We present a model of market competition in which customer preferences are over not only price and quality but also delivery speed. This allows a study of market demand and firms' decisions on price, quality, technology and responsiveness in a competitive environment. When demand arises, a customer chooses the firm that maximizes its expected utility of price, quality and response time. The demand function for each firm is derived by analyzing a queueing system with competing servers. We then study price competition among firms with differentiated processing rates. In the equilibrium, the firm with a higher processing rate always enjoys a price premium, and, further, enjoys a larger market share when its opponent also has adequate processing rate to serve all the customers alone.two-server queues, time-sensitive customers, pricing, delivery-time competition, Nash equilibrium

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