routing algorithms and algorithms for lifetime-optimization in complex sensor-actuator-networks
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Routing Algorithms and Algorithms for Lifetime-Optimization in
Complex Sensor-Actuator-Networks
G. Venkatesh Dr. N. Sambasiva Rao K. Suresh
Asst.Prof. in IT Principal Asst Prof. in ITVCE, Hyderabad VCE, Hyderabad AITS, Rajampet,Kadapa
India. India. India.
AbstractCommunication between sensor nodes is
one of the most energy-consuming activities of a
sensor-actuator-network. Thus, it is important to
use preferably short and energy-efficient
transmission paths for the sensor messages. But
one has also to guarantee that no single node is
overstressed when compared to the others.
Furthermore, the ensuing communication
patterns are usually application-dependent. Thus,they should also be taken into account when
designing a communication structure. A fast
adaptability to changing topologies (i.e. nodes
break done or move) and a distributed planning of
activities are of great importance for almost all
aspects of sensor-actuator-networks. Both are
desirable properties that usually do not arise in
classic scenarios or are only of little importance
there. Thus, we have to be newly develop for our
needs.
Key words Sensor_actuator_network, Energy
Efficient,Topologies.
1. INTRODUCTION
Many wireless sensor network (WSN) Applications
require real-time Communication. For example, a
surveillance System needs to alert authorities of an
intruder within a few seconds of detection. Similarly,
a fire-fighter may rely on timely temperature updates
to remain aware of current fire conditions.
Supporting real-time communication in WSNs is
very challenging. First, WSNs have lossy links that
are greatly affected by environmental factors. As a
result, communication delays are highlyunpredictable. Second, many WSN applications (e.g.,
border surveillance) must operate for months without
wired power supplies. Therefore, WSNs must meet
the delay requirements at minimum energy cost.
Third, different packets may have different delay
requirements. For instance, authorities need to be
notified sooner about high-speed motor vehicles than
slow-moving pedestrians. To support such
applications, a real-time communication protocol
must adapt its behavior based on packet deadlines.
Finally, due to the resource constraints of WSN
platforms, a WSN protocol should introduce minimal
overhead in terms of communication and energy
consumption and use only a fraction of the available
memory for its state.
The rest of the paper is organized as follows.
In section 2 discussed related work, in section 3explained various routing algorithms, and finally
concluded with section 4.
2 .RELATED WORK
There already exists a lot of work in the
field of sensor scheduling and routing with focus on
energy-efficiency and therefore with the goal to
optimize the lifetime of sensor networks. Most often
the presented algorithms either are ad-hoc solutions,
that have only been evaluated empirically without
any theoretical guarantees or they are purelytheoretical works, that base their solutions on models
that are to simple to function in real-world scenarios.
This lack of overlap between theory and practice can
be found throughout this entire field of research.
Our main focus is on algorithms that help to
minimize the energy consumption of sensor-
networks. Generation and storage of energy is still
not solved efficiently on a small scale such as on a
sensor node. Thus, we have to treat the available
energy as a scarce resource and try to optimize the
usage of the remaining energy to extend the lifetime
of the network for as long as possible.
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3. ROUTING ALGORITHAMS
A.Formulation of Power-aware Routing1 The Model
Power consumption in ad-hoc networks can bedivided into two parts: (1) the idle mode and (2)
the transmit/receive mode. The nodes in the
network are either in idle mode or in
transmit/receive mode at all time. The idle mode
corresponds to baseline power consumption.
Optimizing this mode is the focus of. We instead
focus on studying and optimizing the
transmit/receive mode. When messages routed
through the system, all the nodes with the
exception of the source and destination receives
a message and then immediately relay it.
Because of this, we can view the power
consumption at each node as an aggregate
between transmit and receive powers which we
will model as one parameter. More specifically,
we assume an ad-hoc network that can be
represented by a weighted graph G(V;E). The
vertices of the graph correspond to computers in
the network. They have weights that correspond
to the computer's power level. The edges in the
graph correspond to pairs of computers that are
in communication range. Each edge weight is the
power cost of sending a unit message1 between
the two nodes. Our results are independent of the
power consumption model as long as we assume
the power consumption of sending a unit
message between two nodes does not changeduring a run of the algorithm. That is, the weight
of any edge in the network graph is fixed.
