The Value of Dynamic Pricing in Large Queueing Systems

Abstract

We study the value of dynamic pricing to maximize revenues in queueing systems with price and delay sensitive customers. The system queue length is visible so that upon arrival, customers decide to join the system based on the congestion and the price at that time. We analyze this problem in the typical asymptotic regime of large customer market size and capacity. We find that dynamic pricing performs significantly better than static pricing at mitigating the effect of uncertainty. Asymptotically, the revenue in such systems consists of a positive deterministic component and a negative stochastic component; the latter representing the impact of variability.Static pricing leads to the typical √n-scale effect of variability, i.e., the expected steady-state queue-length is K√n for some K > 0, where n represents the system size. However, dynamic pricing can lower this effect of variability to the n^1/3-scale. We further show that a simple policy of using only two prices can achieve most of the benefits of dynamic pricing. We also discuss how our results can apply to other dynamic control problems in queueing systems.

Keywords: Revenue management, dynamic pricing, queueing, asymptotic analysis, diffusion analysis