, and
µ A i ,B l = T l2 .λ A i ,B l
. Then, the MINLP problem can be
re-formulated into the equivalent MILP problem as shown below. We maximize lifetime
T l2
,s.t. ((4.24)-(4.27)).
T l2
withT l2 , V A A k ,B l
i ,A j , V A A k ,B l
i ,B l ≥ 0
,V A A k ,B l
i ,A j ∈ υ A,A , V A A k ,B l
i ,B l ∈ υ A,B
, and1 ≤ i, j, k ≤ M, i 6 = j, k 6 = j, 1 ≤ l ≤ B
.Since, we have only one sink in the network, the network of basestations can form an
aggregation tree toward this common sink. The ow from a basestation can be splitted and
send over multiple routes toward the sink. The ow problem to extend network lifetime at
levelthreecanbewritteninsimilarfashionas(4.9)to(4.12) withtheirappropriatesubscripts
(notethatinthiscase,allthedatagatheredatdierentbasestationsissenttoacommonsink
and hence, the optimal ow solution formulation will results in an NLP formulation (which
can be relaxed using same technique as presented earlier to an equivalent LP formulation),
and is therefore,not presentedhere.
4.7 LEAD-ADP: The LEAD Actuator Discovery Protocol
In order to remove the mixed-integer (MI) component from the MILP, we consider the
fol-lowingdistributed learningmechanismthathelpsinselecting actuators foreach sensorinthe
network. We propose a framework which is tailored toward a standard behavior for most
deployment scenarios, aiming to satiate the time-stringent requirements and energy ecient
resourceutilizationinapurelydistributedfashion[C-1]. Theproposalconsistsofthreephases:
the learning phase, thecoordination phase,andthe failure-and-recovery phase. Inthe
follow-ing, we detailthe three phases.
4.7.1 The Learning-phase
The learning-phase starts during the initial deployment stage when the sensors locate the
neighboring actuators using a one-hop broadcast. The nding of the "optimal-actuator
at-tachment" for eachsensor node isdone through anovelprotocol calledADP.
4.7.1.1 Actuator-discovery Protocol (ADP)
When a sensor node is turned on, it should rst determine an actuator node as the nal
destination. For this end,a sensornode transmits abroadcastmessage named
AttachRequest (cost, M j , C)
to its one-hop neighbors as shown in Figure 4.3. A neighboring node upon receiving an
attach-requestmessagechecksthatithassentanattach-requestintheperiod
T n
(application specic),ifithasalreadysentabroadcasttoitsneighbors,itwillwaitforareplyuntiltimeout.Otherwise, itrepeatsthisprocedureunlesstheprobereachesan actuator. Thereplymessage
named
AttachReply i (cost, M j , A i )
from theactuator follows theprobe and terminates at its origin, dening a discrete path to
thesensor node. If a node receives multiple replies, it chooses a destination actuator based
ontheoutcome of acost function.
InAlgorithm4.1,wehaveinducedacontrolproceduretoobtainapromisedQoSintermsof
delayandenergyconsumption. Wehaveassignedthehop-counttothisfunctiontorestrictthe
ACTOR NODE
Sensor Nodes
AttachRequest
Figure4.3: AttachRequest bysensors at thestart ofADP
search probe(referredas'C').Thishop-count can be treatedasa functionofsensor-actuator
node ratio in the network to limit unnecessary broadcast and also keeping the chances of
actuator-discovery well alive (leaving the issue as implementation concern). We don't take
into account the distance between a sensor and its associated neighbors because theenergy
required to transmit to a node inits sensing radius is a constant (no powercontrol assumed
for transmissions). ADPproducesloop-free pathsto theactuator nodes, asstated below.
LEMMA 1. The next-hop selected by a sensor with ADP has a dened optimal path to
the actuator node, Algorithm. 4.1.
Asdepicted by Figure4.4, now a sensornode hassome dened pathsto route its sensed
datatotheactuatornodesbysimplyforwardingittooneofitsone-hopneighbors(immediate
nextnodeinthepathtotheactuator),andtheactuatoralsokeepsthedenedpathtothenode
(building itstree structurefor thelocalizedcluster). Inasimilar fashionallthenodesreserve
an optimal path to their nearest actors as shown inFigure 4.5, forminga local cluster, thus
giving us the initial deployment in theform of distributed clusters. The cluster information
availableat the actuator will beusedfor scheduling ina later section.
4.7.1.2 Correlation Trees
Once all the nodes have dened paths to their attached actuator, the actuator rearranges
all the paths to exploit correlation properties of the SANETs. As shown in Figure 4.6, the
actuator rearranges all the paths inthe depth-rst arrangement order. In this way, we have
all the one-hop sensor nodes as the rst children of the actuator node, so on and so forth.
This gives a depth-rst search tree structure. All the sensor-nodes have dened identities
(names, address, etc). Butwhen acluster is created and organized into thetree form bythe
actuator,itassignstemporaryaddressestothesensornodesandkeepsthemappingwithitself.
