Optimization of an M/M/∞ Queueing System with Free Experience Service

Abstract

It is a common practice for online service providers to offer free experience service to attract new clients. However, providing experience service requires resources, which may negatively impact current service level and lead to customer turnover. Therefore, providers need to trade off between consequent benefits and costs. We consider a free experience service system where each arriving customer can start his service immediately without waiting, which is a typical situation of many online service platforms. A queueing model with infinite number of servers is employed to study such a service system. The closed forms of the expected numbers of informed and uninformed customers in steady-state are derived by solving nonhomogeneous linear partial differential equations. After that, the expected profit of the service provider is generated and maximized by determining the optimal price and service rates. Our numerical results suggest that with the increase of the market share and the serving cost for the informed customers, the service provider should lay more emphasis on offering the regular service for the informed customers.