Understanding Quota Dynamics in Wireless Networks

In designing new service plans, network service providers need to understand how consumption of voice or data service changes in response to pricing signals. It is difficult to acquire such information from customer usage data because voice minutes and data bandwidth are typically sold in the form of large quotas. We address this issue by studying how end users consume their quotas, both in a prepaid setting (where users pay in advance and refill as needed) and a postpaid setting (where users pay each month for a fixed amount of quota). Our presentation has three main parts. In the first we present data on quota usage for prepaid voice/text services and show that users reduce their voice usage when their balances become low. Moreover, when balances are low there is a tendency to shift from voice to SMS. In the second part, we provide descriptive models of both prepaid and postpaid services. The main feature of these models is that there is a background level of potential demand and the rate at which this potential demand is realized depends on the amount of quota balance available. In the third part, we propose utility-maximizing models that can account for this type of behavior. In the prepaid case the main feature of the model is a discount function that represents the perceived cost to the user of a quota refill that will occur sometime in the future. In the postpaid case, where the end user is attempting to get the maximum amount of utility from their monthly quota, we present a dynamic programming formulation in which utility functions are time-varying and are not known to the user in advance.