This paper studies using price incentives to shift bandwidth demand from peak to non-peak periods. In particular, cost discounts decrease as peak monthly usage increases. We take into account the delay sensitivity of different apps: during peak hours, the usage of hard real-time applications (HRAS) is not counted in the user's monthly data cap, while the usage of other applications (OAS) is counted in the user's monthly data cap. As a result, users may voluntarily delay or abandon OAS in order to get a higher fee discount. Then, a new data rate control algorithm is proposed. The algorithm allocates the data rate according to the priority of the source, which is determined by two factors: (I) the allocated data rate; and (II) the waiting time.