LITERATURE REVIEW
2.4 Distributed Channel Assignment Schemes
2.4.1 Weighted Coloring Scheme
Mishra et al. modeled the channel assignment as a weighted variant of the graph colouring problem in [57]. The weights assigned to each pair of APs reflect the relative importance of assigning different channels for them. The weights are set according to interference information reported from the client nodes associated with each AP since the clients have an extended view of the network.
Similar to the graph formulation earlier, a graph G = ( V,E) corresponding to the network is defined. The set of vertices, V = {ap1, ap2, ... , ap0 } represents n APs that form the network. The weighted graph colouring problem can be stated as follows: A
channel assignment, fc(api), ap; E V is a function fc: V( G)~ C that assigns channels from C, the set of non-overlapping channels, to every AP such that an objective function is optimized.
A weight function defined on G, Wr (ap;, GPj) denotes the normalized weight on the edge (ap;,apj). The weight is proportional to the number of clients associated with the two corresponding APs that are affected if they are assigned the same channel. An interference factor (I-factor), denoted by I(ap;,apj) is assigned to each edge to represent the interference between the channels assigned to both APs. For non-overlapping channels, the I-factor is defined as follows: I(ap;,apj) = 1 if ap; and apj are on the same channel and I(ap;,apj) = 0 otherwise. Subsequently, the product Wr (ap;,apj) x l(ap;,apj) is defined as the I-value. The 1-value represents the total effect of interference on all clients that are located within the overlapping region between the two APs.
Therefore, given G and Wr, the weighted coloring (Hminmax) scheme finds the channel assignment that minimizes the maximum 1-value of each AP:
(2.4.1)
In other words, for each AP, Hminmax assigns channel d that minimizes the maximum impact of interference among all overlap regions between ap; and all other APs. The Hminmax scheme is executed at each AP in a distributed manner and is given as follows [57].
Algorithm 5: Hminmax Scheme
3: dmin Eo- argminhmax(d)
deC
Initially, all APs are assigned the same channel (a random channel assignment can also be used). Next, each AP ap; determines the maximum !-value, hmax(d) on any edge that connects a neighbour AP that is using channel d. The channel dmin is the channel that gives the minimum maximum I-vaiue across all channels. Finally, ap; is assigned the channel dmin that minimizes interference on its maximum edge.
In order to construct the local graph, which consists of the AP and its neighbouring APs, the following method has been proposed. During periods of low activity, an AP ap;
can randomly request its client to perform a passive scan of each channel. During this scan, packets are captured from neighbouring APs and their clients. Thus, an edge is created between ap; and for every ap1 that is contained in the scans performed. The weights of an edge can then be determined as follows. Let Nscanapi be the number of scans performed by clients of ap; and let Nscanap;(ap1) be the number of scans performed by clients of ap; that reported interference with ap1. Hence, the weight on the edge (ap;, ap1) is given by
(2.4.2)
Simulations and field trial results have shown the superior performance of the Hminmax scheme.
However, the method of determining the weights assigned to edges may present some inaccuracies. Firstly, in periods of congestions, all clients may be backlogged with packets to send and are therefore not available to perform scans. Secondly, for similar reasons, clients with a lower load may end up performing more scans than clients with higher loads. Subsequently, the weights assigned will mostly be reflective of the interference encountered by clients that have low traffic only. This is opposed to what is desired, where higher representation in the weights should be given to clients with higher loads. Finally, APs' measurements are not taken into account. Note that the AP is either the destination or the source of all transmissions. Therefore, if an AP suffers high interference, its opportunity to access the medium will be severely limited while packets received from clients will suffer a high probability of collisions.
Furthermore, the most important performance metric, which is the throughput of the Hminmax scheme, is not shown. The only performance metrics used are the maximum
!-value of all edges, the summation of !-value of all edges and the number of edges with nonzero I-values. The authors have argued that a higher I-value on an edge corresponds to lower throughput and performed a simple two APs simulation to support their claim.
However, the generalization of this assertion to the complex interactions of a network of APs is highly uncertain. Due to this reason, whether the performance metrics shown can be taken as a good representation of throughput remains doubtful. In fact, our work on the impact of interference on throughput in Section 5.1 has shown that there are many instances where higher throughputs are obtained for cases corresponding to higher
!-value. In view of this and also because it is one of the more popular works, the
Hminmax scheme has been implemented and its performance evaluation and comparison shown in Section 4.4.