doi:10.1016/j.comcom.2006.01.016
Copyright © 2006 Elsevier B.V. All rights reserved.
Energy efficiency of collision resolution protocols
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Aran Bergmana, 
and Moshe Sidi
, a,
aElectrical Engineering Department, Technion—Israel Institute of Technology, Haifa 32000, Israel
Available online 13 March 2006.
Abstract
Energy consumption of the medium access control (MAC) algorithm is one of the key performance metrics in today’s ubiquitous wireless networks of battery-operated devices. We concentrate on random access MAC algorithms called Collision Resolution Protocols (CRPs) that have the best stable properties and excellent delay characteristics for a large population of “bursty” users. The main concern of the analysis of CRPs has so far been the stability conditions, the throughput-delay tradeoffs and how the algorithms can be optimized for these properties. The contribution of our work is the introduction of a novel utility function that reflects the tradeoff between the energy consumption induced by a MAC protocol and its throughput, thus representing the energy efficiency of the algorithm. We exemplify the use of this utility function by analyzing several CRPs, including full and limited sensing algorithms. In particular, we introduce a modification of the “0.487” algorithm that improves its energy efficiency.
Keywords: Wireless MAC; Energy efficiency; Collision resolution protocols; Performance analysis
Fig. 1. Random variables used in the FCFS analysis.
Fig. 2. (a) The expected number of transmissions per packet for the WA algorithms. (b) The utility function with μ = 1 and p = 0.5 for the WA algorithms. The curves are presented only for Δ for which the algorithm is stable. The maximum value for each curve is marked with a symbol.
Fig. 3. The function Gμ (z) with μ = 1 and μ = 2 for the WA algorithm (a) and for the WA algorithm with the tree pruning mechanism (b).
Fig. 4. The utility function with μ = 1 and p = 0.5 for the WA algorithm with tree pruning and the FCFS algorithm. The curves are presented only for Δ for which the algorithm is stable. The maximum value for each curve is marked with a symbol.
Fig. 5. Comparison between the WA algorithm with tree pruning and the FCFS algorithm with respect to 
(a) and with respect to UF when μ = 1 (b). Only values of λ for which the system is stable are shown.
Fig. 6. Comparison of the utility function for the regular FCFS and the suggested improvement with ζ = 1.4. Only values of Δ for which the system is stable are presented. The maximum value of each curve is marked with a symbol.
Fig. 7. Random variables used in the analysis and description of the LCFS algorithm.
Fig. 9. Comparison between the computed bounds and simulation results of 
and 
for the LCFS algorithm with R = 1 and Δ = 2.58. The simulation results are averaged over 30 simulation runs of 106 slots and the computed bounds use 20 terms of the infinite series for the conditional expectations in [4, Appendix B]. 95% confidence intervals are presented for the simulation samples.
Fig. 10. Comparison between UL as computed using the simulation data and the analytical bounds as computed using the data presented in Fig. 9, where μ = 1 and ξ = 1.
Fig. 11. Expected number of transmissions per packet for the LCFS algorithm, where Δ = 1.5 (a) and Δ = 6 (b). All LCFS results are averaged over 30 simulation runs of 5 · 105 slots. The solid curve is of 
for the FA algorithm with p = 0.5.
Fig. 12. Expected delay per packet for the LCFS algorithm, where Δ = 1.5 (a) and Δ = 6 (b). All LCFS results are averaged over 30 simulation runs of 5 · 105 slots. The solid curve is of 
for the FA algorithm with p = 0.5.
Fig. 13. Expected number of transmissions per packet for the LCFS algorithm, where R = 1 (a) and R = 8 (b). All LCFS results are averaged over 30 simulation runs of 5 · 105 slots.
Fig. 14. Expected delay per packet for the LCFS algorithm, where R = 1 (a) and R = 8 (b). All LCFS results are averaged over 30 simulation runs of 5 · 105 slots. The minimum values are marked with a symbol.
Fig. 15. UL with ξ = 1 and μ = 1 for the LCFS algorithm, where Δ = 1.5 (a) and Δ = 6 (b). All LCFS results are averaged over 30 simulation runs of 5 · 105 slots. The solid curve is of UL for the FA algorithm with p = 0.5.
Fig. 17. UL with ξ = 1 and μ = 0.5 for the LCFS algorithm, where Δ = 1.5 (a) and Δ = 6 (b). All LCFS results are averaged over 30 simulation runs of 5 · 105 slots.
Fig. 18. UL with ξ = 1 and μ = 2 for the LCFS algorithm, where Δ = 1.5 (a) and Δ = 6 (b). All LCFS results are averaged over 30 simulation runs of 5 · 105 slots.
Fig. 16. UL with ξ = 1 and μ = 1 for the LCFS algorithm, where R = 1 (a) and R = 8 (b). All LCFS results are averaged over 30 simulation runs of 5 · 105 slots. The maximum values are marked with a symbol.
Table 1.
Maximum Values and Maximizers of Gμ(z) for the simple WA algorithm (a) and the WA algorithm with tree pruning (b)
Table 2.
The last-come-first-served algorithm parameters
Table 3.
Computed values of 
for the FA algorithm, for various values of λ and p
The computations use 15 terms of the Taylor expansion in λ.
Table 4.
Maximum value of UL for the FA algorithm and the maximizers (λ*, p*)
The computation uses 10 terms of the Taylor expansion in λ.
Table 5.
Maximum value of UL and the maximizers (λ*,Δ*) for the LCFS algorithm with R = 1 using approximations and the maximum values obtained through simulation using (λ*,Δ*)
Table B.1
Notations used in the analysis of the LCFS algorithm
This research was supported by the Israel Short Range Communication (ISRC) consortium.
Corresponding author. Tel.: +972 4 8294650; fax: +972 4 8295757.
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