Wireless Ad Hoc and Sensor Networks

112 Wireless Ad Hoc and Sensor Networksan end-to-end feedback control scheme can be used. For short-term congestion,providing sufficient buffers in the switches is the best solution.Motivation of the end-to-end protocol is that they place the complexfunctionalities in the hosts and not inside the network and, hence, the hoststypically upgrade the software to receive a better service. The second reasonis that by keeping the network simple, it can scale more easily. Throughoutthis chapter, we define the ingress and egress nodes/routers as end hosts.These hosts possess finite buffers and they are connected to the networkvia physical links of finite bandwidth. Depending upon the type of source,we use the feedback accordingly to meet the fairness criteria. For instance,the feedback can be used to alter the source rate or compression ratios/quantization parameters of the codec (Lakshman et al., 1999) and/or todynamically route the packets. The process of selecting the best option isnot dealt with in this paper and will be proposed in the future.The most important step in preventing congestion is to estimate thenetwork traffic via network modeling. Modeling a high-speed network,in general, is quite complex as it involves different time scales (packetlevelcongestion control, source level admission control, error control) inthe networking layers, and the control schemes involve both discrete eventand discrete/continuous dynamics. In this chapter, the congestion controlis accomplished via buffer dynamics modeling in discrete time.Consider the buffer dynamics of a pair of ingress/egress node pairsconnected to a network and characterized as distributed discrete timenonlinear systems to be controlled, given in the following form:xk ( + 1) = Sat ( f( x( k)) + Tu( k) + d( k)).p(3.37)nxk ( )∈R is a state variable for n buffers, which is the buffer occupancynat time instant k, uk ( )∈R a control signal, which is the regulated trafficrate, and T is the measurement interval. The function, f (), ⋅ represents theactual packet accumulation at the network router/node, which is furtherdefined as f() ⋅= [ x( k) + q( k) + ( Ini( k) −Sr( k)) T],where I ( k ) is the packetniarrival rate at the ingress node from n sources, qk ( ) is the bottleneck queuelevel, this value is estimated by ( Ini( k) − Ir( k)) T,Ir( k)is the arrival rate atthe egress/destination node, Sr( k)is the service rate at the egress node,and Sat p()⋅ is the saturation function. The unknown disturbance vector,dk ( ) ∈R , which can be an unexpected traffic burst/load or a networknfault, is assumed to be bounded by a constant, |( dk)| ≤ d M .Given a desired buffer size at the destination x d , define the performancein terms of buffer occupancy errorek ( ) = xk ( ) −xd(3.38)