Service Competition with General Queueing Facilities

In many service industries, companies compete with each other on the basis of the waiting time their customers experience, along with the price they charge for their service. A firm's waiting-time standard may either be defined in terms of the expected value or a given, for example 95%, percentile of the steady state waiting-time distribution. We investigate how a service industry's competitive behavior depends on the characteristics of the service providers' queueing systems. We provide a unifying approach to investigate various standard single-stage systems covering the spectrum from M/M/1 to general G/GI/s systems, along with open Jackson networks to represent multistage service systems. Assuming that the capacity cost is proportional with the service rates, we refer to its dependence on (i) the firm's demand rate, and (ii) the waiting-time standard as the capacity cost function. We show that across the above broad spectrum of queueing models, the capacity cost function belongs to a specific four-parameter class of function, either exactly or as a close approximation. We then characterize how this capacity cost function impacts the equilibrium behavior in the industry. We give separate treatments to the case where the firms compete in terms of (i) prices (only), (ii) their service level or waiting-time standard (only), and (iii) simultaneously in terms of both prices and service levels. The firms' demand rates are given by a general system of equations of the prices and waiting-time standards in the industry.