关于动态优先排队的一个猜想及服务质量敏感市场的纳什均衡
On a Conjecture for Dynamic Priority Queues and Nash Equilibrium for Quality of Service Sensitive Markets
摘要：
许多经济交易，包括在线市场的交易，在交易的开始和结束时间之间具有时滞。客户需要等待完成他们的交易（订单履行），因此也对他们的等待时间作为服务质量（QoS）属性感兴趣。因此，他们在向公司（服务提供商）提供的需求中考虑此QoS，并且一些客户（用户集）愿意为更短的等待时间付费。另一方面，这样的等待时间取决于需求用户设置提供给服务提供者。我们模型的服务提供商和用户集之间的经济QoS战略互动的一个相当通用的调度框架下，作为一个非合作的约束对策。我们使用现有的联合定价和调度模型。在一个猜想的约束下，通过有限步算法保证了该联合定价和调度问题的最优解。我们首先解决这个猜想的排队和优化参数的基础上，并讨论其对上述游戏的影响。我们表明，一个连续的纳什均衡（NE）的存在，它可以很容易地使用约束最佳响应动态计算。通过上述有限步算法确定收益最大NE。我们说明了双方如何通过确定合适的运营决策，即，通过选择一个适当的游戏沿着定价和收入管理的主题。
英文摘要：
Many economic transactions, including those of online markets, have a time lag between the start and end times of transactions. Customers need to wait for completion of their transaction (order fulfillment) and hence are also interested in their waiting time as a Quality of Service (QoS) attribute. So, they factor this QoS in the demand they offer to the firm (service-provider) and some customers (user-set) would be willing to pay for shorter waiting times. On the other hand, such waiting times depend on the demand user-set offers to the service-provider. We model the above economic-QoS strategic interaction between service-provider and user-set under a fairly generic scheduling framework as a non-cooperative constrained game. We use an existing joint pricing and scheduling model. An optimal solution to this joint pricing and scheduling problem was guaranteed by a finite step algorithm subject to a conjecture. We first settle this conjecture based on queuing and optimization arguments and discuss its implications on the above game. We show that a continuum of Nash equilibria (NE) exists and it can be computed easily using constrained best response dynamics. Revenue maximal NE is identified by above finite step algorithm. We illustrate how both players can benefit at such revenue maximal NE by identifying suitable operational decisions, i.e., by choosing an appropriate game along the theme of pricing and revenue management.
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