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Rate Performance Objectives of Multihop Wireless Networks
October 2004 (vol. 3 no. 4)
pp. 334-349
We consider the question of what performance metric to maximize when designing ad hoc wireless network protocols such as routing or MAC. We focus on maximizing rates under battery-lifetime and power constraints. Commonly used metrics are total capacity (in the case of cellular networks) and transport capacity (in the case of ad hoc networks). However, it is known in traditional wired networking that maximizing total capacity conflicts with fairness, and this is why fairness-oriented rate allocations, such as max-min fairness, are often used. We review this issue for wireless ad hoc networks. Indeed, the mathematical model for wireless networks has a specificity that makes some of the findings different. It has been reported in the literature on Ultra Wide Band that gross unfairness occurs when maximizing total capacity or transport capacity, and we confirm by a theoretical analysis that this is a fundamental shortcoming of these metrics in wireless ad hoc networks, as it is for wired networks. The story is different for max-min fairness. Although it is perfectly viable for a wired network, it is much less so in our setting. We show that, in the limit of long battery lifetimes, the max-min allocation of rates always leads to strictly equal rates, regardless of the MAC layer, network topology, channel variations, or choice of routes and power constraints. This is due to the "solidarity” property of the set of feasible rates. This results in all flows receiving the rate of the worst flow, and leads to severe inefficiency. We show numerically that the problem persists when battery-lifetime constraints are finite. This generalizes the observation reported in the literature that, in heterogeneous settings, 802.11 allocates the worst rate to all stations, and shows that this is inherent to any protocol that implements max-min fairness. Utility fairness is an alternative to max-min fairness, which approximates rate allocation performed by TCP in the Internet. We analyze by numerical simulations different utility functions and we show that the proportional fairness of rates or transport rates, a particular instance of utility-based metrics, is robust and achieves a good tradeoff between efficiency and fairness, unlike total rate or maximum fairness. We thus recommend that metrics for the rate performance of mobile ad hoc networking protocols be based on proportional fairness.

[1] P Baldi, L De Nardis, and M.G. Di Benedetto, “Modeling and Optimization of UWB Communication Networks through a Flexible Cost Function,” IEEE J. Selected Areas in Comm., vol. 20, no. 9, pp. 1733-1744, Dec. 2002.
[2] G. Berger-Sabbatel, F. Rousseau, M. Heusse, and A. Duda, “Performance Anomaly of 802.11b,” Proc. INFOCOM '03 Conf., Apr. 2003.
[3] D. Bertsekas and R. Gallager, Data Networks. Prentice-Hall, 1987.
[4] S. Borst and P.A. Whiting, “Dynamic Rate Control Algorithms for HDR Throughput Optimization,” Proc. INFOCOM Conf., 2001.
[5] A. Charny, “An Algorithm for Rate Allocation in a Packet-Switched Network with Feedback,” MS thesis, MIT, May 1994.
[6] T. Cover and J.A. Thomas, Elements of Information Theory. John Whiley & Sons, 1991.
[7] R. Cruz and A.V. Santhanam, “Optimal Link Scheduling and Power Control in CDMA Multihop Wireless Networks,” Proc. Globecom '02, 2002.
[8] F. Cuomo et al. “Radio Resource Sharing for Ad Hoc Networking with UWB,” IEEE J. Selected Areas in Comm., vol. 20, no. 9, pp. 1722-1732, Dec. 2002.
[9] V. Gambiroza, B. Sadeghi, and E. Knightly, “End-to-End Performance and Fairness in Multihop Wireless Backhaul Networks,” technical report, 2004.
[10] P. Gupta and P.R. Kumar, “The Capacity of Wireless Networks,” IEEE Trans. Information Theory, vol. 46, no. 2, pp. 388-404, Mar. 2000.
[11] G. Holland, N. Vaidya, and P. Bahl, “A Rate-Adaptive Mac Protocol for Multihop Wireless Networks,” Proc. MOBIHOC '01, 2001.
[12] X. Huang and B. Bensaou, “On Max-Min Fairness and Scheduling in Wireless Ad Hoc Networks: Analytical Framework and Implementation,” Proc. MobiHoc '01, Oct. 2001.
[13] IEEE P802.15 Working Group, “The UWB Indoor Path Loss Model,” Technical Report P802.15-02/277r0-SG3a, June 2002.
[14] R. Jain, The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling. Wiley-Interscience, 1991.
