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Oblivious Routing for Wireless Mesh Networks by Jonathan Wellons and Yuan Xue

Oblivious Routing for Wireless Mesh Networks by Jonathan Wellons and Yuan Xue Presented by: Golnar Bidkhori. Introduction Model Problem Formulation. I. Introduction

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Oblivious Routing for Wireless Mesh Networks by Jonathan Wellons and Yuan Xue

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  1. Oblivious Routing for Wireless Mesh Networks by Jonathan Wellons and Yuan Xue Presented by: GolnarBidkhori

  2. Introduction • Model • Problem Formulation

  3. I. Introduction • Wireless mesh networks have attracted increasing attention and deployment as a high-performance and low-cost solution to last-mile broadband Internet access. • Proposed approaches for traffic routing usually fall onto two ends of a spectrum. - Heuristic routing algorithms - theoretical studies that formulate mesh network routing as optimization problems

  4. II. Model A. Network and Interference Model • We use w ∈ W to denote the set of gateways in the network • s ∈ S to denote the set of local access points that generate traffic in the network. • local access points, gateways and mesh routers are collectively called mesh nodes and denoted by the set V .

  5. All mesh nodes have the uniform transmission range denote by RT. • We denote the interference range of a mesh node as RI= (1 + Δ)RT, where Δ ≥ 0 is a constant. • r (u, v) is the distance between u and v (u, v ∈ V ).

  6. Packet transmission from node u to v is successful, if and only if (1) the distance between these two nodes r(u, v) satisfies r(u, v) ≤ RT. (2) any other node w ∈ V within the interference range of the receiving node v, i.e., r(w, v) ≤ RI, is not transmitting. • If node u can transit to v directly, they form an edge e = (u, v).

  7. The capacity of this edge is denoted as b(e) which is the maximum data rate. • Let E be the set of all edges. • We say two edges e, e ‘ interfere with each other, if they can not transmit simultaneously based on the protocol model. • Interference set I(e) contains the edges that interfere with edge e and e itself • w∗ represent the internet. w∗ is connected to each gateway with a virtual edge e∗ = (w∗, w). • E is the union of E and the set of all virtual edges and V is the union of V and the virtual node w∗.

  8. B. Traffic Demand and Routing • The aggregated traffic to a local access point is denoted as a flow. • All flows will take w* as their source. • ds is the traffic demand from local access point s ∈ S to w∗. • vector d = (ds, s ∈ S) denotes the demand vector consisting of all flow demands

  9. A routing specifies how traffic of each flow is routed across the network. • Arouting can be characterized by the fraction of each flow that is routed along each edge e ∈ E. • fs(e) denotes the fraction of demand from local access point s that is routed on the edge e ∈ E. • A routing can be specified by the set f = {fs(e), s ∈ S, e ∈ E}.

  10. The demand of node s ∈ S is denoted by ds. • The amount of traffic demand from s that needs to be routed over e under routing f is ds fs(e).

  11. C. Schedulability • y = (y(e), e ∈ E) denotes the wireless link rate vector, where y(e) is the aggregated flow rate along wireless link e. • Link rate vector yis said to be schedulable, if there exists a stable schedule that ensures every packet transmission with a bounded delay.

  12. Sufficient condition for schedulability. Claim 1. The link rate vector y is schedulable if the following condition isthe satisfied: ∀e ∈ E, <= 1

  13. III. PROBLEM FORMULATION • A common routing performance metric with respect to a known traffic demand is resource utilization. • In a multi hop wireless network, such as mesh backbone network, wireless link utilization may be inappropriate as a metric of routing performance due to the channel interference.

  14. A. Mesh Network Routing Under Known Traffic Demand • Let ys(e) be the traffic of s that is routed over e ∈ E. Obviously the aggregated flow rate ye along edge e ∈ E is given by ye =∑s ∈ S ys(e).

  15. Let y’s(e) be the traffic of s on edge e under traffic demand ds. Then y’s(e) = f s(e) .ds • Formally, we define the congestion of an interference set I(e) using its utilization and denote it as ρ(e). • we define the network congestion ρ = maxe∈ Eρ(e) as the maximum congestion among all the interference sets I(e). The congestion minimization routing problem is then formulated as follows:

  16. B. Oblivious Mesh Network Routing • ρ(f, d) is the network congestion under a certain routing f and traffic demand vector d • An optimal routing fopt(d) for a certain demand vector d would give the minimum congestion

  17. The performance ratio γ(f, d) of a given routing f on a given demand vector d is define as the ratio between the network congestion under f and the minimum congestion under the optimal routing. • Let D be a set of traffic demand vectors. • A routing f optis optimal for the traffic demand set D if and only if f opt= argminfγ(f,D) • PO: minimize ρ given ∀d with ρopt(d) = 1 Equations (1) - (6) from PCare true

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