Although our algorithms are independent of the
power consumption model, we fixed one model
for our implementation and simulation
experiments. Suppose a host needs power e to
transmit a message to another host who is d
distance away. We use the model of to compute
the power consumption for sending this message:
e = kdC + a;
where k and c are constants for the specificwireless system (usually 2
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Figure 1: The integer solution problem can be
reduced to set partition as follows. Construct a
network based on the given set. The power of xi
is ai for all 1 i n, and the power of y
is the weight of each edge is markedon the network. For any set of integers S = a 1, a2,
a3, a4 an, we are asked to find the subset of
S, A such that Pai2AWecan construct a network as depicted here. The
maximal flow of the network is , andit can only be gotten when the flow of x iy is aifor all ai A, and for all other x iy, the flow is 0.
3. Competitive Ratio for Online Power-aware
Routing
In a system where the message rates are
unknown, we wish to compute the best path to
route a message. Since the message sequence is
unknown, there is no guarantee that we can find
the optimal path. For example, the path with the
least power consumption can quickly saturate
some of the nodes. The difficulty of solving this
problem without knowledge of the message
sequence is summarized by the theoretical
properties of its competitive ratio. The
competitive ratio of an online algorithm is the
ratio between the performance of that algorithm
and the optimal offline algorithm that has access
to the entire execution sequence prior to making
any decisions.
Theorem 1 No online algorithm for
message routing has a constant competitive ratio
in terms of the lifetime of the network or the
number of messages sent.
Theorem 1, whose proof is shown in Figure 2,
shows that it is not possible to compute online anoptimal solution for power-aware routing.
B. Online Power-aware Routing with max-
min zPmin
In this section we develop an approximation
algorithm for online power-aware routing and
show experimentally that our algorithm has a
good empirical competitive ratio and comes
close to the optimal.
We believe that it is important to develop
algorithms for message routing that do not
assume prior knowledge of the message
sequence because for ad-hoc network
applications this sequence is dynamic and
depends on sensed values and goals
communicated to the system as needed. Our goal
is to increase the lifetime of the network when
the message sequence is not known. We model
lifetime as the earliest time that a message
cannot be sent. Our assumption is that each
message is important and thus the failure of
delivering a message is a critical event. Our
results can be extended to tolerate up to m
message delivery failures, where m is a
parameter. We focus the remaining of this
discussion on the failure of the first message
delivery. Intuitively, message routes shouldavoid nodes whose power is low because
overuse of those nodes will deplete their battery
power. Thus, we would like to route messages
along the path
Figure 2: In this network, the power of each
node is 1+ and the weight on each edge is 1.
The First figure gives the network; the center one
is the route for the online algorithm; and the
right one is the route for the optimal algorithm.
Consider the message sequence that begins with
a message from S to T, say, ST. Without loss of
generality (since there are only two possible
paths from S to T), the online algorithm routes
the message via the route SX1X2X3.Xn-1XnT.
The message sequence is X1X2, X2X3, X3X4, .,
Xn-1Xn. It is easy to see that the optimalalgorithm (see right figure) routes the first
message through SY1Y2Y3..Yn-1YnT, then
routes the remaining messages through X1X2,
X2X3, X3X4,., and Xn-1Xn. Thus the optimal
algorithm can transmit n messages. The online
algorithm (center) can transmit at most 1
message for this message sequence because the
nodes X1;X2;. . . ;Xn are all saturated after
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routing the first message. The competitive ratio
is small when n is large. with the maximal
minimal fraction of remaining power after the
message is transmitted. We call this path the
max-min path. The performance of max-min
path can be very bad, as shown by the example
in Figure 3. Another concern with the max-min
path is that going through the nodes with high
residual power may be expensive as compared to
the path with the minimal power consumption.
Too much power consumption decreases the
overall power level of the system and thus
decreases the life time of the network. There is a
trade-off between minimizing the total power
consumption and maximizing the minimal
residual power of the network. We propose to
enhance a max-min path by limiting its total
power consumption.
Figure 3: The performance of max-min path can
be very bad. In this example, each node except
for the source S has the power 20 + , and the
weight of each edge on the arc is 1. The weight
of each straight edge is 2. Let the power of the
source be the network can send 20 messages
from S to T according to max-min strategy by
taking the edges on the arc (see the arc on thetop). But the optimal number of messages
follows the straight edges with black arrows is
10(n - 4) where n is the number of nodes.
