cs dept, city univ.1 low latency broadcast in multi-rate wireless mesh networks luo hongbo
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CS Dept, City Univ. 1
Low Latency Broadcast in Multi-Rate Wireless Mesh
Networks
LUO Hongbo
CS Dept, City Univ. 2
Outline
Introduction Heuristic Algorithms Discussion
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Introduction- Wireless Mesh Networks
Mesh routers & mesh clients Mesh routers have minimal mobility No strict constraint on power consumption
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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
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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
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Introduction- Impact of Multi-rate Links
(Interference range is 520m)
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Introduction- The Model Assumptions
Single radio & single channel Fixed transmission power and multi-rate
broadcast by adjusting the modulation scheme Receiver based interference model
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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.
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Heuristic Algorithm - Problem Decomposition
Topology Construction SPT CDS BIB WCDS
Downstream Multicast GroupingMultiple transmission per node is allowed
Transmission Scheduling
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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)
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Heuristic Algorithm – An Example with BIB
1
2
88
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Heuristic Algorithm – An Example with BIB
1
8 8
2
1
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Heuristic Algorithm – An Example with BIB
1
1
1
2
8 8
8
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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
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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.
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Heuristic Algorithm – An Example with WCDS
1
f(c,r) =1
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Heuristic Algorithm – An Example with BIB
1
2 f(c,r) =2*1/2 =1
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Heuristic Algorithm – An Example with BIB
1
2
88
f(c,r) =4*1/8 =1/2
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Heuristic Algorithm – An Example with WCDS
1
1
2
2
88
8
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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.
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Heuristic Algorithm – Transmission Scheduling
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:
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Heuristic Algorithm – Transmission Scheduling
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.
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Heuristic Algorithm – Transmission Scheduling
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Discussion
Lack of quantitative analysis Is the joint optimization via combing the routing
and scheduling possible? Should mesh clients be considered?
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Thanks!