As depicted inAlgorithm 4.2 oncethe tree structure is maintained we dene the temporary
addresses of nodes by addressing all the nodes on the same hop-count rst, following their
Algorithm 4.1LEAD-ADP
Pseudo-code executed by all the sensor nodes
N i
during initial deployment-phase.Initially:
cost =
∞
attached-actuator =
∞
C = constant (the trade-off is explained in Section 4.7.1.1).
A i
= Identity of the Actuator.For any sensor node
N i
do
ActorDiscovery
() {if cost (
N i , A i
) =∞
thenfor each neighbor
M j
ofN i
doSend
AttachRequest
(cost, M j , C
)Receive
AttachReply i (cost, M j , A i )
#Determine optimal Actuator, and the next-hop among the neighbors to reach
it.
for each
AttachReply
doif path(
cost, M j
) < path(cost, M j −1
) thenfor
N i
MinCost =path
(cost,M j
)AttachedActuator =
A i
next_ho_to_actuator =
M j
end-if
end-for
end-for
end-if
}
After deciding the actuator, each node sends a JoinRequest to its actuator.
send
JoinRequest
(A i
)The actuator sends a JoinAck back to the sensor node confirming cluster
joining.
send
JoinAck
(M j ,N i
)The procedure attach-request is implemented recursively as follows.
AttachRequest
(cost, M j , C
){if (
cost
!=∞
)return (
U pdateCost(cost), M j , A i
)else if (C != 0) then
for all neighbors
M j
ofN i
do
AttachRequest
(cost, M j , C − 1
)end-for
end-if
}
Actuator Reply to the broadcast messages from the one-hop away nodes contains the
following.
AttachRequest(cost, M j , C)← ActorReply
(cost = 1,A i
)U pdateCost()
is the part of the control semantics, and for this specific case,it is chosen to be hop-count
U pdateCost(cost)
{return cost + 1
}
Attach−Replies
not chosen due more hop−count Paths
Sensor−Node Actor−Node
Attach−Reply
Figure4.4: Actuator-replies (AttachReply)for correspondingAttachRequest messages
descendants aiming toward a breadth-rst addressing scheme. The mapping between the
actual node-address and temporary-address is managed by the actuator (
N add (i) → T add (i)
) inevery cluster. Thisstrategy helps in optimizing thesearch to theattached neighbors incase
of nodemobility andfailure, and exploitingthecorrelation properties (see[C-1] for details).
LEMMA 2. All the sensor-nodes are attached to the actuator withincreasing hop-count
in a depth-rst order, Algorithm. 4.2.
4.7.2 The Coordination-phase
The deployedsensornodesstart sensingthedistributedenvironment,andtransmit theirdata
through the dened path to the attached actuator. For the sensor-actuator coordination,
the actuator-attachment andthe paths obtained to routedata to the actors provide eective
energy optimizationforthesensornodes. There canbe twodeployment congurationsforthe
SANETs:
Static Deployment: Inthiscase,bothsensorandactuatornodesarestaticandthegain
is maximumdueto ecient routingof datato the acquired actuators.
Mobile Deployment: For mobiledeployment, wehave fourdierenttypesof
congura-tions (detailed inSection 4.7.3). Thelearning phaseformobile-case isessentiallythesameas
for thestatic-deployment. But at any point intime, thediscrete path to theactuator nodes
maychange due to themobility of the nodes. The purpose behind organizing thecluster in
theabove-explainedbehavioristoexploitthecorrelationproperties(see[C-1])oftheSANETs
not only at the data-centric levelbut also at thenode-centric level (direct-addressing).
4.7.3 Failure and Recovery-phase
We assumed that every sensor node has a pre-dened maximum battery life-time with a
minimumthresholdindicatingfailureinnearfuture. TheFailureandRecovery-phasemonitors
this time line and inform the actuator before the actual failure to take a few precautionary
measures which includes: (i) exploiting the local cluster for an alternate path to nodes that
lost their routes to the actuator. (ii) do nothing ifthere was no further attached node. (iii)
θ = (0, 2π)
Actor Node
Sensor Nodes
Figure4.5: The LocalCluster formulated at thetermination ofADP
update the cluster information of the attached-actuator for local management as shown in
Figure 4.7. Furtherdetails can be found in[C-1].
To decide on the optimal actuator, we consider thatthe cost function is set to min. hop
count and the actuators chosen by sensors are optimal inmin. hop sense. An advantage of
setting the cost-function to min. hop routing is that the lower-tier (level one) of our
hetero-geneousnetwork can be organized into clusters, where each cluster iscentrally managed by an
actuator. It will also result inthe disappearance of the mixed-integer (MI) component from
the optimization problem and the resultant is a relaxed linear optimization problem (LP)
which iscomparatively easierto solve[94 ]. In thisfashion,asensorcan receive itsscheduling
information (detailed in Section 4.9) by its mapped destination-actuator that corresponds to
the optimal (s.t. energy constraints)routing solution, andhence, canresultintherealization
of optimal network lifetime in practice. We denote theresulting destination for a sensor via
the above mapping as
d (i)
. Therefore we have,µ s i ,d(i) = T
, andµ s i ,A l = 0
forA l 6 = d (i)
.Then, we can nd a routing solution by replacing