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End-to-End Fair Bandwidth Allocation in Multi-hop Wireless Ad Hoc Networks Baochun Li Department of Electrical and Computer Engineering University of Toronto IEEE ICDCS 2005 Presented by Yeong-cheng Tzeng

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Outline I. Introduction II. Objective and Constraints III. Optimal Allocation Strategies IV. Achieve Allocation Strategies: Algorithms V. Performance Evaluation VI. Conclusions

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I. Introduction In wireless networks Flows compete for shared channel bandwidth if they are within the transmission ranges of each other Contention in the spatial domain In wireline networks Flows contend only at the packet router with other simultaneous flows through the same router Contention in the time domain

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I. Introduction Design an topology-aware resource allocation algorithm Contending flows fairly share channel capacity Increasing spatial reuse of spectrum to improve utilization Previous works - break a multi-hop flow into multiple independent subflows The inherent correlation between upstream and downstream subflows are lost The probability of dropping packets is increased

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I. Introduction

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II. Objective and Constraints Objective Maximize spatial reuse of spectrum Constraint Maintain basic fairness among contending flows

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II.A Preliminaries Contending subflows Two active subflows if one subflow is within the transmission range of the other Contending flows If any of their subflows are contending subflows Contending flow group If multi-hop flows are contending flows i.e. G(F i )=G(F j )={F i,F j } G(F i )=G(F j ) and G(F j )=G(F k ), then G(F i )=?G(F k )

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II.A Preliminaries Subflow contention graph Represents the spatial contention relationship among contending subflows Vertices correspond to subflows Connected vertices correspond to contending subflows

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II.B Objective: Maximizing Spatial Reuse of Spectrum In single hop case, the objective of maximizing spatial reuse of spectrum Translated to maximizing the aggregate channel utilization Total effective single-hop throughput max

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II.B Objective: Maximizing Spatial Reuse of Spectrum The throughput decreases when we take the end-to-end effect into consideration

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II.B Objective: Maximizing Spatial Reuse of Spectrum The end-to-end throughput of multi-hop flows is determined by the minimum throughput of its subflows, i.e., u i =min(u ij ), j=1,…l i We define the total effective throughput as the total end-to-end throughput of all multi-hop flows, i.e., Our objective To maximize the total effective throughput Subtly different from the objective in the single- hop case

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II.C Fairness: the case of multi-hop flows In wireline networks, an allocation strategy (r 1,…,r n ) is weighted max-min fair, if Both and hold for all n contending flows For each flow F i, any increase in r i would cause a decease in the allocation r j for some flow F j satisfying r j /w j < r i /w i

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II.C Fairness: the case of multi-hop flows

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Generally, if r i.j is allocated to the subflow F i.j, we have u ij =r i.j, thus u i =min(r i.j ) If we equalize channel allocations for all subflows belonging to the same flow i.e., We have From the viewpoint of channel allocation, we define the fairness constraint as

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II.C Fairness: the case of multi-hop flows Definition: In a multi-hop wireless network, the allocation strategy is fair for contending flows (F 1,…F n ) in the same contending flow group, if Within any local neighborhood (that flows contend for the same channel capacity B),,with m i being the number of contending subflows of F i in this local neighborhood over any time period [t 1,t 2 ]

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II.D Basic Fairness The allocation strategy is to allocate B to all subflows in the same contending flow group, regardless of whether they actually contend in the same local neighborhood The total effective throughput is

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II.D Basic Fairness For a flow F i, each subflow F i.k only contends with its immediate upstream flow F i.k-1 and immediate downstream flow F i.k+1 If l i ≥ 3, we may classify the subflows into three independent sets, where subflows in each set may transmit concurrently: {F i.j, j = 3k + 1, k ≥ 0} {F i.j, j = 3k + 2, k ≥ 0} {F i.j, j = 3k + 3, k ≥ 0}

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II.D Basic Fairness We define the virtual length of a flow F i, v i, as follows: The basic share of F i : The total effective throughput We claim an allocation strategy satisfies the constraint of basic fairness, if the allocation of any flow is equal to or higher than its basic share Still satisfies the fairness constraint Achieve a higher total effective throughput

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III. Optimal Allocation Strategies Develop an estimation algorithm to calculate the optimal allocation strategies that achieve our objective of maximizing spatial bandwidth reuse, while satisfying The fairness constraint The basic fairness constraint

