Optimal price and delay differentiation in large-scale queuing systems

摘要

Price discrimination based on the speed at which a service is delivered, such as parcel delivery, is a prevalent business practice. A debate is ongoing to apply the same for internet service providers. The question is whether an essentially identical service should provide varying quality levels based on delay and segments the market in a way that enables the firm to provide faster processing for impatient customers and shift system congestion to more patient customers. The study explores this service differentiation problem in the context of a large-scale stochastic service system that is prone to congestion as a result of queuing. A model is presented that considers a monopolistic revenue-maximizing firm that offers a single service to a market of heterogeneous price-and delay-sensitive customers. The system is modelled as a multi-server queue and may have multiple service classes that are differentiated in terms of price and delay. The market is composed of distinct customer segments or types. All customers of a particular type have the same linear delay sensitivity and a random service valuation, or willingness to pay, drawn from a common distribution. The study proposes a deterministic relaxation of the revenue maximization problem and shows that its solution yields an intuitive price-delay menu and suggests a simple priority sequencing rule. This translates to a solution in the stochastic setting that achieves near-optimal revenue performance in large scale systems. The framework is applied to two customer types to show that it easily extends to multiple customer segments. The results show that first-order features of the stochastic solution can be immediately determined from the solution to the deterministic relaxation. It was also found that in systems with two service classes, strategic delay is a first-order effect when there is ample capacity, but second-order effect when there is not, including settings for which the service provider decides to set capacity at a level that avoids permanently idle servers. In systems in which it is optimal to offer three or more service classes, strategic delay is always a first-order consideration.