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Optimal pricing in a free market wireless network

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Abstract

We consider an ad-hoc wireless network operating within a free market economic model. Users send data over a choice of paths, and scheduling and routing decisions are updated dynamically based on time varying channel conditions, user mobility, and current network prices charged by intermediate nodes. Each node sets its own price for relaying services, with the goal of earning revenue that exceeds its time average reception and transmission expenses. We first develop a greedy pricing strategy that maximizes social welfare while ensuring all participants make non-negative profit. We then construct a (non-greedy) policy that balances profits more evenly by optimizing a profit fairness metric. Both algorithms operate in a distributed manner and do not require knowledge of traffic rates or channel statistics. This work demonstrates that individuals can benefit from carrying wireless devices even if they are not interested in their own personal communication.

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Notes

  1. This i.i.d. assumption simplifies analysis but is not essential, and our results can be extended to general ergodic channel processes with steady state probabilities \(\pi_{\user2{S}},\) using the T-slot Lyapunov arguments of [28, 30].

  2. Inelastic traffic can be treated via techniques of [8, 28].

  3. We say a queue U(t) is stable if \(\limsup_{t\rightarrow\infty}\frac{1}{t} \sum_{\tau=0}^{t-1} {\mathbb{E}}\left\{U(\tau)\right\} < \infty.\) This type of stability is usually referred to as strong stability.

  4. A bound on the O(1/V) term in the theorem can be computed explicitly, but we omit this computation for brevity.

  5. Specifically, it can be shown that \(B \le \frac {1} {2} \sum_n (\mu_n^{max, out})^2 + \frac {1} {2} \sum_n(\mu_n^{max, in} + R_n^{max})^2,\) as in [30].

  6. Indeed, without assuming users have infinite backlog for admission decisions (as, for example, when new data is not always available but arrives randomly to the transport layer at each source), the SGP algorithm would need to be modified by introducing auxiliary variables or “flow state variables,” a technique developed in a related flow control context (without profit metrics) in [8, 28].

  7. Note that the largest possible throughput between two mobile nodes would be only 1/25  =  0.04 packets/slot if they did not use any relays (as this is the probability that both nodes are in the same cell). Hence, as all three sources achieve throughput larger than 0.1 packets/slot, we see that they are all actively utilizing relays.

References

  1. Neely, M. J. (2007). Optimal pricing in a free market wireless network. Proceedings of the IEEE INFOCOM, May.

  2. MacKie-Mason, J. K., & Varian, H. R. (1995). Pricing congestible network resources. IEEE Journal on Selected Areas in Communications, 13(7).

  3. Kelly, F. (1997). Charging and rate control for elastic traffic. European Transactions on Telecommunications, 8, 33–37.

    Article  Google Scholar 

  4. Kelly, F. P., Maulloo, A., & Tan, D. (1998). Rate control for communication networks: Shadow prices, proportional fairness, and stability. Journal of the Operational Research Society, 49, 237–252.

    Article  MATH  Google Scholar 

  5. Low, S. H., & Lapsley, D. E. (1999). Optimization flow control, i: Basic algorithm and convergence. IEEE/ACM Transactions on Networking, 7(6), 861–75.

    Article  Google Scholar 

  6. Lee, J. W., Mazumdar, R. R., & Shroff, N. B. (2002). Downlink power allocation for multi-class cdma wireless networks. Proceedings of the IEEE INFOCOM.

  7. Neely, M. J. (2003). Dynamic power allocation and routing for satellite and wireless networks with time varying channels. Ph.D. thesis, Massachusetts Institute of Technology, LIDS.

  8. Neely, M. J., Modiano, E., & Li, C. (2005). Fairness and optimal stochastic control for heterogeneous networks. Proceedings of the IEEE INFOCOM, March.

  9. Chen, L., Low, S. H., Chiang, M., & Doyle, J. C. (2006). Cross-layer congestion control, routing, and scheduling design in ad hoc wireless networks. Proceedings of the IEEE INFOCOM, April.

  10. Andrews, M. (2005). Maximizing profit in overloaded networks. Proceedings of the IEEE INFOCOM, March.

  11. Acemoglu, D., Ozdaglar, A., & Srikant, R. (2004). The marginal user principle for resource allocation in wireless networks. Proceedings of the 43rd IEEE Conference on Decision and Control, December.

  12. Marbach, P., & Berry, R. (2002). Downlink resource allocation and pricing for wireless networks. Proceedings of the IEEE INFOCOM.

  13. Basar, T., & Srikant, R. (2002). Revenue-maximizing pricing and capacity expansion in a many users regime. Proceedings of the IEEE INFOCOM, June.

