Service provider competition: Delay cost structure, segmentation, and cost advantage

We model competition between two providers who serve delay-sensitive customers. We compare a generalized delay cost structure, where a customer's delay cost depends on her service valuation, with the traditional additive delay cost structure, where the delay cost is independent of the customer's service valuation. Under the additive delay cost structure, service providers offer different prices and expected delays, but customers are indifferent between the providers. Under the generalized delay cost structure, when the providers have different capacity or operating costs, we obtain value-based market segmentation, whereby higher-value customers choose one provider and lower-value customers choose the other. We study how the delay cost parameters, the market size, and the service providers' costs affect the structure of the equilibrium.