We derive a revenue-maximizing scheme that charges customers who are homogeneous with respect to their waiting cost parameter for a random fee in order to become premium customers. This scheme incentivizes all customers to purchase priority, each at his/her drawn price. We also design a revenue-maximizing scheme for the case where customers are heterogeneous with respect to their waiting cost parameter. Now lower cost parameter customers are encouraged to join the premium class at a low price: Given that, those with high cost parameter would be willing to pay even more for this privilege.

中文翻译：

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一种队列优先级计费优化机制

我们推导出一种收入最大化方案，该方案向在等待成本参数方面同质的客户收取随机费用，以便成为优质客户。该计划鼓励所有客户优先购买，每个客户都以他/她的抽奖价格购买。我们还为客户在等待成本参数方面具有异质性的情况设计了收入最大化方案。现在鼓励较低成本参数的客户以低价加入高级课程：鉴于此，那些具有高成本参数的客户愿意为此特权支付更多费用。