There are two types of market mechanism that can be used to allocate network resources effciently based on users' preference. One, mainly considered in previous works, is the Tatonnement process; the allocation is not changed until the price reaches equilibrium. When the user preference changes dynamically, the resource allocation derived by the Tatonnement process may not reflect the curent preference. The other is the Non-Tatonnement process, where the allocation is chan-ged dynamically even while the allocation is being calculated. Conse-quently, it suits resource allocation in dynamic environments. However, the property of this process in terms of the time needed to complete all calculations has not been studied suffciently. As a first step,this paper compares the quality of the results derived by the Non-Tatonnement process to that by the Tatonnement process for dynamic network resource allocation.We find that the Non-Tatonnement process works better in rapidly changing environments and that the Tatonnement process offers superior results when there is enough time for the market to converge to equilibrium.