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Research ArticleA Proactive Complex Event Processing Method forLarge-Scale Transportation Internet of Things

Yongheng Wang and Kening Cao

College of Information Science and Engineering Hunan University Changsha 410082 China

Correspondence should be addressed to Yongheng Wang yhwangcngmailcom

Received 25 December 2013 Revised 23 January 2014 Accepted 18 February 2014 Published 23 March 2014

Academic Editor Gelan Yang

Copyright copy 2014 Y Wang and K CaoThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The Internet ofThings (IoT) provides a newway to improve the transportation systemThe key issue is how to process the numerousevents generated by IoT In this paper a proactive complex event processing method is proposed for large-scale transportation IoTBased on a multilayered adaptive dynamic Bayesian model a Bayesian network structure learning algorithm using search-and-score is proposed to support accurate predictive analytics A parallel Markov decision processes model is designed to supportproactive event processing State partitioning and mean field based approximation are used to support large-scale application Theexperimental evaluations show that this method can support proactive complex event processing well in large-scale transportationInternet of Things

1 Introduction

The Internet of Things (IoT) bridges the gap between thephysical world and its representationwithin the digital worldIn recent years with the rapid development of informationand communication technologies bandwidth and storage areno longer restricted in IoT applications The key issue is howto process the massive events produced by large-scale IoTapplications (an eventmeans an atomic occurrence of interestin time)

In IoT applications event processing engines need toprocess events that arrive from various kinds of sources suchas sensors RFID readers and GPS The events generatedby devices directly are called primitive events The semanticinformation inside primitive events is quite limited In realapplication users pay more attention to high level infor-mation such as business logic and rules For example eachreading operation of the RFID reader at a garage generatesa primitive event but complex events like ldquothe car leaves thegaragerdquo are the kind of events that users are really concernedwith To get complex events many primitive events needto be combined based on some rules In IoT applicationsystems business logic is converted into complex eventsand business logic is processed based on complex events

detection Complex event processing (CEP) [1] is used toprocess massive primitive events and get valuable high levelinformation from them As an example in logistics industryCEP is used to track the goods and trigger some actions whenexception is found

In many real-time IoT applications events are uncertaindue to some factors such as measuring inaccuracy signaldisturbance or privacy protection Usually we use probabil-ities to process such uncertainty Therefore it is necessary todevelop probabilistic event processing engine

The traditional type of the event processing is reactiveprocessing which means that actions are triggered by eventsor by the system states A proactive event processing system isable to mitigate or eliminate undesired future events or statesor to identify and take advantage of future opportunities byusing prediction and automated decision making methods[2] For example in a transportation system we can predictsome possible congestion states and take some actions tomitigate or eliminate the congestion states The proactiveevent processing systems use predictive analytics (PA) tech-nology which predicts future events or system states throughanalysis of historical events The system also uses iterateddecision processes (DP) technology which analyzes systemstates and selects appropriate actions to achieve expected

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2014 Article ID 159052 8 pageshttpdxdoiorg1011552014159052

2 International Journal of Distributed Sensor Networks

states The CEP PA and DP technologies have been studiedwidely but there are few papers about how to integrate themtogether to support proactive event-driven system Proactiveevent processing in large-scale transportation IoT needs toprocess massive historical events and analyze complex statesiteratively which makes most of the existing algorithmsunable to be used directly Furthermore proactive eventprocessing systems need high performance since they usuallyhave to take actions in time

In this paper we propose a proactive complex event proc-essing (Pro-CEP) method for large-scale transportation In-ternet of Things We designed a multilayered adaptive dy-namic Bayesian network (mADBN)model for predictive ana-lytics Based on probabilistic complex event processing ourmethod uses concurrent actions Markov decision processes(MDP) to integrate CEP and PA

2 Related Works

21 CEP and Probabilistic CEP Complex event processingdetects complex events based on a setsequence of occur-rences of primitive events by monitoring the event flowcontinuously Etzion and Niblett introduced the conceptarchitecture and methods of complex event processing intheir book [3] Event processing agent (EPA) is a componentthat applies some rules to generate complex events as outputbased on a set of input events Event processing network(EPN) is a network of a collection of EPAs event producersand event consumers linked by channels The network inEPN is used to describe the event processing flow executionLuckhamfirst introduced the event processing network in thefield of modeling [1]

Most of the CEP methods in active databases and RFIDapplications use fixed data structures such as tree directedgraph or Petri-Net Those methods cannot extend eventquery language according to the change of requirement oroptimize event query language flexibly SASE [4] is a highperformance complex event processing method which usesnondeterministic finite automaton (NFA) Recently there issome work about improving the SASE method

Most probabilistic CEP engines are based on sequentialvariants of probabilistic graphical models such as hiddenMarkov models dynamic Bayesian Networks and con-ditional random fields Recently some probabilistic CEPmethods based on NFA are proposed In the work of [5] adata structure called chain instance queues is used to detectcomplex events with a single scanning of probabilistic eventstream In another paper [6] an optimized method basedon SASE is used to calculate the probability of complexevents and to obtain the confidence value of the complexpatterns given by user against uncertain raw input eventstream Comparedwith our work these CEPmethods are notintegrated with PA and DP to support proactive application

22 Predictive Analytics with Bayesian Networks Predictiveanalytics applies some statistical and data mining techniquessuch as clustering classification and regression In the caseof predictive analytics methods for complex event data some

attributes of the monitored system are predicted based on thepreviously monitored events

Recently Bayesian network (BN) has been used in predic-tive analytics Castillo et al used BN to predict the randomcharacter of the total mean flow level and the variability oforigin-destination pair flows [7] In the work of Pascale andNicoli an adaptive BN was proposed in which the networktopology changes according to the nonstationary featuresof traffic [8] Gaussian mixture model (GMM) was used todescribe the joint probability distribution between the causenodes and the effect node in a Bayesian network In the workof Hofleitner et al dynamic Bayesian network (DBN) is usedin PA and a model based on hydrodynamic traffic theory isalso proposed to learn the distribution of vehicles on arterialroad segments [9] Compared with our work these methodsare not designed for large-scale IoT applications and cannotprocess massive event data in proactive event-based system

23 Proactive Event Processing andMarkov Decision ProcessesRecently many proactive applications have been developedfor example proactive security systems proactive routing inmobile wireless networks and proactive service level agree-ment negotiation in service oriented systems In the work ofEngel et al a proactive event-driven computing frameworkbased on CEP PA and Markov decision processes (MDP)is proposed [2 10] In this framework the event processingmodel is extended and two more types of agent are includedpredictive agents which can predict future uncertain eventsbased on the prediction models and proactive agents whichcan select the best proactive action that should be taken

