In Cognitive Radio (CR) networks, one of the well-known challenges is the opportunistic utilization of the available spectrum, which should be performed by avoiding the interference with the Primary Users (PUs). There exists several works to deal with this PU interference avoidance problem for single PU type. However, with the increased traffic heterogeneity of the wireless PU profiles, this challenge of PU interference avoidance is to be also considered for heterogeneous traffics. Taking this into account, in this paper, we propose an optimal spectrum utilization mechanism for CR networks under different PU types. More specifically, the PUs are classified into four different types according to their spectrum occupancy. Moreover, the optimization of the spectrum utility is done by defining the entire CR system as a Priced Timed Automata (PTA) model. The proposed PTA-based mechanism is evaluated for different number of users. Using the evaluations, the optimum CR spectrum utilizations are analyzed by sweeping the number of CR users.