The two extreme solutions to power-aware
routing for one message are: (1) compute a path
with minimal power consumption Pmin; and (2)
compute a path that maximizes the minimal
residual power in the network. We look for an
algorithm that optimizes both criteria. We relax
the minimal power consumption for the message
to be zPmin with parameter z 1 to restrict the
power consumption for sending one message to
zPmin. We propose an algorithm we call max-minzPmin that consumes at most zPmin while
maximizing the minimal residual power fraction.
The rest of the section describes the max-min
zPmin algorithm, presents empirical justification
for it, a method for adaptively choosing the
parameter z and describes some of its theoretical
properties.
The following notation is used in the
description of the max-min zPmin algorithm.
Given a network graph (V;E), let P(vi) be the
initial power level of node v i, eij the weight of the
edge vivj, and Pt(vi) is the power of the node vi at
time t. Let
utij = Pt(vi)-eij / p (vi)
P(vi) be the residual power fraction after sending
a message from i to j.
Alg. 1 describes the algorithm. In each
round we remove at least one edge from the
graph. The algorithm runs the Dijkstra algorithm
to find the shortest path for at most |E| times
where |E| is the number of edges. The running
time of the Dijkstra algorithm is O(|E| + |V| log
|V|) where |V| is the number of nodes. Then the
running time of the algorithm is at most O (|E| *
(|E| + |V | log |V |)). By using binary search, the
running time can be reduced to
O(log |E| - (|E|+|V| log |V |)). To find the pure
max-min path, we can modify the Bellman-ford
Algorithm by changing the relaxation procedure.
The running time is O (|V | * |E|).
Algorithm 1 max-min zPmin-path algorithm
1: Find the path with the least power
consumption, Pmin by using the Dijkstra
algorithm
2: while true do
3: Find the path with the least power
consumption in the graph
4: if the power consumption > z * Pmin or no path
is found then
5: the previous shortest path is the solution, stop
6: Find the minimal utij on that path, let it be
umin7: Find all the edges whose residual power
fraction utij umin, remove them from the graph
1.Adaptive Computation for zAn important factor in the max-min zPmin
algorithm is the parameter z which measures the
trade-off between the max-min path and the
minimal power path. Whenz = 1 the algorithm
computes the minimal power consumption path.
When z = it computes the max-min path. We
would like to investigate an adaptive way of
computing z > 1 such that max-min zPmin thatwill lead to a longer lifetime for the network than
each of the max-min and minimal power
algorithms. Alg. 2 describes the algorithm for
adaptively computing z. P is the initial power of
a host. Pt is the residual power decrease at time
t compared to time t - T. Basically,
gives an estimation for the lifetime of that node
if the message sequence is regular with some
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cyclicity. The adaptive algorithm works well
when the message distributions are similar as the
time elapses. We conducted several simulation
experiments to evaluate the adaptive
computation of z. In a first experiment we
generated the positions of hosts in a square field
randomly using the following parameters. The
scope of the network is 10*10, the number of
hosts in the network is 20, the power
consumption weights for transmitting a message
are eij = 0:001 * d3 ij , and the initial power of
each host is 30. Messages are generated between
all possible pairs of hosts and are distributed
evenly. Figure 4 (first) shows the number of
messages transmitted until the first message
delivery failure for different values of z. Using
the adaptive method for selecting z with zinit =
10, the total number of messages sent increases
to 12; 207, which is almost the best performance
by max-min zPmin algorithm.
Figure 4: The effect of z on the maximal number
of messages in a square network space. The
positions of hosts are generated randomly. In the
first graph the network scope is 10 *10, the
number of hosts is 20, the weights are generatedby eij = 0:001 *d
3ij , the initial power of each
host is 30, and messages are generated between
all possible pairs of the hosts and are distributed
evenly. In the second graph the number of hosts
is 40, the initial power of each node is 10, and
all other parameters are the same as the first
graph. In the second experiment we generated
the positions of hosts evenly distributed on the
perimeter of a circle. The radius of the circle is
20, number of hosts 20;
the weight formula: eij = 0:0001 * d3
ij ; and
the initial power of each host is 10. Messages are
generated between all possible pairs of the hostsand are distributed evenly. The performance
according to various z can be found in Figure 5
(first). By using the adaptive method, the total
number of messages sent until reaching a
network partition is 11; 588, which is much
better than the most cases when we choose a
fixed z.