MDP has been studied for many years and some variantsemerged recently In the area of large-scale IoT the mainchallenge is the combination explosion problem caused bylarge state space Mainly there are two research directions onthis problem The first one tries to simplify the problem byusing the information from the application domain includ-ing state aggregation methods time aggregation methodsand action elimination methods These methods are relatedto specific application domain and it is not easy to finda common solution In the second direction approximatemethods are developed including approximate dynamicprogramming dynamic programming based on events andselective approximation The key issue in these methods ishow to approximate the value function during the optimiza-tion processWhen applied to large-scale IoTMDPhas largersize and some new properties The model design and large-scale calculation become a new challenge Compared withour work current MDP methods are not combined withCEP and cannot process the large state space in large-scaleproactive event-based system

3 Backgrounds

31 System Architecture The system architecture of our workis shown in Figure 1 Raw events are generated by devicessuch as RFID reader radar and GPS We assume the eventscan be imprecise because of the limitation of measuringaccuracy or signal disturbance The probabilistic raw events

International Journal of Distributed Sensor Networks 3

PEPA

PEPA

PEPA

PEPA

PEPA

Probabilistic event processing

Devices

PRA

Proactive

iii

Event DBRaw

events

PA withmultilayered

adaptivedynamicBayesiannetwork

PRA

PRA

States

Decision

network

maker

executor

Figure 1 System architecture

are processed by the probabilistic event processing network(PEPN) which is composed of many interconnected proba-bilistic event processing agents (PEPA) Different PEPAs canbe connected since hierarchical complex event is supportedThe PA component can predict the system states from thecomplex events based on the mADBN model Complexevents are saved to event database and the historical data canbe used to train the models in PA components The decisionmaker selects appropriate actions according to the predictedstates and assigns some proactive agents (PRA) to execute theactions

32 Event Model and Probabilistic CEP

Definition 1 (primitive event) A primitive event in a streammeans an atomic occurrence of interest in time A probabilis-tic primitive event is represented by ⟨119860 119879Pr⟩ where 119860 isthe set of attributes and 119879 is the timestamp that the eventoccurs Pr is the concrete probability value used to presentthe occurrence probability of the event

The probability value represents the possibility that anevent is converted accurately from truthful data of nature todigital data used for computing in electronic devices

Definition 2 (complex event) A complex event is a combina-tion of primitive events or complex events by some rule Aprobabilistic complex event is represented by ⟨119864 119877TsPr⟩where 119864 is the set of elements that compose the complexevent 119877 is the rule of the combination Ts is the time spanof the complex event and Pr is the probability value

The main complex event patterns in our work includeALL ANY COUNT and SEQ In this paper the COUNTpattern can be used to count the number of vehicles in aspecified area during specified time span The SEQ patterncan be used to represent the moving path of a vehicle Thedetailed meaning of the patterns can be found in [3] Thosepatterns can be composed to create hierarchical complexpatterns

In a large-scale IoT application we may need to sup-port distributed event streams processing In this paper weassume the primitive events from different event streams areindependent In the same event stream someprimitive eventshave Markov property which means that the probability ofnext event is only related to the current event in the sequencebut has nothing to do with previous events Like the work of[6] we use condition probability table (CPT) to save and sortthe condition probability

We extended the SASE method to support probabilisticCEP by adding probability value for each event in the activeinstance stacks (AIS) Detailed method and algorithm can befound in another paper of the same author [11]

4 Proactive CEP Method

41 Predictive Analytics Model ThemADBNmodel is shownin Figure 2 In this model there are a state plane and a setof location planes Each plane is represented by an adaptivedynamic Bayesian network with two dimensions time andspace In the state plane nodes denote the states of the systemobserved at different time instants andor spatial locationsedges being their probabilistic relations In Figure 2 thedirected edges mean that the state of (119894 119905) depends on a setof other states before time 119905 The term ldquodynamicrdquo in mADBNmeans that we are modeling a dynamic system The termldquoadaptiverdquo means that the graph structure is created based onmachine learning from historical data Each location planerepresents the location change of a vehicle (moving path)The directed edges represent the transaction probability fromone location to another and the directed edges with solid linerepresent the real paths

The graph structure of the state plane can be learnedbased on analysis of the vehicle location planes Given a nodeset 119881 and a constraint set 119862 the Bayesian network structurelearning problem is to find an optimized set of edges and anoptimized set of distribution parameters Mainly there aretwo types of methods for Bayesian network structure learn-ing constraint-based method and search-and-score methodConstraint-basedmethod checks the conditional dependencein data systematically and creates the network structure basedon the dependence Search-and-scoremethod creates reason-able network structure based on a score function Search-and-score method gets better result but the performance isnot good for massive data In this paper we combine thetwo methods together Global CPT can be created usingthe historical data in object location planes Candidates areselected based on global CPT using constraint-basedmethodand then a search-and-score algorithm is used to learn thestructure of Bayesian network In our method local CPT isfirst created for each object plane and then all local CPTsare summed up and normalized to get the global CPT Themethod was implemented with a MapReduce algorithm tosupport parallel calculation

The main idea of the structure learning algorithm usingsearch-and-score is to maximize the score function Like


Timeindex

Timeindex

t

SpaceSpace

1

N

i

t

StateObject location

t minus NTt minus NT

t minus 1 t minus 1

Figure 2 The mADBN model

the work of [12] we use Bayesian information criterion (BIC)score function which is defined as follows

SBIC (119863 119866Θ) = log119875 (119863 | Θ 119866) minus119889

2log119898 + 119900 (1) (1)

where 119863 is the data set 119866 is the graph structure Θ is themaximum likelihood distribution parameters for 119863 119889 is thenumber of edges and 119898 is the sample size per vertex Thealgorithm has an expansion stage and a contraction stageDuring the expansion stage edges that can increase the scorefunction are added During the contraction stage edges areremoved if that does not decrease the score function Thecandidate parent vertexes for a specific vertex are selectedaccording to the CPT

42 Predictive Analytics Method In the mADBN model ofFigure 2 let 119891

119894119905represent the flow state of node (119894 119905) and

let pa(119894 119905) represent all the parent nodes of (119894 119905) 119873119875is the

number of nodes in pa(119894 119905) The set of flow states for pa(119894 119905)is 119865pa(119894119905) = 119891

119895119904 (119895 119904) isin pa(119894 119905) The joint distribution of all

nodes in the state plane can be expressed as follows

119901 (119865) = prod119894119905

119901 (119891119894119905| 119865pa(119894119905)) (2)

