Wireless Ad Hoc and Sensor Networks

306 Wireless Ad Hoc and Sensor Networksreceived by it in the interval [ t1, t2], then an allocation is fair when bothflows f and m are backlogged and satisfies (Goyal et al. 1997)Wf( t1, t2) Wm( t1, t2)− = 0 . (7.1)φ φfClearly, this is an idealized definition of fairness, as it assumes thatflows can be served in infinitesimally divisible units. The objective of fairpacket scheduling algorithms is to ensure thatWf( t1, t2) Wm( t1, t2)− ≤εφ φf(7.2)where ε is a small positive number. However, it has been shown inGolestani (1994) that if a packet scheduling algorithm guarantees thatmmWf( t1, t2) Wm( t1, t2)− ≤H( f, m)φ φfm(7.3)for all intervals[ t1, t2]thenmax1 ⎛ l f lmH( f, m)≥ +2 ⎝⎜ φfφ(7.4)maxwhere H( f, m) is a function of the properties of flows f and m, while l fmaxand l m denote the maximum lengths of packets of flow f and m,respectively. Several fair, yet centralized, scheduling algorithms thatachieve values of H( f, m)close to the lower bound have been proposedin the literature (Golestani 1994, Demers 2000, Bennett and Zhang 1996)first for wired networks, and then for wireless networks. This chapterwill discuss the ADFS scheme from Regatte and Jagannathan (2004) forad hoc networks and its extension to WSN by hardware implementationusing UMR motes (Fonda et al. 2006). Besides taking into accountchannel uncertainties, the proposed analysis is applicable to wirednetworks.maxm⎞⎠⎟7.3 Adaptive and Distributed Fair Scheduling (ADFS)Note that service rate of flow-controlled broadcast medium and wirelesslinks may fluctuate over time. Two service models, fluctuation constrained(FC) and exponential bounded fluctuation (EBF) service model, which aresuitable for modeling many variable rate servers have been introducedin Lee (1995).