Newsvendor model of capacity sharing

Abstract

Capacity sharing in the form of roaming agreements have long been a fixture of cellular service. Historically, the main driver behind roaming agreements is to extend the coverage of a wireless carrier’s network into regions where that carrier has no infrastructure, thus making the service more attractive to customers who “roam” into a new region. Here we focus on a different form of capacity sharing, namely acquiring “overflow” capacity from another provider during periods of high demand. Such sharing may provide carriers with an attractive means to better meet their rapidly increasing bandwidth demands. On the other hand, the presence of such a sharing agreement could encourage providers to under-invest in their networks, resulting in poorer performance. We consider a stylized model of such a situation to gain insight into these trade-offs. Specifically, we adapt the newsvendor model from operation management [8] to this situation. The newsvendor model applies to a single firm that is determining how much inventory to stock in the face of uncertain demand. Here, we consider two wireless carriers, who are determining how much capacity to invest in, also in the face of uncertain demand. Without any capacity sharing, this reduces to the standard newsvendor model for each carrier. However, with sharing, the carriers’s investment decisions become coupled since the revenue one carrier earns form sharing capacity with another depends on the other’s capacity investment. We model this interaction as a game and give conditions for when the game has a unique pure strategy Nash equilibrium. Our analysis applies for two different sharing models one in which a carrier first serves its own customers before allocating an excess capacity to the other provider’s customers and one in which carriers do not discriminate between their own traffic and the other carrier’s. Numerical comparisons of the resulting equilibria are also given for different demand distributions. In terms of related work, there has been a line of literature studying how carriers set prices in roaming agreements (see e.g. [4]). Much of this work focuses on a known demand and