Download Scheduing Algorithms for Wireless Ad

Scheduling Algorithms for
Wireless Ad-Hoc Sensor
Networks
Department of Electrical Engineering
California Institute of Technology.
[Cedric Florens, Robert McEliece]
Outline



Introduction
Model and Problem Statement
Directional Antennas System






Line Networks
2-branch Networks
Multi-branch Networks
Tree Networks
Omni directional Antennas System
Conclusion and Future work
2
Introduction



As we known, Sensor nodes collect data, and
then transmit the data to BS (Base Station).
The problem here is how to route the packets
efficiently?
Assume there are two main phases of sensor
operations.


First phase: Collect data
Second phase: Transmit data to some processing
center located within the sensor network
3
Model and Problem Statement(1/3)



Define a sensor network as a finite collection
of n identical sensor nodes. {N1 ,..., N n }
Each node N i is associated with an integer
Pi that represents the number of data packets
stored at this node.
There is one special node N 0 , the processing
center (also called Base Station here).
4
Model and Problem Statement(2/3)



Assume that time is slotted and a one hop
transmission consumes one time slot (TS).
Assume sensor can only transmit/receive one
data packet per TS.
Multiple transmissions may occur within the
network in one TS.
5
Model and Problem Statement(3/3)


Our goal is to route the data contained at
each node to the BS as efficiently as possible.
Represent our sensor network as weighted
graph {V,E,p}.



V = {N0 ,..., N n }.
E denote the set of links (the set of edges).
p  ( p1 ,..., pn )
6
Directional Antennas SystemLine Networks (Assumption)





Goal: spend minimal TS to send data packet.
We consider a line network. A BS is placed at
one end of the network.
Let’s denote node N i by its distance to the
BS in number of hops, that is i.
We denote i  i+1 a transmission from node i
to node i+1.
For purpose of solving this problem we look
initially at the following converse problem.
7
Directional Antennas SystemLine Networks (Figure)
Distribution
Collection
8
Directional Antennas SystemLine Networks (Assumption)



The BS is to send first data packets destined
for the furthest node, then data packets for
the second furthest one and so on.
Nodes between the BS and its destinations
are required to forward packets as soon as
they arrive.
Depend on above assumption, we propose
the following simple greedy algorithm.
9
Directional Antennas SystemLine Networks (Algorithm)
Force the BS to remain idle one TS
When sending two consecutive
packet
The BS can send packet to
The nearest node without
Remain idle one TS.
10
Directional Antennas SystemLine Networks (Example)
11
Directional Antennas SystemLine Networks (Example)




Denote Ti the last busy TS at node i in the
execution of our distribution algorithm.
In the example, we have T1  10, T2  9, T3  10,...
Clearly, our algorithm run in max(Ti).
Next, we determine the performance of our
algorithm in general.
12
Directional Antennas SystemLine Networks (Proof)
13
Directional Antennas SystemLine Networks (Proof)


We define, for a given sensor network, Tu(p) the
minimum length of a time schedule over all time
schedules that perform the distribution job.
In particular we have,
14
Directional Antennas SystemLine Networks (Proof)
15
Directional Antennas SystemLine Networks (Proof)
16
Directional Antennas System2-branch Networks (Assumption)




Consider now a line network and place the BS
anywhere on that line.
We look at this problem is to consider it as a two
branch line network.
Let p and q represent the two branches data packet.
We denote
the optimal performance
achievable on a 2-branch network.
17
Directional Antennas System2-branch Networks (Assumption)



The BS transmits in the direction that require
most work first and then alternates
transmissions between the two branches.
Furthest nodes are served first then second a
furthest and so on.
A data packet is automatically forward in the
slot that followed its reception by a non
destination node.
18
Directional Antennas System2-branch Networks (Figure)
19
Directional Antennas System2-branch Networks (Assumption)
20
Directional Antennas SystemMulti-branch Networks (Assumption)




The direction of transmission is greedily decided,
base on estimates of the completion time of the data
transfer.
Initial estimate for a given branch is determined by
previous equation of Tu(p).
The legal direction associated with the biggest
estimate is chosen.
After a decision has been made the estimates at
each branch are updated according to the following
rules:


If a legal direction was not chosen, its new estimate is its
old estimate plus one
Illegal direction estimates remain unchanged.
21
Directional Antennas SystemMulti-branch Networks (Figure)
22
Directional Antennas SystemTree-branch Networks (Assumption)




We define the equivalent linear network
of a network
If
and
then
,
={(i-1,i); 1<=i<=m) and
where m
=
and
The equivalent linear network’s schedule may serve
as a schedule for the initial tree network.
Next, we explain how transmission time slots for
may be mapped onto
23
Directional Antennas SystemTree-branch Networks (Mapping)

Consider an element in E, say

Define
Each packet P follows a path path(P) from the BS
to its detination node where path(P) denotes the
finite sequence of edges(e1,…,ek).
We define


such that


24
Directional Antennas SystemTree-branch Networks (Mapping)



We define a one to one correspondence g between
and
.
We finally define
is associated with time slots
25
Directional Antennas SystemTree-branch Networks (Figure)

We illustrate a tree network in below figure
26
Directional Antennas SystemTree-branch Networks (example)

In the previous figure, we have {P} =

We have

The edge (N1,N2) is associated with time slots
27
Directional Antennas SystemTree-branch Networks (example)


Thus algorithm 1 run on the equivalent linear
network provides a BS transmission schedule.
Next problem is to generalize Tree-branch
networks


Linearize the sub-trees attached to the BS
according to the procedure.
Apply multi-branch algorithm described before to
the resulting multi-branch system
28
Conclusion and Future work

Looking at the impact of network cycles on
the optimality of our algorithms.
31