According to the Bayesian formula the conditional prob-ability 119901(119891

119894119905| 119865pa(119894119905)) can be calculated by

119901 (119891119894119905119865pa(119894119905)) =

119901 (119891119894119905 119865pa(119894119905))

119865pa(119894119905) (3)

The joint distribution 119901(119891119894119905 119865pa(119894119905)) is modeled with

GMM as follows

119901 (119891119894119905 119865pa(119894119905)) =

119872

sum119898=1

120572119898119892119898(119891119894119905 119865pa(119894119905) | 120583119898 119862119898) (4)

where 119872 is the number of nodes and 119892119898(sdot | 120583

119898 119862119898) is the

119898th Gaussian distribution which has a (119873119875+ 1) times 1 vector of

mean values 120583119898and a (119873

119875+ 1) times (119873

119875+ 1) covariance matrix

119862119898 Like the work of [13 14] we use the EM algorithm to

infer the parameters 120572119898 120583119898 119862119898119872

119898=1from the historical data

The conditional distribution 119901(119891119894119905

| 119865pa(119894119905)) can be derivedfrom 119901(119891

119894119905| 119865pa(119894119905)) and the estimate 119891

119894119905can be calculated

from 119865pa(119894119905) using the minimum mean square error (MMSE)method

43 Decision Making with MDP According to the propertiesof proactive complex event processing in IoT application weextend the traditional MDP as follows

Definition 3 (parallel MDP for proactive complex event proc-essing) A parallelMDP for proactive complex event process-ing is represented as ⟨119868 119878

rarr

119860 119875 119877 119864119888 119862 119879119888⟩ where 119868 denotesthe finite set of agents that process actions and 119878 denotesthe set of states with a special initial state 119878

0rarr

119860= times119894isin119868119860119894

denotes the set of actions where 119860119894is the action from the

119894th agent 119875 119878 times 119860 times 119878 rarr [0 1] denotes the set ofstate transformation functions where 119875(119904 120572 1199041015840) representsthe probability that state 119904 transforms to 1199041015840 with the executionof action 120572 119877 119878 rarr Re denotes the set of reward functions(Re means the set of real numbers) Every (119904 120572) isin 119878 times 119860

satisfiessum1199041015840isin119878119901(119904 120572 119904

1015840) = 1 119864

119904is the set of complex events in

IoT which affects the system states 119862 is the context of eventand agents act according to different context119879

119904 119878times119864

119904times119878 rarr

[0 1] denotes the transforming probability which representsthe affection of complex events to the system states

The proactive event processing system starts from anoriginal state and selects one or more actions executed byagents according to the policy The execution of actions


Normal nodeImportant node

Figure 3 Network partition based on important nodes

changes the primitive events and the transforming probabilityvalues fromold states to new states are calculated based on theanalysis of the complex eventsThe key issue ofMDP is to finda policy 120587 119878 rarr 119860 which reflects a state to a set of actionsThe best policy maximizes the total rewards The selection ofpolicy is based on the following equation (value function)

V120587 (119904) = 119903 (119904 120587 (119904)) + 120574 sum

1199041015840isin119878

119901 (1199041015840| 119904 120587 (119904)) V120587 (119904

1015840) (5)

The update of policy is based on the following equation

120587lowast(119904) = arg max

119886isin119860

(119903 (119904 119886) + 120574 sum

1199041015840isin119878

119875 (1199041015840| 119904 119886) V

120587(1199041015840))

(6)

where 120574 is the decay factor In traditional MDP actions areexecuted in order Recently some work of parallel MDP isproposed in which actions are partitioned into groups andgroup of actions executed parallel without affecting eachother In this paper the MDPmodel executes actions parallelto the same state and all actions work together to transformthe state into an expected one Our MDPmethod is based onthe following assumptions

Assumption 4 The vehicles in large-scale IoT can be parti-tioned based on context and each group is related to a substateof the systemWe need to consider the substates of the systembut not the state of each vehicle

An event context is a specification of conditions thatgroups event instances so that these instances can be pro-cessed in a related manner For example when processingthe traffic congestion problem the traffic flows at roadsor junctions are substates and the system global states arecomposed of all substates

Assumption 5 In large-scale transportation IoT the state ofa node depends on the states of its neighbors (the neighborshere mean the nodes that are linked with the current nodewithin some distance)

Assumption 6 In large-scale transportation IoT nodes canbe partitioned into two classes important and normal

The nodes whose states we want to control proactively areimportant nodes The network can be partitioned based onimportant nodes and the state of important nodes can bechanged by changing the state of their neighbors as shownin Figure 3

According to Assumptions 4 5 and 6 a new variable119866 =

(119881 119864)which represents the structure of subgraphs is added tothe parallel MDP model where 119881 is the set of vertexes and 119864is the set of edges An edge (119894 119895) exists which means that thestate of node 119894 affects the state of node 119895

Definition 7 (neighbor state nodes) For any state node 119894 isin 119881the neighbor state nodes are119873(119894) = 119895 isin 119881 | 119889

119894119895le 119896 where

119889119894119895is the distance of nodes 119894 and 119895 and 119896 is a threshold value

Definition 8 (state transformation decomposition) Assumethere are 119899 substate nodes and 119899 corresponding actionsaccording to the assumptions we get

119901 (1199041015840| 119904 119886) =

119899

prod119894=1

119875119894(1199041015840

119894| 119904119873(119894)

119886119894) (7)

where 119904119873(119894)

= 119904119895| 119895 isin 119873(119894)

Definition 9 (reward decomposition) Assume there are 119899

substate nodes and 119899 corresponding actions the total rewardcan be written as follows

119903 (119904 119886) =

119899

sum119894=1

119903119894(119904119873(119894)

119886119894) (8)

A policy 120587 can also be decomposed as (1205871 1205872 120587

119899)

Definition 10 (occupation measure) Let S be the state spaceand let 1199090 isin S be the original state of MDP The occupationmeasure 119875

1199090120587120574

S rarr [0 1] is defined as follows

1198751199090120587120574

(119910) = (1 minus 120574)

infin

sum119905=0

120574119905119875120587(119878119905= 119910 | 119878

0= 1199090) (9)

where 119910 isin S With occupation measure the value functioncan be rewritten as follows

119881120587(1199090) =

1

1 minus 120574sdot sum119910isinS

1198751199090120587120574

(119910) sdot 119903 (119910 120587 (119910)) (10)

The key issue is to find a solution to calculate 119875120587(119878119905= 119910 | 119878

