A two-sided matching system is considered, where servers are assumed to arrive at a fixed rate, while the arrival rate of customers is modulated via a price-control mechanism. We analyse a loss model, wherein customers who are not served immediately upon arrival get blocked, as well as a queueing model, wherein customers wait in a queue until they receive service. The objective is to maximize the platform profit generated from matching servers and customers, subject to quality of service constraints, such as the expected wait time of servers in the loss system model, and the stability of the customer queue in the queuing model. For the loss system, subject to a certain relaxation, we show that the optimal policy has a bang-bang structure. We also derive approximation guarantees for simple pricing policies. For the queueing system, we propose a simple bi-modal matching strategy and show that it achieves near optimal profit.

翻译：考虑一种双向匹配系统,假设服务器可以达到固定费率,而客户的到达率则通过价格控制机制加以调节。我们分析一种损失模式,即没有在抵达后立即服务的客户被堵住,以及一种排队模式,即客户在得到服务之前排队等候。目的是尽量扩大平台从匹配服务器和客户中获得的利润,但须视服务质量的限制而定,例如损失系统模型中服务器的预期等待时间以及排队模式中客户排队的稳定性。对于损失系统,只要有一定的放松,我们就显示最佳政策有一个爆炸式结构。我们还为简单的定价政策提供近似保证。对于排队系统,我们提出一个简单的双模式匹配战略,并表明它几乎能达到最佳利润。