In wireless networks, it is still a challenge to allocate the limited resources among users to meet their specific quality of service (QoS) requirements, especially when the users have different traffic types, i.e., the hard QoS traffic, the best effort traffic, and the soft QoS traffic. In this paper, we develop the utility-based resource allocation algorithms in the following three tasks: 1) resource allocation among the hard QoS traffic and the soft QoS traffic; 2) resource allocation among the best effort traffic and the soft QoS traffic; and 3) finally resource allocation among the hard QoS traffic, the best effort traffic, and the soft QoS traffic, by solving the network utility maximization problem using the Karush-Kuhn-Tucker condition. We develop a number of critical theorems to give the conditions that find the optimal solutions for the above three cases in a unified framework. These theorems then act as design guidelines for the three algorithms. The proposed algorithms take into account the traffic type, the total available resources and the users' channel qualities. We evaluate the time complexity of the proposed algorithms, which comes out to be polynomial, and study the network performance by numerical examples. Numerical results demonstrate the bandwidth allocations, the fairness index and the total maximum utility under different channel qualities and resource situations.