Wireless Ad Hoc and Sensor Networks

Predictive Congestion Control for Wireless Sensor Networks 447the packet weight at each hop. However, this algorithm is necessary in adynamic wireless networking environment.Dynamic weight adaptation given in Equation 9.33 is utilized in theADFS scheme. ADFS follows the weighted fairness criterion defined inEquation 9.1. The initial weights are selected by using the user-definedQoS criteria. Then, the packet weights are dynamically adapted withnetwork state defined as a function of delay experienced, number ofpackets in the queue, and the previous weight of the packet. In fact,analytical results are included in Chapter 7 to demonstrate the throughputand end-to-end delay bounds in contrast with the existing literature. TheNS simulation results indicate that the proposed scheme renders a fairprotocol for WSN even in the presence of congestion due to fading channels.The weights are updated as follows.9.3.3.1 Dynamic Weight AdaptationTo account for the changing traffic and channel conditions that affect thefairness and end-to-end delay, the weights for the flows are updateddynamically asϕˆ ( k+ 1) = ξϕˆ ( k ) + ςEij ij ij(9.33)where ϕˆ ij ( k)is the actual weight for the ith flow, jth packet at time k ,ξ and ς are design constants, {x, z} ∈ [−1,1], and E ij is defined asEij = ebi +1 eij, delay where e bi is the error between the expected length of thequeue and the actual size of the queue and e ij,delay is the error between theexpected delay and the delay experienced by the packet so far.According to E ij , when queues build up, the packet weights will beincreased to clear the backlog. Similarly, with large end-to-end delays,the packet weights will be assigned high, so that the nodes can servicethese packets sooner. Note that the value of E ij is bounded because offinite queue length and delay, as packets experiencing delay greater thanthe delay error limit will be dropped. The updated weights are utilizedto schedule packets. Then, the packet to be transmitted is sent to the MAClayer, where the backoff interval scheme is implemented. Next, the proposedbackoff selection algorithm is presented, followed by the convergenceof the backoff interval selection scheme and the fairness andthroughput guarantee of the scheduling scheme.9.3.3.2 Fairness and Throughput GuaranteeTo prove that the dynamic weight adaptation is fair, we need to show abound on | Wf( t1, t2)/ φf − Wm( t1, t2)/ φm|for a sufficiently long interval [ t1, t2]in which both flows, f and m,are backlogged. Next, three theorems are