Network traffic load usually differs significantly at different times of a day due to users' different time preference. Network congestion may happen in traffic peak times. In order to prevent this from happening, network service providers (NSPs) can either over-provision capacity for demand at peak times of the day, or use dynamic time-dependent pricing (TDP) scheme to reduce the demand at traffic peak times. Since over-provisioning network capacity is costly, many researchers have proposed TDP schemes to control congestion as well as to improve the revenue of NSPs. To the best of our knowledge, all these studies consider only the monopoly NSP case. In our previous work, the duopoly and oligopoly NSP cases have been studied. NSPs try to maximize their overall revenue by setting time-dependent prices, while users choose NSPs by considering their own time preference, congestion statuses in the networks and the prices set by the NSPs. One assumption that has been made is that Quality of Service (QoS) function of each NSP is linear, which means that the level of QoS degradation is proportional to the number of users in the network. However, in reality, the level of QoS may degrade rapidly after a certain point, which is not reflected through linear QoS functions. Therefore, concave QoS function is a better choice. In this paper, the case of concave QoS function is considered. TDP is evaluated under different QoS functions. The results shows that TDP is also effective under concave QoS functions.