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Wireless Networks

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01-10-2009

Optimal pricing in a free market wireless network

Author: Michael J. Neely

Published in: Wireless Networks | Issue 7/2009

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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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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].

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

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.

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

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].

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].

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.

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Title: Optimal pricing in a free market wireless network
Author: Michael J. Neely
Publication date: 01-10-2009
Publisher: Springer US
Published in: Wireless Networks / Issue 7/2009
Print ISSN: 1022-0038
Electronic ISSN: 1572-8196
DOI: https://doi.org/10.1007/s11276-007-0083-0

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