cs dept, city univ.1 low latency broadcast in multi-rate wireless mesh networks luo hongbo

CS Dept, City Univ. 1

Low Latency Broadcast in Multi-Rate Wireless Mesh

Networks

LUO Hongbo


Outline

Introduction Heuristic Algorithms Discussion


Introduction- Wireless Mesh Networks

Mesh routers & mesh clients Mesh routers have minimal mobility No strict constraint on power consumption


Introduction- Low Latency Broadcast

Energy-efficient broadcast Broadcast advantage is exploited Broadcast latency:

computed as the maximum delay between the transmission of a packet by a source node and its eventual reception by all the intended receivers.

Multi-rate natures in WMNs


Introduction- Transmission and Interference Model

Transmission model: Pr =Pt

The transmission range is a decreasing function of transmission rate

Interference Model: The distance between the transmitter and receiver dij Ri;

No transmitter nk within a finite distance Rk’ (such that dkj <=Rk’) is transmitting concurrently.

ijd


Introduction- Impact of Multi-rate Links

(Interference range is 520m)


Introduction- The Model Assumptions

Single radio & single channel Fixed transmission power and multi-rate

broadcast by adjusting the modulation scheme Receiver based interference model


Introduction- Optimization Problem

Problem: Minimize the broadcast latency with possibly multiple number of transmissions per node in a multi-rate

wireless mesh network This problem is NP-Hard Key Issues:

Whether a node should broadcast and if so, to which of its neighbors;

The timing of these broadcasts.


Heuristic Algorithm - Problem Decomposition

Topology Construction SPT CDS BIB WCDS

Downstream Multicast GroupingMultiple transmission per node is allowed

Transmission Scheduling


Mathematical notations The mesh network can be represented as a graph G=(V,E).

denotes the direct unicast link between nodes i

and j, which is associated with a transmission rate Rij.

Basic Idea (from BIP) Initially, every node except the root node will be set to a

cost with 1/Rij

In each iteration, the node with the minimum of incremental cost will be added to the tree

Eji ),(

Heuristic Algorithm - Broadcast Incremental Bandwidth (BIB)


Heuristic Algorithm – An Example with BIB

1

2

88



1

8 8

2

1



1

1

1

2

8 8

8


Heuristic Algorithm – Weighted Connected Dominating Set (WCDS) MCDS performs poorly in multi-rate case

Minimum WCDS problem For a given graph G= (V,E), we suppose there are k different

rates given by r1,r2,…,rk, Let N(x,ri) denote the nodes that are

reachable from node using rate ri. The aim is to find a

subset Y = {y1,y2,…} in V and the broadcast rate wi for node yi

such that: Every element of V\Y is in The set Y is connected The weighted sum is minimal

Vx

),( iiy wyNYi

ii

wYy

1


Heuristic Algorithm – Weighted Connected Dominating Set (WCDS) The basic idea of the algorithm

We suppose the set C including the nodes which have received the message and are eligible to transmit.

Initially, we make the source node s eligible to transmit, C={s} In each iteration, for every eligible node c and rate r, we choose

the (c, r) combination that maximizes the rate of increase of not-yet-covered nodes, as measured by f(c,r) = |N(c,r)\C| * r.


Heuristic Algorithm – An Example with WCDS

1

f(c,r) =1



1

2 f(c,r) =2*1/2 =1



1

2

88

f(c,r) =4*1/8 =1/2


Heuristic Algorithm – An Example with WCDS

1

1

2

2

88

8


Heuristic Algorithm – Transmission Scheduling

Some Notations Vb : Let Vb={b1,b2,…,bk} V be the set of the branch points

in the broadcast tree T b1: Source node Gb: A directed graph(tree) Gb=(Vb, Eb) such that (bi, bj) Eb if

and only if it is an edge in the tree T t(bi): For every node bi Vb, we assign a cost t(bi) which is

the minimum multicast transmission time it takes the node bi to transmit a fixed-size packet to all its children.

Gc: An undirected conflict graph Gc = (Vc, Ec) such tat Vc = Vb and (bi, bj) Ec if and only if the multicast of bi interferes with the reception of the children of bj in T.



Problem Formulation Formally, a schedule can be defined as a mapping

which gives the transmission time of node bi Vb. Given Gb,

t(bi) and Gc, a valid schedule is one which meets the followingconstraints: The source multicasts at time zero: =0. . For any edge , we have

The objective is to find a valid schedule which minimizes thebroadcast latency

)( 1b)()()(,),( iijbji btbbEbb

cji Gbb ),( ))()(),(())()(),(( bjtbjbjbitbibi

))()((max iib btbVbi

bV:



Basic idea of the greedy algorithm In each iteration, for each qualified node in Q ={q1,q2,…,qm}, we

select the the node qi with the largest value of f(qi). The metric f(qi)

is defined as follows:

Where e(qi) is the earliest possible multicast time for the node qi,

and w(bi) is the time needed to reach all the descendants of bi in T

in the absence of interference and can be written:

Where D(bi) denote the set of all descendants of bi in Gb. For any x

in D(bi), let P(bi,x) denote the set of nodes on the path from b i to x.


Discussion

Lack of quantitative analysis Is the joint optimization via combing the routing

and scheduling possible? Should mesh clients be considered?


Thanks!

cs dept, city univ.1 low latency broadcast in multi-rate wireless mesh networks luo hongbo

Documents

cs dept

introduction transmission

exploited broadcast

transmission range

wmns slide

power consumption slide

multirate natures

finite distance r