0=

1199090) approximately According to the decomposition we have

defined it can be inferred from 119901119894(119909119905

119894| 119909119905minus1

119873(119894) 120587(119909119905minus1

119873(119894))) Now

the problem is to find an approximation 119866119905119894

120587(119909119905

119894| 119909119905minus1

119894) which

satisfies

119862119905

120587(119910 | 119909

0) = sum

119904119905minus1

119866119905

120587(119910 | 119909

119905minus1) sdot 119862119905minus1

120587(119909119905minus1

| 1199090)

=

119899

prod119894=1

sum

119909119905minus1

119894

119866119905119894

120587(119910119894| 119909119905minus1

119894) sdot 119862119905minus1119894

120587(119909119905minus1

119894| 1199090

119894)

(11)


where 119862 is the approximation of the conditional probability119875120587(119878119905= 119910 | 119878

0= 1199090) defined by 1198621

120587(119910 | 119909

0) = prod

1198941198661119894

120587(119910119894| 1199090

119894)

and forall119905 119862119905120587(119910 | 119909

0) = prod

119899

119894=1119862119905119894

120587(119910119894| 1199090

119894)

As an effective method for analyzing large and complexstochastic models mean field theory is widely used inmany areas Using mean field theory the effect of all otherindividuals on any given individual is approximated by asingle averaged effect Like the work of Sabbadin et al [15]we applied mean field approximation which approximates amultidimensional distribution 119875(119906

1 1199062 119906

119898) as the joint

distribution 119866 of 119898 independent variables 1199061 119906

119898 119866

should be as close to 119875 as possible according to Kullback-Leibler divergence

KL (119866119875) = 119864119876[log(119866

119875)] (12)

For state 1 (1 is the first time point and 0 is the start point)we get the following approximation using Kullback-Leiblerdivergence

1198661

120587= arg min

1198751120587

KL (1198661120587(1198781| 1198780)

sdot1198750(1198780) | 119875120587(11987811198780) sdot 1198750(1198780))

(13)

After state transformation decomposition the approximationcan be written as

1198661119894

120587(1199091

119894| 1199090

119894)

prop exp1198641199010 [log119901

119894(1199091

119894| 1199090

119894 1198780

119873(119894)119894 120587119894(1199090

119894 1198780

119873(119894)119894)) ]

(14)

The rest of the iteration is similar to (14) The data processingservers include a master node and 119873 slave nodes The mainiteration is executed at themaster node and the calculation ofsubstates is partitioned into slave nodes and executes parallel

5 Experimental Evaluations

We developed a transportation IoT simulation system basedon the road traffic simulation package SUMO [16] Thesystem supports mobility trace of vehicles by using anOpenStreetMap [17] roadmap of BeijingOn the roads we setmany virtual induction loops which can detect vehicles thatpass corresponding areas The virtual RFID or GPS readersare implemented using the TraCI interface of SUMO to getthe induction loop variables Each virtual induction loopcovers a region We selected 114 junctions from the map andset 160 thousand vehicles in the system In order to simulatereal traffic system a series of rules are defined Each vehiclehas a home location and an office location A vehicle V

119894runs

between home and office with probability 119901119894 The vehicles

also go to other places such as supermarket and hospitalwith corresponding probabilities Based on this simulationsystem we evaluated the precision and performance of Pro-CEP We used 5 Lenovo ThinkServer RD series servers with4GBmemory as a cluster and the operating system is Ubuntu12

Table 1Deviation of twomethodsThe average percent is calculatedby ((average deviation)(average observed vale)) lowast 100

DeviationABN Pro-CEP

Max 286 122Min 16 12Average 12633 715Average percent 1644 93

0

500

1000

1500

2000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Traffi

c flow

ObservedABNPro-CEP

Time (times60 s)

Figure 4 PA accuracy for a typical node

We first run the simulation for many times to get thehistorical data of the vehicle paths In the first experiment theaccuracy of our PAmethod is compared with ABN [8] whichuses Bayesian network but has no vehicle location planes likeour model The result is shown in Figure 4 and Table 1 Fromthe figure we can see that the accuracy of Pro-CEP is betterthan traditionalmethodABNThe reason is that Pro-CEPusethe object location plane to create a more precise Bayesiannetwork structure

In the next experiment we compared the mean conges-tion of the system with and without Pro-CEP Since we havenot found other methods that have the same function asPro-CEP no other method is compared The congestion ispartitioned into 10 levels where ldquo0rdquo means no congestionand ldquo9rdquo means the highest congestion The result is shownin Figure 5 We can see the mean congestion level reducedobviously when Pro-CEP is used The reason is that Pro-CEP can predict the congestion and take some actions toavoid it The reduction of congestion level is more obviouswhen the congestion level becomes high because the systemcan redirect more vehicles to light loaded nodes in suchcircumstance

In the next experiment we evaluated the performanceof Pro-CEP with different server number and data size Theimportant node number is fixed at 30 and Bayesian modelconstructing time is not included The result is shown inFigure 6 As we can see the running time increases whenthe vehicle numbers become larger The reason is that morevehicles need to be rerouted which increases the calculationof the algorithmThe performance for 5 servers is higher than


Time (times60 s)

0

2

4

6

8

10

1 4 7 10 13 16 19 22 25 28 31

Con

gesti

on le

vel

DefaultPro-CEP

Figure 5 Mean congestion level over time

0

5

10

15

20

6 8 10 12 14 16

Runn

ing

time (

min

)

Vehicle number (times10000)

3 servers5 servers

Figure 6 Performance of Pro-CEP with different server numberand data size

3 servers and the running time of the former increases slowlybecause the parallel method can take advantage of multipleservers

We also evaluated the performance of Pro-CEP withdifferent server number and important node number Theresult is shown in Figure 7The vehicle number is fixed at 160thousand The result shows that the running time increasesobviously when the important node number becomes largerThe reason is that more important nodes means moresubstates in the parallel MDP which increases the calculationof the algorithm

From all the experiments we can see that Pro-CEP cansupport proactive complex event processing in large-scaletransportation Internet of Things The PA method gets highaccuracy based on themADBNmodel and Bayesian networkThe parallel MDP model has obvious effect for congestioncontrol in large transportation IoT The performance of Pro-CEP decreases when the vehicle number and important nodenumber become large butwe can get better performancewithmore servers

6 Discussions and Conclusion

In this paper we proposed a proactive complex event process-ing method for large-scale transportation Internet of Thingsbased on a novel mADBN model and parallel MDP A struc-ture learning algorithm using search-and-score is proposed

0

5

10

15

20

25

10 15 20 25 30 35

Runn

ing

time (

min

)

