We model competition between two firms selling identical goods to customers who arrive in the market stochastically. Shoppers choose where to purchase based upon both price and the time cost associated with waiting for service. One seller provides two separate queues, each with its own server, while the other seller has a single queue and server. We explore the market impact of the multi-server seller engaging in waiting cost-based-price discrimination by charging a premium for express checkout. Specifically, we analyze this situation computationally and through the use of controlled laboratory experiments. We find that this form of price discrimination is harmful to sellers and beneficial to consumers. When the two-queue seller offers express checkout for impatient customers, the single queue seller focuses on the patient shoppers thereby driving down prices and profits while increasing consumer surplus.