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The cross-layer utility maximization problem, which is subject to stability constraints for a multicommodity wireless network where all links share the same number of orthogonal channels, is considered in this paper. We assume a time-slotted network, where the channel gains randomly change from one slot to another. The optimal cross-layer network control policy can be decomposed into the folloing three subproblems: 1) flow control; 2) next-hop routing and in -node scheduling; and 3) power and rate control, which is also known as resource allocation (RA). These subproblems span the layers from the physical layer to the transport layer. In every time slot, a network controller decides the amount of each commodity data admitted to the network layer, schedules different commodities over the network's links, and controls the power and rate allocated to every link in every channel. To fully exploit the available multichannel diversity, we consider the general case, where multiple links can be activated in the same channel during the same time slot, and the interference is controlled solely through power and rate control. Unfortunately, the RA subproblem is not yet amendable to a convex formulation, and in fact, it is NP-hard. The main contribution of this paper is to develop efficient RA algorithms for multicommodity multichannel wireless networks by applying complementary geometric programming and homotopy methods to analyze the quantitative impact of gains that can be achieved at the network layer in terms of end-to-end rates and network congestion by incorporating different RA algorithms. Although the global optimality of the solution cannot be guaranteed, the numerical results show that the proposed algorithms perform close to the (exponentially complex) optimal solution methods. Moreover, they efficiently exploit the available multichannel diversity, which provides significant gains at the network layer in terms of end-to-end rates and network congestion. In additio- - n, the assessment of the improvement in performance due to the use of multiuser detectors at the receivers is provided.