[15] D. Julian, M. Chiang, D. O'Neill, and S. Boyd, “Qos and Fairness Constrained Convex Optimization of Resource Allocation for Wireless Cellular and Ad Hoc Network,” Proc. INFOCOM Conf., 2002.
[16] F.P. Kelly, A.K. Maulloo, and D.K.H. Tan, “Rate Control in Communication Networks: Shadow Prices, Proportional Fairness and Stability,” J. Operational Research Soc., vol. 49, pp. 237-252, 1998.
[17] J.Y. Le Boudec, “A Tutorial on Rate Adaptation, Congestion Control and Fairness in the Internet,” technical report, pdf , 2000.
[18] X. Lin and N. Shroff, “Joint Rate Control and Scheduling in Multihop Wireless Networks,” technical report, 2004.
[19] A. Mas-Colell, M. Whinston, and J. Green, Microeconomic Theory. Oxford Univ. Press, 1995.
[20] L. Massoulie and J. Roberts, “Bandwidth Sharing: Objectives and Algorithms,” IEEE/ACM Trans. Networking, vol. 10, no. 3, pp. 320-328, June 2002.
[21] J. Mo and J. Walrand, “Fair End-to-End Window-Based Congestion Control,” IEEE/ACM Trans. Networking, vol. 8, no. 5, pp. 556-567, Oct. 2000.
[22] T. Nandagopal, T.-E. Kim, X Gao, and V. Bharghavan, “Achieving Mac Layer Fairness in Wireless Packet Network,” Proc. MOBICOM, 2000.
[23] M.J. Neely, E. Modiano, and C.E. Rohrs, “Dynamic Power Allocation and Routing for Time Varying Wireless Networks,” Proc. INFOCOM Conf., 2003.
[24] P. Bender et al., “Cdma/hdr: A Bandwidth-Efficient High-Speed Wireless Data Service for Nomadic Users,” IEEE Comm. Magazine, pp. 70-77, July 2000.
[25] B. Radunović and J.-Y. Le Boudec, “A Unified Framework for Max-Min and Min-Max Fairness with Applications,” Proc. Allerton '02, 2002.
[26] B. Radunović and J.-Y. Le Boudec, “Optimal Power Control, Scheduling and Routing in UWB Networks,” IEEE J. Selected Areas in Comm., to appear in 2004.
[27] S. Sarkar and L. Tassiulas, “Fair Allocation of Discrete Bandwidth Layers in Multicast Networks,” Proc. INFOCOM '00 Conf., pp. 1491-1500, 2000.
[28] A. Tang, J. Wang, and S. Low, “Is Fair Allocation Always Efficient,” Proc. INFOCOM Conf., 2004.
[29] L. Tassiulas and A. Ephremides, “Jointly Optimal Routing and Scheduling in Packet Radio Networks,” IEEE Trans. Information Theory, vol. 38, no. 1, pp. 165-168, Jan. 1992.
[30] L. Tassiulas and S. Sarkar, “Max-Min Fair Scheduling in Wireless Networks,” Proc. INFOCOM '02 Conf., 2002.
[31] S. Toumpis and A.J. Goldsmith, “Capacity Regions for Wireless Ad Hoc Networks,” IEEE Trans. Wireless Comm., to appear.
[32] D. Tse and S. Hanly, “Multi-Access Fading Channels— Part I: Polymatroid Structure, Optimal Resource Allocation and Throughput Capacities,” IEEE Trans. Information Theory, vol. 44, no. 7, pp. 2796-2815, Nov. 1998.
[33] M.Z. Win and R.A. Scholtz, “Ultra-Wide Bandwidth Time-Hopping Spread-Spectrum Impulse Radio for Wireless Multiple-Access Communications,” IEEE Trans. Comm., vol. 48, no. 4, pp. 679-689, Apr. 2000.
[34] Y. Yi and S. Shakkottai, “Dynamic Power Allocation and Routing for Time Varying Wireless Networks,” Proc. INFOCOM Conf., 2004.

Index Terms:
System design, mathematical programming/optimization, wireless, max-min, utility fairness, best-effort.
Bo?idar Radunovic, Jean-Yves Le Boudec, "Rate Performance Objectives of Multihop Wireless Networks," IEEE Transactions on Mobile Computing, vol. 3, no. 4, pp. 334-349, Oct. 2004, doi:10.1109/TMC.2004.45
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