Important node number

3 servers5 servers

Figure 7 Performance of Pro-CEP with different server numberand important node number

to support accurate PA A GMM based approximation forBayesian network a state partition method and a mean fieldbased approximation method of parallel MDP are proposedto support large-scale transportation IoT The experimentalevaluations show that this method can support proactivecomplex event processing well in large-scale transportationInternet of Things

The performance and scalability of Pro-CEP still need tobe improved In the PAmethod the EMalgorithmneeds to beparallelized to improve scalabilityThemaster node in parallelMDP is the bottleneck and the iteration algorithm still needsto be parallelized further

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (no 61371116) and theHunan ProvincialNatural Science Foundation (no 13JJ3046)

References

[1] D C LuckhamThePower of Events An Introduction toComplexEvent Processing in Distributed Enterprise Systems AddisonWesley Boston Mass USA 2002

[2] Y Engel and O Etzion ldquoTowards proactive event-driven com-putingrdquo in Proceedings of the 5th ACM International ConferenceonDistributed Event-Based Systems (DEBS rsquo11) pp 125ndash136NewYork NY USA July 2011

[3] O Etzion and P Niblett Event Processing in Action ManningPublications Greenwich Conn USA 2010

[4] EWu Y Diao and S Rizvi ldquoHigh-performance complex eventprocessing over streamsrdquo in Proceedings of the ACM SIGMODInternational Conference on Management of Data pp 407ndash418Chicago Il USA June 2006

[5] X Chuanfei L Shukuan W Lei and Q Jianzhong ldquoComplexevent detection in probabilistic streamrdquo in Proceedings of the12th International Asia Pacific Web Conference (APWeb rsquo10) pp361ndash363 April 2010


[6] H Kawashima H Kitagawa and X Li ldquoComplex event proc-essing over uncertain data streamsrdquo in Proceedings of the5th international conference on P2P Parallel Grid Cloud andInternet Computing pp 521ndash526 2010

[7] E Castillo J M Menendez and S Sanchez-Cambronero ldquoPre-dicting traffic flow using Bayesian networksrdquo TransportationResearch B vol 42 no 5 pp 482ndash509 2008

[8] A Pascale andM Nicoli ldquoAdaptive Bayesian network for trafficflow predictionrdquo in Proceedings of the IEEE Statistical SignalProcessing Workshop (SSP rsquo11) pp 177ndash180 June 2011

[9] A Hofleitner R Herring and P Abbeel ldquoLearning the dynam-ics of arterial traffic from probe data using a dynamic Bayesiannetworkrdquo IEEE Intelligent Transportation Systems Society vol13 no 4 pp 1679ndash1693 2012

[10] Y Engel O Etzion and Z Feldman ldquoA basic model for proac-tive event-driven computingrdquo in Proceedings of the 6th ACMInternational Conference on Distributed Event-Based Systemspp 107ndash118 Busan Republic of Korea 2012

[11] Y H Wang and X M Zhang ldquoComplex event processing overdistributed probabilistic event streamsrdquo in Proceedings of the9th International Conference on Fuzzy Systems and KnowledgeDiscovery (FSKD rsquo12) pp 1489ndash1493 2012

[12] S Samaranayake S Blandin and A M Bayen ldquoLearning thedependency structure of highway networks for traffic forecastrdquoin Proceedings of the 50th IEEE Conference onDecision and Con-trol and European Control Conference pp 5983ndash5988 2011

[13] J J Verbeek N Vlassis and B Krose ldquoEfficient greedy learningof gaussian mixture modelsrdquoNeural Computation vol 15 no 2pp 469ndash485 2003

[14] N Kumar S Satoor and I Buck ldquoFast parallel expectationmax-imization for gaussian mixture models on GPUs using CUDArdquoin Proceedings of the 11th IEEE International Conference on HighPerformance Computing and Communications (HPCC rsquo09) pp103ndash109 June 2009

[15] R Sabbadin N Peyrard and N Forsell ldquoA framework and amean-field algorithm for the local control of spatial processesrdquoInternational Journal of Approximate Reasoning vol 53 no 1pp 66ndash86 2012

[16] M Behrisch L Bieker and J Erdmann ldquoSumomdashsimulation ofurban mobility an overviewrdquo in Proceedings of the 3rd Inter-national Conference on Advances in System Simulation pp 63ndash68 Barcelona Spain October 2011

[17] MHaklay andPWeber ldquoOpenstreetmap user-generated streetmapsrdquo IEEE Pervasive Computing vol 7 no 4 pp 12ndash18 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



states The CEP PA and DP technologies have been studiedwidely but there are few papers about how to integrate themtogether to support proactive event-driven system Proactiveevent processing in large-scale transportation IoT needs toprocess massive historical events and analyze complex statesiteratively which makes most of the existing algorithmsunable to be used directly Furthermore proactive eventprocessing systems need high performance since they usuallyhave to take actions in time

In this paper we propose a proactive complex event proc-essing (Pro-CEP) method for large-scale transportation In-ternet of Things We designed a multilayered adaptive dy-namic Bayesian network (mADBN)model for predictive ana-lytics Based on probabilistic complex event processing ourmethod uses concurrent actions Markov decision processes(MDP) to integrate CEP and PA

2 Related Works

21 CEP and Probabilistic CEP Complex event processingdetects complex events based on a setsequence of occur-rences of primitive events by monitoring the event flowcontinuously Etzion and Niblett introduced the conceptarchitecture and methods of complex event processing intheir book [3] Event processing agent (EPA) is a componentthat applies some rules to generate complex events as outputbased on a set of input events Event processing network(EPN) is a network of a collection of EPAs event producersand event consumers linked by channels The network inEPN is used to describe the event processing flow executionLuckhamfirst introduced the event processing network in thefield of modeling [1]

Most of the CEP methods in active databases and RFIDapplications use fixed data structures such as tree directedgraph or Petri-Net Those methods cannot extend eventquery language according to the change of requirement oroptimize event query language flexibly SASE [4] is a highperformance complex event processing method which usesnondeterministic finite automaton (NFA) Recently there issome work about improving the SASE method

Most probabilistic CEP engines are based on sequentialvariants of probabilistic graphical models such as hiddenMarkov models dynamic Bayesian Networks and con-ditional random fields Recently some probabilistic CEPmethods based on NFA are proposed In the work of [5] adata structure called chain instance queues is used to detectcomplex events with a single scanning of probabilistic eventstream In another paper [6] an optimized method basedon SASE is used to calculate the probability of complexevents and to obtain the confidence value of the complexpatterns given by user against uncertain raw input eventstream Comparedwith our work these CEPmethods are notintegrated with PA and DP to support proactive application

