Abstract
Abstract In this article, we consider the network utility maximization (NUM) problem for the random access network with multiclass traffic. The utilities associated with the users are not only concave, but also nonconcave functions. Consequently, the random access NUM problem becomes more difficult to solve. Based on the successive approximation method, we propose an algorithm that jointly controls the rate and the persistent probability of the users. The proposed algorithm converges to a suboptimal solution to the original problem which also satisfies the Karush–Kuhn–Tucker conditions. We also generalize the framework so that a broader choice of utility functions can be applied.
Highlights
The network utility maximization (NUM) for the random access wireless networks is thoroughly studied in the literature, e.g., [1-3]
The analysis frameworks in [1-3] cannot be applied in the case of multiclass traffic and it is very difficult to address the nonconvexity of the problem
We address the random access NUM for multiclass traffic using the successive approximation method
Summary
The network utility maximization (NUM) for the random access wireless networks is thoroughly studied in the literature, e.g., [1-3]. The inelastic traffic from the real-time applications does not have the strictly concave form anymore They are usually modeled by sigmoidal utilities, which are convex at the lower region and concave at the higher region as depicted in Figure 1 [4]. The analysis frameworks in [1-3] cannot be applied in the case of multiclass traffic and it is very difficult to address the nonconvexity of the problem. The authors utilize the standard dual-based algorithm to allocate the rate This algorithm does not result to an optimal solution because of the nonconvexity of the primal problem. We address the random access NUM for multiclass traffic using the successive approximation method. Similar to our previous work [14] which jointly controls the rate and power in a multi-hop wireless network with multiclass traffic, the nonconcave objective of the problem is approximated to a concave function.
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