  14. He, L., & Walrand, J. (2003). Pricing internet services with multiple providers. Proceedings of the Allerton Conference on Comm., Control, and Computing.

  15. He, L., & Walrand, J. (2005). Pricing differentiated internet services. Proceedings of the IEEE INFOCOM, March.

  16. Shen, H., & Basar, T. (2004). Incentive-based pricing for network games with complete and incomplete information. Proceedings of the 11th International Symposium on Dynamic Games and Applications, December.

  17. Paschalidis, I. Ch., & Tsitsiklis, J. N. (2000). Congestion-dependent pricing of network services. IEEE/ACM Transactions on Networking, 8(2), 171–181.

    Article  Google Scholar 

  18. Lin, X., & Shroff, N. B. (2005). Simplification of network dynamics in large systems. IEEE/ACM Transactions on Networking, 13(4), 813–826.

    Article  Google Scholar 

  19. Buttyan, L., & Hubaux J.-P. (2003). Stimulating cooperation in self-organizing mobile ad hoc networks. ACM/Kluwer Mobile Networks and Applications (MONET), 8(5), 579–592.

    Article  Google Scholar 

  20. Crowcroft, J., Gibbens, R., Kelly, F., & Ostring, S. (2003). Modeling incentives for collaboration in mobile ad-hoc networks. Presented at the 1st International Symposium on Modeling and Optimization in Mobile, Ad-Hoc, and Wireless Networks (WiOpt ’03), Sophia-Antipolis, France.

  21. Shang, L., Dick, R. P., & Jha, N. K. (2004). Desp: A distributed economics-based subcontracting protocol for computation distribution in power-aware mobile ad hoc networks. IEEE Transactions on Mobile Computing, 3(1), January–March.

  22. Marbach, P., & Qui, Y. (2005). Cooperation in wireless ad hoc networks: A market-based approach. IEEE/ACM Transactions on Networking, 13(6), December.

  23. Huang, J., Berry, R., & Honig, M. Auction-based spectrum sharing. ACM/Kluwer Journal of Mobile Networks and Applications (MONET) special issue on WiOpt’04, to appear.

  24. Sun, J., Modiano, E., & Zheng, L. (2006). Competitive fairness: Wireless channel allocation using an auction algorithm. IEEE Journal on Selected Areas in Communications.

  25. Ji, Z. J., Yu, W., & Liu, K. J. R. (2006). An optimal dynamic pricing framework for autonomous mobile ad hoc networks. Proceedings of the IEEE INFOCOM, April.

  26. Jain, R. (2004). Efficient market mechanisms and simulation-based learning for multi-agent systems. PhD thesis, University of California, Berkeley.

  27. Maheswaran, R., & Basar, T. (2002). Auctions for divisible resources: Price functions, Nash equilibrium and decentralized update schemes (pp. 87–102). Springer Verlag.

  28. Georgiadis, L., Neely, M. J., & Tassiulas, L. (2006). Resource allocation and cross-layer control in wireless networks. Foundations and Trends in Networking, 1(1), 1–149.

    Article  Google Scholar 

  29. Tassiulas, L., & Ephremides, A. (1992). Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Transacations on Automatic Control, 37(12), 1936–1949.

    Article  MATH  MathSciNet  Google Scholar 

  30. Neely, M. J., Modiano, E., & Rohrs, C. E. (2005). Dynamic power allocation and routing for time varying wireless networks. IEEE Journal on Selected Areas in Communications, 23(1), 89–103.

    Article  Google Scholar 

  31. Neely, M. J. (2006). Energy optimal control for time varying wireless networks. IEEE Transactions on Information Theory, 52(7).

  32. Bertsekas, D. P., & Gallager, R. (1992). Data networks. New Jersey: Prentice-Hall, Inc.

    MATH  Google Scholar 

  33. Neely, M. J., & Modiano, E. (2005). Capacity and delay tradeoffs for ad-hoc mobile networks. IEEE Transactions on Information Theory, 51(6), 1917–1937.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Southern California, 3740 McClintock Ave., EEB 520, Los Angeles, CA, 90089, USA

    Michael J. Neely

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  1. Michael J. Neely
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Correspondence to Michael J. Neely.

Additional information

This work was presented in part at the IEEE INFOCOM conference, Anchorage, May 2007 [1]. This work is supported in part by one or both of the following: The DARPA IT-MANET program grant W911NF-07-1-0028, the National Science Foundation grant OCE 0520324.

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Neely, M.J. Optimal pricing in a free market wireless network. Wireless Netw 15, 901–915 (2009). https://doi.org/10.1007/s11276-007-0083-0

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