22 Predictive Analytics with Bayesian Networks Predictiveanalytics applies some statistical and data mining techniquessuch as clustering classification and regression In the caseof predictive analytics methods for complex event data some

attributes of the monitored system are predicted based on thepreviously monitored events

Recently Bayesian network (BN) has been used in predic-tive analytics Castillo et al used BN to predict the randomcharacter of the total mean flow level and the variability oforigin-destination pair flows [7] In the work of Pascale andNicoli an adaptive BN was proposed in which the networktopology changes according to the nonstationary featuresof traffic [8] Gaussian mixture model (GMM) was used todescribe the joint probability distribution between the causenodes and the effect node in a Bayesian network In the workof Hofleitner et al dynamic Bayesian network (DBN) is usedin PA and a model based on hydrodynamic traffic theory isalso proposed to learn the distribution of vehicles on arterialroad segments [9] Compared with our work these methodsare not designed for large-scale IoT applications and cannotprocess massive event data in proactive event-based system

23 Proactive Event Processing andMarkov Decision ProcessesRecently many proactive applications have been developedfor example proactive security systems proactive routing inmobile wireless networks and proactive service level agree-ment negotiation in service oriented systems In the work ofEngel et al a proactive event-driven computing frameworkbased on CEP PA and Markov decision processes (MDP)is proposed [2 10] In this framework the event processingmodel is extended and two more types of agent are includedpredictive agents which can predict future uncertain eventsbased on the prediction models and proactive agents whichcan select the best proactive action that should be taken

MDP has been studied for many years and some variantsemerged recently In the area of large-scale IoT the mainchallenge is the combination explosion problem caused bylarge state space Mainly there are two research directions onthis problem The first one tries to simplify the problem byusing the information from the application domain includ-ing state aggregation methods time aggregation methodsand action elimination methods These methods are relatedto specific application domain and it is not easy to finda common solution In the second direction approximatemethods are developed including approximate dynamicprogramming dynamic programming based on events andselective approximation The key issue in these methods ishow to approximate the value function during the optimiza-tion processWhen applied to large-scale IoTMDPhas largersize and some new properties The model design and large-scale calculation become a new challenge Compared withour work current MDP methods are not combined withCEP and cannot process the large state space in large-scaleproactive event-based system

3 Backgrounds

31 System Architecture The system architecture of our workis shown in Figure 1 Raw events are generated by devicessuch as RFID reader radar and GPS We assume the eventscan be imprecise because of the limitation of measuringaccuracy or signal disturbance The probabilistic raw events


PEPA

PEPA

PEPA

PEPA

PEPA


Devices

PRA

Proactive

iii

Event DBRaw

events

PA withmultilayered


PRA

PRA

States

Decision

network

maker

executor















Timeindex

Timeindex

t

SpaceSpace

1

N

i

t



t minus 1 t minus 1



SBIC (119863 119866Θ) = log119875 (119863 | Θ 119866) minus119889

2log119898 + 119900 (1) (1)








119901 (119865) = prod119894119905

119901 (119891119894119905| 119865pa(119894119905)) (2)



119901 (119891119894119905119865pa(119894119905)) =

119901 (119891119894119905 119865pa(119894119905))

119865pa(119894119905) (3)


GMM as follows

119901 (119891119894119905 119865pa(119894119905)) =

119872

sum119898=1

120572119898119892119898(119891119894119905 119865pa(119894119905) | 120583119898 119862119898) (4)


119898 119862119898) is the


mean values 120583119898and a (119873

119875+ 1) times (119873












rarr


0rarr

119860= times119894isin119868119860119894




1015840) = 1 119864



119904 119878times119864








V120587 (119904) = 119903 (119904 120587 (119904)) + 120574 sum

1199041015840isin119878

119901 (1199041015840| 119904 120587 (119904)) V120587 (119904

1015840) (5)



119886isin119860

(119903 (119904 119886) + 120574 sum

1199041015840isin119878

119875 (1199041015840| 119904 119886) V

120587(1199041015840))

(6)










119894119895le 119896 where



119901 (1199041015840| 119904 119886) =

119899

prod119894=1

119875119894(1199041015840

119894| 119904119873(119894)

119886119894) (7)

where 119904119873(119894)

= 119904119895| 119895 isin 119873(119894)



119903 (119904 119886) =

119899

sum119894=1

119903119894(119904119873(119894)

119886119894) (8)


119899)


1199090120587120574


1198751199090120587120574

(119910) = (1 minus 120574)

infin

sum119905=0

120574119905119875120587(119878119905= 119910 | 119878

0= 1199090) (9)


119881120587(1199090) =

1


1198751199090120587120574

(119910) sdot 119903 (119910 120587 (119910)) (10)


0=



119894| 119909119905minus1

119873(119894) 120587(119909119905minus1

119873(119894))) Now


120587(119909119905

119894| 119909119905minus1

119894) which

satisfies

119862119905

120587(119910 | 119909

0) = sum

119904119905minus1

119866119905

120587(119910 | 119909

119905minus1) sdot 119862119905minus1

120587(119909119905minus1

| 1199090)

=

119899

prod119894=1

sum

119909119905minus1

119894

119866119905119894

120587(119910119894| 119909119905minus1

119894) sdot 119862119905minus1119894

120587(119909119905minus1

119894| 1199090

119894)

(11)



0= 1199090) defined by 1198621

120587(119910 | 119909

0) = prod

1198941198661119894

120587(119910119894| 1199090

119894)

and forall119905 119862119905120587(119910 | 119909

0) = prod

119899

119894=1119862119905119894

120587(119910119894| 1199090

119894)


1 1199062 119906



119898 119866


KL (119866119875) = 119864119876[log(119866

119875)] (12)


1198661

120587= arg min

1198751120587

KL (1198661120587(1198781| 1198780)

sdot1198750(1198780) | 119875120587(11987811198780) sdot 1198750(1198780))

(13)


1198661119894

120587(1199091

119894| 1199090

119894)

prop exp1198641199010 [log119901

119894(1199091

119894| 1199090

119894 1198780

119873(119894)119894 120587119894(1199090

119894 1198780

119873(119894)119894)) ]

(14)




119894runs






0

500

1000

1500

2000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Traffi

c flow

ObservedABNPro-CEP

Time (times60 s)






Time (times60 s)

0

2

4

6

8

10

1 4 7 10 13 16 19 22 25 28 31

Con

gesti

on le

vel

DefaultPro-CEP


0

5

10

15

20

6 8 10 12 14 16

Runn

ing

time (

min

)


3 servers5 servers







0

5

10

15

20

25

10 15 20 25 30 35

Runn

ing

time (

min

)


