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In the paper we propose a way of solving the problem of allocating capacity of virtual paths to the links of an ATM network. We propose an effective stochastic method, called Simulated Allocation, which is able to find almost optimal allocation patterns in a short computation time. The method is simple to implement and can be used to the whole class of multicommodity flow problems, including the one considered in the paper. We present numerical examples illustrating effectiveness of the method.

In the paper we investigate the methods of constructing the routing tree in WiMAX networks with mesh topology. The concept of network efficiency optimization by building the routing tree characterized by selected topological properties that are independent on network load is presented. As an important partial result, correlations between topological parameters of the tree and network efficiency have been estimated. The parameters exhibiting the strongest correlations allow creation of well performing routing trees by optimizing the tree topology only. In order to estimate the network performance under load a fast, modular WiMAX network simulator has been created. Keywords-IEEE802.16, Mesh Networks, WiMax, Multi-hop Routing, Mesh Mode I. INTRODUCTION iMAX (Worldwide Interoperability for Microwave Access) is the radio technology based on the IEEE 802.16 standard [1], which allows broadband wireless access over long distance.WiMax networks can be deployed in two modes: point to multipoint (PMP) in which all subscriber stations (SS) communicate only with the base station (BS) connected directly to external network and mesh mode where direct communication between subscriber stations is allowed. In the case of a mesh network data is transmitted over a subset of potentially available links, forming the routing tree with BS as a root. If the routing tree is built correctly the mesh network could be more effective then PMP network, because of better use of transmission resources (more than one SS may transmit in the same time and in the same channel unless some interferences occur) and increased throughput of network links (resulting from using proxy SSs in transmissions) [2], [3], [4].The main purpose of this paper is to show the correlation between network efficiency and selected topological parameters of the routing tree. It would allow increasing the network throughput by building the routing tree characterized by selected topological properties that are independent on network load. The results would be also useful for improving the routing tree construction algorithms based on various heuristic approaches.

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