Wireless Ad Hoc and Sensor Networks

308 Wireless Ad Hoc and Sensor Networks7.3.2 Fairness Protocol DevelopmentTo achieve fairness at the scheduling level, the proposed ADFS protocolimplements the start-time fair queuing (SFQ) (Goyal et al. 1997) scheme,defined as follows:1. On arrival, a packet of flow f is stamped with start tag ( ),defined asp fjSp fj{ } ≥( f ) = ( ( f )) ( f )S p j v A p j F p j−1max , j 1(7.7)jwhere ( ), finish tag of packet p f , is defined asFp fjjlF pjfS pj f( ) = ( f ) + j ≥ 1φf(7.8)0where Fp ( f ) = 0 and φ f is the weight of flow f .2. Initially, the virtual time of the wireless node is set to zero. Duringtransmission, the node’s virtual time at time t , vt () is defined tobe equal to the start tag of the packet being transmitted at time t.At the end of a transmission, vt () is set to the maximum of finishtag assigned to any packets that have been transmitted by time t.3. Packets are transmitted in the increasing order of the start tags;ties are broken arbitrarily.7.3.2.1 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. The actual weight for the ith flow, jth packet denoted by ˆφ ij ,is updated asˆ φ ( k+ 1 ) = α.ˆ φ ( k ) − β.Eij ij ij(7.9)where φijˆ ( k ) is the previous weight of the packet, α and β are designconstants, { α, β} ∈−11 [ , ], and is defined as:E ijEij1= eij,queue +eij,delay(7.10)