Time-Dependent Network Pricing and Bandwidth Trading

The usage of a network usually differs significantly at different times of a day, due to users' time-preference. This phenomenon is also prominent in the market of "bandwidth- on-demand", since the demand is typically higher during large events. Thus, an unselfish "social planner" should deploy a proper pricing scheme to reduce congestions and achieve efficient use of the network (i.e., maximize the "social welfare"); whereas a selfish service provider (SP) can exploit the time-preference to increase its revenue. In this paper, we present a model to study the important role of time-preference in network pricing. In this model, each user chooses his access time based on his preference, the congestion level, and the price he would be charged. Without pricing, the "price of anarchy" (POA) can be arbitrarily bad. We then derive a simple pricing scheme to maximize the social welfare. Next, from the SP's viewpoint, we consider the revenue- maximizing pricing strategy and its effect on the social welfare. We show that if the SP can differentiate its prices over different users and times, the maximal revenue can be achieved, as well as the maximal social welfare. However, if the SP has insufficient information about the users and can only differentiate its prices over the access times, then the resulting social welfare can be much less than the optimum, especially when there are many low-utility users. Otherwise, the difference is bounded and less significant.