2 Empirical Evaluation of Max-min zPmin
Algorithm
We conducted several experiments for
evaluating the performance of the max-min zPmin
algorithm. In the first set of experiments (Figure
4), we compare how z affects the performance of
the lifetime of the network. In the first
experiment, a set of hosts are randomly
generated on a
Figure 5: The first figure shows the effect of z
on the maximal number of messages in a ring
network. The radius of the circle is 20, the
number of hosts is 20, the weights are generated
by eij = 0:0001* d3 ij , the initial power of each
host is 10 and messages are generated betweenall possible pairs of the hosts and are distributed
evenly. The second figure shows a network with
four columns of the size 1 * 0:1. Each area has
ten hosts which are randomly distributed. The
distance between two adjacent columns is 1. The
right figure gives the performance when z
changes. The vertical axis is the maximal
messages sent before the first host is saturated.
The number of hosts is 40; the weight formula is
eij = 0:001 *d3ij ; the initial power of each host is
1; messages are generated between all possible
pairs of the hosts and are distributed evenly.
square. For each pair of nodes, one message is
sent in both directions for a unit of time. Thus
there is a total of n * (n - 1) messages sent in
each unit time, where n is the number of the
hosts in the network. We experimented with
other network topologies.Figure 5 (first) shows
the results obtained in a ring network. Figure 5
(second) shows the results obtained when the
network consists of four columns where nodes
are approximately aligned in each column. The
same method used in experiment 1 varies the
value of z. These experiments show that
adaptively selecting z leads to superior
performance over the minimal power algorithm
(z = 1) and the max-min algorithm (z = 1).Furthermore, when compared to an optimal
routing algorithm, max-min zPmin has a constant
empirical competitive ratio (see Figure 6 (first)).
Figure 6 (second) shows more data that
compares the max-min zPmin algorithm to the
optimal routing strategy. We computed the
optimal strategy by using a linear programming
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package2. We ran 500 experiments. In each
experiment a network with 20 nodes was
generated randomly in a 10 * 10 network space.
The messages were sent to one gateway node
repeatedly.
We computed the ratio of the lifetime of the
max-min zPmin
algorithm to the optimal lifetime.
Figure 6 shows that max - min zPmin performs
better than 80% of optimal for 92% of the
experiments and performs within more than 90%
of the optimal for 53% of the experiments. Since
the optimal algorithm has the advantage of
knowing the message sequence, we believe that
max-min zPmin is practical for applications where
there is no knowledge of the message sequence.
Figure 6: The first graph compares the
performance of max-min zPmin to the optimal
solution. The positions of hosts in the network
are generated randomly. The network scope is
10*10, the weight formula is eij = 0:0001 *d3ij ,
the initial power of each host is 10, messages are
generated from each host to a specific gateway
host, the ratio z is 100:0. The second figure
shows the histogram that compares max-minzPmin to optimal for 500 experiments. In each
experiment the network consists of 20 nodes
randomly placed in a 10*10 network space. The
cost of messages is given by eij = 0:001 * d3ij .
The hosts have the same initial power and
messages are generated for hosts to one gateway
host. The horizontal axis is the ratio between the
lifetime of the max-min zPmin max-min
algorithm and the optimal lifetime, which is
computed offline.
3 Analysis of the Max-min zPmin Algorithm
In this section we quantify the experimentalresults from the previous section in an attempt to
formulate more precisely our original intuition
about the trade-o_ between the minimal power
routing and max-min power routing. We provide
a lower bound for the lifetime of the max- min
zPmin algorithm as compared to the optimal
solution. We discuss this bound for a general
case where there is some cyclicity to the
messages that flow in the system and then show
the specialization to the no cyclicity case.
Suppose the message distribution is regular, that
is, in any period of time [t1; t1 + ), the message
distributions on the nodes in the network are the
same. Since in sensor networks we expect some
sort of cyclicity for message transmission, we
assume that we can schedule the message
transmission with the same policy in each time
slice we call . In other words, we
partition the time line into many time slots [0; );
[; 2); [2; 3); . Note that is the lifetime
of the network if there is no cyclical behavior in
message transmission. We assume the same
messages are generated in each slot but their
sequence may be different. Let the optimal
algorithm be denoted by O, and the max-min
zPmin algorithm be denoted by M. In M, each
message is transmitted along a path whose
overall power consumption is less than z times
the minimal power consumption for thatmessage. The initial time is 0. The lifetime of the
network by algorithm O is TO, and the lifetime
by algorithm M is TM. The initial power of each
node is: P10, P20, P30, ., P(n-1)0, Pn0. The
remaining power of each node at TO by running
algorithm O is: P1O, P2O, P3O,, Pn-1O, PnO. The
remaining power of each node at TM by running
algorithm M is: P1M, P2M, P3M,, Pn-1M, PnM.
