Duopoly competition in time-dependent pricing for improving revenue of network service providers

Due to network users' different time-preference, network traffic load usually significantly differs at different time. In traffic peak time, network congestion may happen, which make the quality of service for network users deteriorate. There are essentially two ways to improve the quality of services in this case: (1) Network service providers (NSPs) overprovision network capacity by investment; (2) NSPs use time-dependent pricing (TDP) to reduce the traffic at traffic peak time. However, overprovisioning network capacity can be costly. Therefore, some researchers have proposed TDP to control congestion as well as improve the revenue of NSP. But to the best of our knowledge, all of the literature related timedependent pricing scheme only consider the monopoly NSP case. In this paper, a duopoly NSP case is studied. The NSPs try to maximize their overall revenue by setting time-dependent price, while users choose NSP by considering their own preference, congestion status in the networks and the price set by the NSPs. Analytical and experimental results show that the TDP benefits the NSPs, but the revenue improvement is limited due to the competition effect.