Wireless Ad Hoc and Sensor Networks

Predictive Congestion Control for Wireless Sensor Networks 441goal is to select the backoff interval, BO i , at the ith transmitting node suchthat the actual throughput meets the desired outgoing rate fi( k). To simplifycalculations, we consider the inverse of the backoff interval, whichis denoted as VRi= 1 BOi, where VR i is the virtual rate at the ith nodeand BO i is the corresponding backoff interval. The fair scheduling algorithmschedules the packet transmissions according to the calculatednode’s backoff interval; the fair scheduling scheme is discussed in thenext subsection. The interval is counted down when a node does notdetect any transmission, and pauses otherwise. Consequently, a node willgain access to the channel proportional to its virtual rate and inverselyproportional to the sum of virtual rates of its neighbors. The actual rateof the ith node is a fraction of the channel bandwidth, Bt (), defined asR () t =B() t ⋅VR () t VR() t =B() t ⋅VR () t TVR () ti i l i il∈∑Si(9.11)where TVR i is the sum of all virtual rates for all neighbor nodes.Because the scheme considers only a single modulation scheme, thebandwidth, B, is assumed time-invariant until the backoff interval isselected. It is assumed that the total bandwidth is constant as long ascommunication is possible on a link (when the received power is abovea certain threshold). However, when severe fading occurs, the bandwidthwill drop to zero. In such a case, backoff intervals are set at a largevalue, lar, to prevent unnecessary transmissions when a suitable signalto-noiseratio (SNR) cannot be achieved at a destination node because ofpower constraints. Additionally, under normal circumstances, the algorithmpresented as follows is used to calculate the backoff interval BO i ,which is then randomized to minimize probability of collision on accessbetween nodes. Consequently, the MAC layer backoff timer BT i value isdefined as⎧ BOi⎪ρ ∗ ( k), for B( k)= 1BT i = ⎨⎩⎪ lar, for B( k)= 0(9.12)where ρ is a random variable with mean 1, lar , a large value of the backoffinterval, and Bk ( ),the variable used to identify whether there is an onsetof channel fading or not.Equation 9.11 represents the relationship between the backoff intervalsand the outgoing flow rate. To design a controller that will track the targetvalue of that rate, the system equation is differentiated and then transformedinto discrete-time domain. This allows the design of a feedbackcontroller for the selection of the appropriate backoff interval.