳增益的增益。我们从数值结果中了解到，即使对于站点1的中等大小的缓冲区，建议的静态策略也具有最佳动态策略的性能。我们还了解到，存在某些情况下，最佳静态定价策略既不是最优也不是近乎最优的。