Let the message sequence in any slot be m1;m2;
;ms, and the minimal power consumption to
transmit those messages be P0m1 , P0m2 , P0m3 ,,
P0ms .
Theorem 2 The lifetime of algorithm M satisfies
TM
+
Proof:We have
ko = kM +
Mmk= PM
where MTM is the number of messagestransmitted from time point 0 to TM. PMmk is
the power consumption of the k-th messageby running algorithm M. We also have:
ko = ko +
omk= Po
where MTO is the number of messagestransmitted from time point 0 to TO. POmk isthe power consumption of of the k-thmessage by running algorithm O.
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Since the messages are the same for any two
slots without considering their sequence, we can
schedule the messages such that the message
rates along the same route are the same in the
two slots (think about divide every message into
many tiny packets, and average the message rate
along a route in algorithm O into the two
consecutive slots evenly.). We have:
omk=
. omk=
. omk
And
Mmk=
Mmkj
So we have:
Po= ko+
. omk
And
PO = PM PMmkj is the power consumption of the
k-th message in slot j by running algorithm M.
We also have the following assumption and the
minimal power of P0mk. For any 1 j TM/ and
k, we have only one corresponding l,
Then
PM kM+
. omk
Thus
kM+
. omk
ko+
. omk
We have
TM
+
Theorem 2 gives us insight into how well themessage routing algorithm does with respect to
optimizing the lifetime of the network. Given a
network topology and a message distribution, TO,
, ko, Mk are all fixed in Equation
3. The variables that determine the
actual lifetime are kM and z. The smaller kM 3 is, the better the performance lowerbound is. And the smaller z is, the better the
performance lower bound is. However, a small z
will lead to a large kMThis explains the trade-off between minimal
power path and max-min path.Theorem 2 can be used in applications that
have a regular message distribution without the
restriction that all the messages are the same in
two different slots. For these applications, theratio between and Ps 0mk must be changed
to mk, where P0mk is the minimalpower consumption for the message generated in
a unit of time.
Theorem 3 The optimal lifetime of the
network is at most
where tSPT and
PSPT Ph are the life time of the network and
remaining power of host h by using the least
power consumption routing strategy. Ph is the
initial power of host h.
Proof:
tOPT
= /(
)=
4 CONCLUSIONS
We have described several online algorithms
for power-aware routing of messages in large
net- works dispersed over large geographical
areas. In most applications that involve ad-hoc
networks made out of small hand-held
computers, mobile computers, robots, or smart
sensors, battery level is a real issue in the
duration of the network. Power management can
be done at two complementary levels (1) during
communication and (2) during idle time. We
believe that optimizing the performance of
communication algorithms for power
consumption and for the lifetime of the network
is a very important problem. It is hard to analyze
the performance of online algorithms that do notrely on knowledge about the message arrival and
distribution. This assumption is very important
as in most real applications the message patterns
are not known ahead of time. In this paper we
have shown that it is impossible to design an on-
line algorithm that has a constant competitive
ratio to the optimal offline algorithm, and we
computed a bound on the lifetime of a network
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whose messages are routed according to this
algorithm. These results are very encouraging.
We developed an online algorithm called the
max-min zPmin algorithm and showed that it had
a good empirical competitive ratio to the optimal
o_-line algorithm that knows the message
sequence. We also showed empirically that max-
min zPmin achieves over 80% of the optimal
(where the optimal router knows all the messages
ahead of time) for most instances and over 90%
of the optimal for many problem instances. Since
this algorithm requires accurate power values for
all the nodes in the system at all times, we
proposed a second algorithm which is
hierarchical. Zone-based power-aware routing
partitions the ad-hoc network into a small
number of zones. Each zone can evaluate its
power level with a fast protocol. These power
estimates are then used as weights on the zones.
A global path for each message is determined
across zones. Within each zone, a local path forthe message is computed so as to not decrease
the power level of the zone too much. Finally,
we have developed a distributed version of the
max-min zPmin, in which all the decisions use
local information only, and showed that this
algorithm outperforms significantly a distributed
greedy-style algorithm.
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