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Price-based Resource Allocation in Wireless Ad Hoc Networks Yuan Xue, Baochun Li and Klara Nahrstedt University of Illinois at Urbana-Champaign University of Toronto {xue,klara}@cs.uiuc.edu bli@eecg.toronto.edu

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Introduction Wireless ad hoc network Wireless – scarce bandwidth resource Multihop – an end-to-end flow passes multiple wireless links Problem Resource allocation for end-to-end flows in ad hoc networks Goal – Optimal resource allocation Maximize the aggregated utilities of all flows Challenges – unique characteristics of ad hoc networks Location-dependent contention Spatial reuse 12345 7 8 6 f1f1 f2f2 f3f3

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Network Model Network Model G T = ( N, L ) Node set N = {1,2,…,N} Wireless links set L = {1,2,…,L} End-to-end flows Flow set F = {1,2,…,F} Each flow f F passes a set of wireless links: f L Subflow Wireless Channel Capacity C Interference model Two transmissions(subflows) contend if their sources/destinations are within range 12345 7 8 6 f1f1 f2f2 f3f3

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Resource Constraint Wireless link contention graph G C = ( L,E c ) For l 1,l 2 L, (l 1,l 2 ) E c, iff l 1, l 2 contend “Resource” A maximal clique in wireless contention graph q Feasible allocation A wireless link bandwidth allocation y = (y l, l L ), iff Constraint for resource allocation Clique-flow matrix R, R qf = |q f| rate allocation x= (x f,f F ) is feasible, iff Rx C 320 311 202 f1f1 f2f2 f3f3 q1q1 q2q2 q3q3 l 12 l 26 l 23 l 34 l 45 l 47 l 78 q1q1 q2q2 q3q3 12345 7 8 6 f1f1 f2f2 f3f3

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Problem Formulation Utility function For f F, U f (x f ): R + R + On the interval I f = [m f, M f ], the utility functions U f are increasing, strictly concave and twice continuously differentiable. The curvatures of U f are bounded away from zero on I f : - U'' f (x f ) 1/ f > 0 U f is additive Optimization problem

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A Price-based Approach Lagrangian form Use price signal for a distributed algorithm Price model q – shadow price for a maximal clique Flow price

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Pricing Model Comparison 12345 f 11 2 2 3 3 4 4 An example of a wireline network 12345 f 11 2 2 An example of an ad hoc network f = 1 + 2 + 3 + 4 f = 3 1 + 3 2 = 1 +( 1 + 2 )+( 1 + 2 )+ 2

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Algorithm – First Tier Per-clique resource allocation and price calculation Clique q at iteration k Compute new clique price Flow f at iteration k Calculate flow price Compute new rate where Convergence The algorithm converges to the unique optimal point Supply and demand relation Demand function

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Algorithm – Second Tier Per-node resource allocation and price calculation Cliques is a “virtual” concept Resource allocation and price calculation tasks of cliques need to be distributed to nodes that constitute the clique Distributed maximal clique construction algorithm Problem Directly apply centralized maximal clique construction algorithm [Bierstone] is not feasible Observation unique characteristics of wireless link contention graph Approach Distribution rule Necessary topological information – neighbors within 3 hops. 12345 7 8 6 f1f1 f2f2 f3f3

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An example Every node Distribute connectivity information Relaying node Calculate cliques evaluate aggregated rate in each clique calculate per-clique prices Update subflow price Destination node Feedback price Source node Calculate and update rate 12345 7 8 6 f1f1 f2f2 f3f3

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Resource allocation comparison 12345 f5f5 11 2 2 3 3 4 4 12345 f5f5 11 2 2 f1f1 f2f2 f3f3 f4f4 f1f1 f2f2 f3f3 f4f4

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Simulation Result Simulation setup in ns-2 Channel capacity 2Mbps 15 nodes in a 600*800 region 3 flows starting at different times

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Related Works Fair scheduling at MAC Layer Can not achieve global optimal resource allocation and global fairness Price-base resource allocation in wireline networks Link-based price vs. clique-based price Incentive Pricing in ad hoc network Selfish relaying nodes maximizing its own revenue

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Conclusion and Future Directions Concluding remarks (too much) Optimal resource allocation in the sense of maximizing aggregated utilities Maximal Clique Price-based approach to address the unique characteristics of multihop wireless ad hoc networks Two-tier distributed algorithm Future direction Impact of variable topology Impact of traffic-aware channel capacity Impact of ad hoc routing Impact of power control (topology control)

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