An Algorithm for Incremental Joint Routing and Scheduling in Wireless Mesh Networks

Abdullah-Al Mahmood and Ehab S. ElmallahDepartment of Computing Science

University of Alberta, Canada

IEEE WCNC 2010

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Outline

Introduction System Model Problem Formulation The Main Algorithm Experimental Results Conclusion

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Introduction

Multi-hop wireless mesh networks (WMNs) offer a cost effective alternative to wired networks for deployment in both urban and remote areas

WMN aspects defined in the IEEE 802.16 Family of standards Broadband Wireless Access (BWA) Quality of service (QoS)

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Introduction

Effective dynamic allocation of bandwidth to Mesh routers

Motivated by the above objectives TDMA-based WMNs

Providing throughput Delay guarantees

4

Introduction

Goal A joint routing and scheduling problem in TDMA-base

wireless mesh networks(WMNs) All flows contend for using one of the available wireless channel A new flow demand that needs to be routed along with the ongoing

flows Minimum cost single flow routing and scheduling(MC-

SFRS)problem

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Slot 1 Slot 2 Slot 3 Slot 4 Slot 5 Slot6 Slot 7 Slot 8 Slot 9 Slot 10 …..

System Model

Multi-hop WMNs with fixed mesh routers One or more mesh router act as a gateway Using one channel TDMA

RI ≧ RT

Frame i Frame i+1

RT

R I

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System Model

Assume that the mesh routers periodically forward bandwidth requests to a designated node that computes routes

The computed results are conveyed back to the mesh routers

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Problem Formulation

Assumption A WMN G = (V, ET, EI)

V ： a set of nodes ET ： a set of transmission links

EI ： a set of interference edges between pairs of transmission links

π ： a total order relation over a subset of nodes in the give WMN G

Ex. π = (π1, π2…. πn), π1= u and πn = v

E′T ： be selected to be any set of links between the nodes in π

R(π, E′T) ： a Routing set(shortest length routes)

Table T ： at most Nframe slot cost(e, c) ： using slot c on link e

a b

c

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Problem Formulation

The cost of a route is the sum of the costs of slots assigned to each of its links

A solution to the problem is a minimum cost feasible route

A route that serves a flow between nodes u and v is feasible Assigned a time slot that no two interfering transmissions

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Example

The network G = (V, ET, EI) on 11 nodes and 15 links

RT

RI =2RT

a

c’ c

b

d’e

d

f’

f

g

h

(g, h) does not interfere with any of the links(a, b), (b, c), (a, c), (a, c′),(c′, c′).

Neither link (f, g)nor(f ′, g) interfere with links (a, c), (a, c′)and(c, c′).

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Problem Formulation

List coloring problem The available time slots (colors) that do not conflict with

any time slot (colors) in the existing schedule T

Maximum Interference Distance(MID) Given a route R = (e1, e2,…,em)

Define the MID of R to be the largest integer k |i - j|≦k, ei and ej ∈ R

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Example

The MID of route R = ((a, b), (b, e), (e, f ), (f, g) , (g, h)) is 3 Since links (a, b) and (f, g) interfere with each other

RT

RI =2RT

a

c’ c

b

d’e

d

f’

f

g

h

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Problem Formulation

Performance benefit Solving the MC-SFRS problem in maximizing network

throughput

RI =1.5RT

link A only interferes withlinks B, C, a and b

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The Main Algorithm

Node Ordering

Maximum Interference Distance

The Main Algorithm

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The Main Algorithm

Node Ordering π = (π1, π2, π3… πn′), n′≧2

RT

RI =2RT

a

c’ c

b

d’e

d

f’

f

g

h

π = (a, (c, b, c′), (d, d′, e,),( f′, f), g, h )

R(π, E′T)={(a, c′), (a, c), (a, b), (b, d),

(b, e), (b, d′), (e, f′), (e, f), (f′, c′), (a, c′), (a, c′)}

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The Main Algorithm

Maximum Interference Distance E′I ： the set of possible interference edges in E′T dI (eI, π) ： the maximum number of links separating ei

and ej on any such valid route R

dmax(x) = the maximum number of links in any valid route between nodes 1 and x.

dmin(x) = the minimum number of links in any valid route between nodes 1 and x.

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a

c’ c

b

d’e

d

f’

f

g

h

The Main Algorithm

Example suppose we want to route a flow f(a, h), and we choose

π = (a, (c, b, c′), (d, d′,e),( f′, f ), g, h)

RT

RI =2RT

a

c’ c

b

d’e

d

f’

f

g

h

dmax(h) ： a→c →b →d →e →f →g →h

dmin(h) ： a→b →e →f →g →h

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The Main Algorithm

dmax(x) = 1 + max{dmax(w) : w < x, and (w, x) ∈ ET}

dmin(x) = 1+min{dmin(w) : w < x, and (w, x) ∈ ET}

Observe that the following inequality for

eI =((i, i), (j, j)) gives an upper bound on dI (eI, π) dI (eI, π)≦ dmax(j) - dmin(i′)

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dmax(x) = 1 + max{dmax(w) : w < x, and (w, x) ∈ ET}

RT

RI =2RT

a

c’ c

b

d’e

d

f’

f

g

h

dmax(f) = 1+dmax(e)

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dmin(x) = 1+min{dmin(w) : w < x, and (w, x) ∈ ET}

RT

RI =2RT

a

c’ c

b

d’e

d

f’

f

g

h

dmin(f) = 1+dmax(e)

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Observe that the following inequality for

eI =((i, i), (j, j)) gives an upper bound on dI (eI, π) dI (eI, π)≦ dmax(j) - dmin(i′)

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RT

RI =2RT

a

c’ c

b

d’e

d

f’

f

g

h

dmax(x) = 1 + max{dmax(w) : w < x, and (w, x) ∈ ET}dmin(x) = 1+min{dmin(w) : w < x, and (w, x) ∈ ET}

dI (eI, π) = 3 ≤ dmax(f)−dmin(b) = 5−1 = 4

eI =((a, b), (f, g))

The Main Algorithm

Ongoing flow f(a, h) New flow flow(e, g )

Slot Link

1 a→b, g→h

2 b→e

3 e→f

4 f→g

5

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RT

RI =2RT

a

c’ c

b

d’e

d

f’

f

g

h Ongoing ： a→b →e →f→g →h

new flow ： d→e→f →f′

d→e e→f f →f′

Experimental Results

Topology

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Experimental Results

Traffic to Gateway

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Experimental Results

Additional Traffic over Tree-based Routing

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Conclusion

This paper deals with the MC-SFRS problem that asks for finding a minimum cost schedulable route for serving a given flow in a multi-hop TDMA wireless mesh network.

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