Thus, the average number of transmissions per active www.selleckchem.com/products/Gefitinib.html session is expressed asNT��=1ns��j=1nsNT(Tj).(4)Since more transmissions take longer time on scheduling frame, minimizing the number of transmissions helps to improve the network’s throughput. In a typical multicast/broadcast tree Tj, there are three kinds of nodes: source node sj, forwarding nodes set (FWDj), and leaf nodes set (LFj). For example, consider the multicast tree shown in Figure 1. Here, the number associated with each link represents the channel assigned to that link. All nodes of tree, except the source node, have one parent. The source node (e.g., node A), as the root of the tree, sends data toward its children. A forwarding node (e.g.

, nodes B, C, E, F, and I) acts as both parent and child node; as a child node, it receives data from its parent, while in the role of a parent node, it sends the traffic toward its children. A leaf node (e.g., nodes D, K, L, M, N, and P) only plays the role of a child and receives data from its parent. It is clear from Figure 1 that NTAj = NTBj = NTCj = NTEj = 1, while NTIj = NTFj = 2 (i.e., NT(Tj) = 8).Figure 1 A typical multicast routing tree.Since we assume the bandwidth-guaranteed trees with bandwidth requirement trsj, the created load by the jth session on the ith node can be generally formulated by the role of node and the number of its transmissions aslij={trsj(1+NTij)if??i��FWDj,trsj��NTijif??i=sj,trsjif??i��LFj,0if??i?Tj.(5)Here, we define the utilization of the ith mesh router, denoted by U(i), as follows:U(i)=l(i)C(i)=1C(i)��j=1nslij,(6)where U(i) indicates the percentage of the ith node’s capacity used for routing of ns multicast/broadcast sessions.

For this case, the average utilization of the nodes is defined asU��=1n��i=1nU(i),(7)where n is the total number of nodes in the network.On the other hand, due to the shared nature of the wireless medium, adjacent transmissions cannot occur simultaneously on the same channel. To formulate this issue, we use the channel utilization concept defined in [17] with minor modifications. For the described MCMR-WMN model, consider a fixed transmission rate of c0. Each MAC multicast transmission in the jth routing tree uses a time fraction of the scheduling frame that is equal to trsj/c0. By definition, the utilization of channel k observed by node y (Xyk) is the sum of the time fractions assigned to all nodes within the interference range of node y that are intended to transmit on channel k.

Thus, considering ns admitted multicast/broadcast sessions, the utilization of channel k observed by node y is formulated asXyk=��j=1ns??��i��intf(y)trsjc0qi,kj,(8)where intf(y) denotes the set of interfering nodes located within the interference range of node y. For this case, the channel capacity constraint is given ?y��V,???k��ch_list(y),(9)where ch_list(y) indicates the set of?byXyk��1, assigned channels Entinostat to the radios of node y.