3 servers5 servers






Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










PEPA

PEPA

PEPA

PEPA

PEPA


Devices

PRA

Proactive

iii

Event DBRaw

events

PA withmultilayered


PRA

PRA

States

Decision

network

maker

executor















Timeindex

Timeindex

t

SpaceSpace

1

N

i

t



t minus 1 t minus 1



SBIC (119863 119866Θ) = log119875 (119863 | Θ 119866) minus119889

2log119898 + 119900 (1) (1)








119901 (119865) = prod119894119905

119901 (119891119894119905| 119865pa(119894119905)) (2)



119901 (119891119894119905119865pa(119894119905)) =

119901 (119891119894119905 119865pa(119894119905))

119865pa(119894119905) (3)


GMM as follows

119901 (119891119894119905 119865pa(119894119905)) =

119872

sum119898=1

120572119898119892119898(119891119894119905 119865pa(119894119905) | 120583119898 119862119898) (4)


119898 119862119898) is the


mean values 120583119898and a (119873

119875+ 1) times (119873












rarr


0rarr

119860= times119894isin119868119860119894




1015840) = 1 119864



119904 119878times119864








V120587 (119904) = 119903 (119904 120587 (119904)) + 120574 sum

1199041015840isin119878

119901 (1199041015840| 119904 120587 (119904)) V120587 (119904

1015840) (5)



119886isin119860

(119903 (119904 119886) + 120574 sum

1199041015840isin119878

119875 (1199041015840| 119904 119886) V

120587(1199041015840))

(6)










119894119895le 119896 where



119901 (1199041015840| 119904 119886) =

119899

prod119894=1

119875119894(1199041015840

119894| 119904119873(119894)

119886119894) (7)

where 119904119873(119894)

= 119904119895| 119895 isin 119873(119894)



119903 (119904 119886) =

119899

sum119894=1

119903119894(119904119873(119894)

119886119894) (8)


119899)


1199090120587120574


1198751199090120587120574

(119910) = (1 minus 120574)

infin

sum119905=0

120574119905119875120587(119878119905= 119910 | 119878

0= 1199090) (9)


119881120587(1199090) =

1


1198751199090120587120574

(119910) sdot 119903 (119910 120587 (119910)) (10)


0=



119894| 119909119905minus1

119873(119894) 120587(119909119905minus1

119873(119894))) Now


120587(119909119905

119894| 119909119905minus1

119894) which

satisfies

119862119905

120587(119910 | 119909

0) = sum

119904119905minus1

119866119905

120587(119910 | 119909

119905minus1) sdot 119862119905minus1

120587(119909119905minus1

| 1199090)

=

119899

prod119894=1

sum

119909119905minus1

119894

119866119905119894

120587(119910119894| 119909119905minus1

119894) sdot 119862119905minus1119894

120587(119909119905minus1

119894| 1199090

119894)

(11)



0= 1199090) defined by 1198621

120587(119910 | 119909

0) = prod

1198941198661119894

120587(119910119894| 1199090

119894)

and forall119905 119862119905120587(119910 | 119909

0) = prod

119899

119894=1119862119905119894

120587(119910119894| 1199090

119894)


1 1199062 119906



119898 119866


KL (119866119875) = 119864119876[log(119866

119875)] (12)


1198661

120587= arg min

1198751120587

KL (1198661120587(1198781| 1198780)

sdot1198750(1198780) | 119875120587(11987811198780) sdot 1198750(1198780))

(13)


1198661119894

120587(1199091

119894| 1199090

119894)

prop exp1198641199010 [log119901

119894(1199091

119894| 1199090

119894 1198780

119873(119894)119894 120587119894(1199090

119894 1198780

119873(119894)119894)) ]

(14)




119894runs






0

500

1000

1500

2000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Traffi

c flow

ObservedABNPro-CEP

Time (times60 s)






Time (times60 s)

0

2

4

6

8

10

1 4 7 10 13 16 19 22 25 28 31

Con

gesti

on le

vel

DefaultPro-CEP


0

5

10

15

20

6 8 10 12 14 16

Runn

ing

time (

min

)


3 servers5 servers







0

5

10

15

20

25

10 15 20 25 30 35

Runn

ing

time (

min

)


3 servers5 servers






Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Timeindex

Timeindex

t

SpaceSpace

1

N

i

t



t minus 1 t minus 1



SBIC (119863 119866Θ) = log119875 (119863 | Θ 119866) minus119889

2log119898 + 119900 (1) (1)








119901 (119865) = prod119894119905

119901 (119891119894119905| 119865pa(119894119905)) (2)



119901 (119891119894119905119865pa(119894119905)) =

119901 (119891119894119905 119865pa(119894119905))

119865pa(119894119905) (3)


GMM as follows

119901 (119891119894119905 119865pa(119894119905)) =

119872

sum119898=1

120572119898119892119898(119891119894119905 119865pa(119894119905) | 120583119898 119862119898) (4)


119898 119862119898) is the


mean values 120583119898and a (119873

119875+ 1) times (119873












rarr


0rarr

119860= times119894isin119868119860119894




1015840) = 1 119864



119904 119878times119864








V120587 (119904) = 119903 (119904 120587 (119904)) + 120574 sum

1199041015840isin119878

119901 (1199041015840| 119904 120587 (119904)) V120587 (119904

1015840) (5)



119886isin119860

(119903 (119904 119886) + 120574 sum

1199041015840isin119878

119875 (1199041015840| 119904 119886) V

120587(1199041015840))

(6)










119894119895le 119896 where



119901 (1199041015840| 119904 119886) =

119899

prod119894=1

119875119894(1199041015840

119894| 119904119873(119894)

119886119894) (7)

where 119904119873(119894)

= 119904119895| 119895 isin 119873(119894)



119903 (119904 119886) =

119899

sum119894=1

119903119894(119904119873(119894)

119886119894) (8)


119899)


1199090120587120574


1198751199090120587120574

(119910) = (1 minus 120574)

infin

sum119905=0

120574119905119875120587(119878119905= 119910 | 119878

0= 1199090) (9)


119881120587(1199090) =

1


1198751199090120587120574

(119910) sdot 119903 (119910 120587 (119910)) (10)


0=



119894| 119909119905minus1

119873(119894) 120587(119909119905minus1

119873(119894))) Now


120587(119909119905

119894| 119909119905minus1

119894) which

satisfies

119862119905

120587(119910 | 119909

0) = sum

119904119905minus1

119866119905

120587(119910 | 119909

119905minus1) sdot 119862119905minus1

120587(119909119905minus1

| 1199090)