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III.A. Satisfying the Fairness Constraint Clique A complete subgraph in the weighted subflow contention graph, which represents a set of subflows that mutually contend with each other Weighted clique size, The sum of weights on all vertices in a clique Weighted clique number,

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III.A. Satisfying the Fairness Constraint Assume that for each flow F i, there are n i,k subflows in the cliqueΩ k (n i,k ≥ 0) Since all subflows in the same clique contends for the channel capacity B, for contending flows (F 1,…,F n ) in the same contending flow group, we have

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III.A. Satisfying the Fairness Constraint Channel allocation per unit weight Proposition 1: Under the fairness constraint, the upper bound of total effective throughput is, where denotes the weighted clique number

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III.B. Satisfying the Basic Fairness Constraint Let Basic share constraint x i : additional share total effective throughput capacity constraint

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III.B. Satisfying the Basic Fairness Constraint A basic feasible solution Total effective throughput It is known that there exist polynomial-time algorithms to solve such a linear programming problem Simplex algorithm

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III.B. Satisfying the Basic Fairness Constraint Proposition 2: The solution to the above linear programming problem constitutes the optimal allocation strategy, while supplying the basic fairness property. Such an allocation strategy maximized the total effective throughput

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IV. Achieving Allocations Strategies: Algorithms We propose a two-phase algorithm to achieve and implement near-optimal allocation strategies The first phase determines the allocation strategy for subflows at each nodes The second phase is fully distributed and seeks to implement the calculated allocation strategy for each of the subflows

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IV.A. First Phase: The Centralized Form Need a centralized node Process per-flow information Construct the weighted subflow contention graph Steps Each Node collects information Virtual length Weight Deliver information to centralized node The centralized node constructs the weighted subflow contention graph Solve the linear programming problem Broadcast the allocation strategy

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IV.B. First Phase: The Distributed Form Steps Construction of local cliques Overhearing Exchange information with immediate neighbors Intra-flow exchange of constraints Local channel capacity constraint Local basic fairness constraint Achieving locally optimal allocation strategies

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IV.B. First Phase: The Distributed Form

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IV.C. Second Phase: Scheduling Use the calculated allocation strategy (allocated share) as the weights

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IV.C. Second Phase: Scheduling Due to lack of centralized coordination: Intra-node coordinations Packet from different subflows are queued separately Select the next packet to sent, obeying the allocated share Inter-node coordinations Determine the backoff timer Think of all subflows on one node as one virtual flow Adjust their contention window to proportional to node share Others Follow the standard RTS-CTS-DATA-ACK handshaking protocol as Each node is required to maintain a virtual clock, v i (t) Each node is need a local table to keep track of service tags Use RTS, CTS and ACK packets to piggyback service tags

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IV.C. Second Phase: Scheduling Scheduling algorithm When a packet arrives at node i, it enqueues in its own subflow queue When a packet reaches the head of its queue, three tags are assigned Start tag: Internal finish tag: External finish tag:

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IV.C. Second Phase: Scheduling Scheduling algorithm Set backoff timer Sender estimates a backoff value Receiver estimates a backoff value Backoff timer is uniformly distributed in [0,CW min +max(Q,R,0)] When sender sends a packet successfully Update its virtual clock as the external finish tag of the previous packet Select packet have the smallest internal finish tag

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V. Performance Evaluation Simulate results in two network scenarios a simpler topology shown in Fig. 1; a more elaborate topology shown in Fig. 6. Compare the performance of 2PA with standard IEEE MAC the two-tier fair scheduling algorithm maximizes single-hop total effective throughput guarantees basic fairness among single-hop flows Others Implement with a channel capacity of 2Mbps with Two Ray Ground Reflection as the propagation model Dynamic Source Routing (DSR) as the routing protocol CBR of 200 packets per second with a packet size of 512 bytes use identical weights of 1 for each flow each simulation session is T = 1000 seconds

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V. Performance Evaluation Interested parameters The number of packets successfully delivered for each of the flows to evaluate the allocated share to each of the flows and subflows The total number of successfully delivered packets to evaluate the extent of spatial spectrum reuse The total number of packets lost

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V.A. Scenario 1

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V.B. Scenario 2

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VI. Conclusion Study the issue of end-to-end fairness in multi-hop wireless ad hoc networks Propose estimation algorithms A two-phase algorithm is presented to approximate the optimal allocation strategies Evaluation performance is effective

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