=

119899

prod119894=1

sum

119909119905minus1

119894

119866119905119894

120587(119910119894| 119909119905minus1

119894) sdot 119862119905minus1119894

120587(119909119905minus1

119894| 1199090

119894)

(11)



0= 1199090) defined by 1198621

120587(119910 | 119909

0) = prod

1198941198661119894

120587(119910119894| 1199090

119894)

and forall119905 119862119905120587(119910 | 119909

0) = prod

119899

119894=1119862119905119894

120587(119910119894| 1199090

119894)


1 1199062 119906



119898 119866


KL (119866119875) = 119864119876[log(119866

119875)] (12)


1198661

120587= arg min

1198751120587

KL (1198661120587(1198781| 1198780)

sdot1198750(1198780) | 119875120587(11987811198780) sdot 1198750(1198780))

(13)


1198661119894

120587(1199091

119894| 1199090

119894)

prop exp1198641199010 [log119901

119894(1199091

119894| 1199090

119894 1198780

119873(119894)119894 120587119894(1199090

119894 1198780

119873(119894)119894)) ]

(14)




119894runs






0

500

1000

1500

2000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Traffi

c flow

ObservedABNPro-CEP

Time (times60 s)






Time (times60 s)

0

2

4

6

8

10

1 4 7 10 13 16 19 22 25 28 31

Con

gesti

on le

vel

DefaultPro-CEP


0

5

10

15

20

6 8 10 12 14 16

Runn

ing

time (

min

)


3 servers5 servers







0

5

10

15

20

25

10 15 20 25 30 35

Runn

ing

time (

min

)


3 servers5 servers






Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













V120587 (119904) = 119903 (119904 120587 (119904)) + 120574 sum

1199041015840isin119878

119901 (1199041015840| 119904 120587 (119904)) V120587 (119904

1015840) (5)



119886isin119860

(119903 (119904 119886) + 120574 sum

1199041015840isin119878

119875 (1199041015840| 119904 119886) V

120587(1199041015840))

(6)










119894119895le 119896 where



119901 (1199041015840| 119904 119886) =

119899

prod119894=1

119875119894(1199041015840

119894| 119904119873(119894)

119886119894) (7)

where 119904119873(119894)

= 119904119895| 119895 isin 119873(119894)



119903 (119904 119886) =

119899

sum119894=1

119903119894(119904119873(119894)

119886119894) (8)


119899)


1199090120587120574


1198751199090120587120574

(119910) = (1 minus 120574)

infin

sum119905=0

120574119905119875120587(119878119905= 119910 | 119878

0= 1199090) (9)


119881120587(1199090) =

1


1198751199090120587120574

(119910) sdot 119903 (119910 120587 (119910)) (10)


0=



119894| 119909119905minus1

119873(119894) 120587(119909119905minus1

119873(119894))) Now


120587(119909119905

119894| 119909119905minus1

119894) which

satisfies

119862119905

120587(119910 | 119909

0) = sum

119904119905minus1

119866119905

120587(119910 | 119909

119905minus1) sdot 119862119905minus1

120587(119909119905minus1

| 1199090)

=

119899

prod119894=1

sum

119909119905minus1

119894

119866119905119894

120587(119910119894| 119909119905minus1

119894) sdot 119862119905minus1119894

120587(119909119905minus1

119894| 1199090

119894)

(11)



0= 1199090) defined by 1198621

120587(119910 | 119909

0) = prod

1198941198661119894

120587(119910119894| 1199090

119894)

and forall119905 119862119905120587(119910 | 119909

0) = prod

119899

119894=1119862119905119894

120587(119910119894| 1199090

119894)


1 1199062 119906



119898 119866


KL (119866119875) = 119864119876[log(119866

119875)] (12)


1198661

120587= arg min

1198751120587

KL (1198661120587(1198781| 1198780)

sdot1198750(1198780) | 119875120587(11987811198780) sdot 1198750(1198780))

(13)


1198661119894

120587(1199091

119894| 1199090

119894)

prop exp1198641199010 [log119901

119894(1199091

119894| 1199090

119894 1198780

119873(119894)119894 120587119894(1199090

119894 1198780

119873(119894)119894)) ]

(14)




119894runs






0

500

1000

1500

2000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Traffi

c flow

ObservedABNPro-CEP

Time (times60 s)






Time (times60 s)

0

2

4

6

8

10

1 4 7 10 13 16 19 22 25 28 31

Con

gesti

on le

vel

DefaultPro-CEP


0

5

10

15

20

6 8 10 12 14 16

Runn

ing

time (

min

)


3 servers5 servers







0

5

10

15

20

25

10 15 20 25 30 35

Runn

ing

time (

min

)


3 servers5 servers






Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0= 1199090) defined by 1198621

120587(119910 | 119909

0) = prod

1198941198661119894

120587(119910119894| 1199090

119894)

and forall119905 119862119905120587(119910 | 119909

0) = prod

119899

119894=1119862119905119894

120587(119910119894| 1199090

119894)


1 1199062 119906



119898 119866


KL (119866119875) = 119864119876[log(119866

119875)] (12)


1198661

120587= arg min

1198751120587

KL (1198661120587(1198781| 1198780)

sdot1198750(1198780) | 119875120587(11987811198780) sdot 1198750(1198780))

(13)


1198661119894

120587(1199091

119894| 1199090

119894)

prop exp1198641199010 [log119901

119894(1199091

119894| 1199090

119894 1198780

119873(119894)119894 120587119894(1199090

119894 1198780

119873(119894)119894)) ]

(14)




119894runs






0

500

1000

1500

2000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Traffi

c flow

ObservedABNPro-CEP

Time (times60 s)






Time (times60 s)

0

2

4

6

8

10

1 4 7 10 13 16 19 22 25 28 31

Con

gesti

on le

vel

DefaultPro-CEP


0

5

10

15

20

6 8 10 12 14 16

Runn

ing

time (

min

)


3 servers5 servers







0

5

10

15

20

25

10 15 20 25 30 35

Runn

ing

time (

min

)


3 servers5 servers






Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Time (times60 s)

0

2

4

6

8

10

1 4 7 10 13 16 19 22 25 28 31

Con

gesti

on le

vel

DefaultPro-CEP


0

5

10

15

20

6 8 10 12 14 16

Runn

ing

time (

min

)


3 servers5 servers







0

5

10

15

20

25

10 15 20 25 30 35

Runn

ing

time (

min

)


3 servers5 servers






Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article A Proactive Complex Event Processing ...downloads.hindawi.com › journals › ijdsn › 2014 › 159052.pdf · using the information from the application domain,