III-CXT: Spatio-temporal Graph Databases for TransportationScience

December 6, 2006

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Project Summary

The recent loss of lives, and traffic jams stretching for tens of miles as hurricanes Rita and Katrina ap-proached the Gulf Coast demonstrate the enormous difficulty of evacuating urban areas. Mass evacuationsare among the most difficult problem areas in Transportation Science because they violate key assumptionsunderlying traditional theories, e.g., Wardrop equilibrium among selfish commuters. A key challenge inthis domain is to develop an understanding of non-equilibrium traffic dynamics over transportation networkstowards the design of emergency traffic management techniques. This is a formidable task due to the data-intensive nature of the problem, and the semantic gap between current database management systems andtransportation science.

The goal of this project is to research novel and scalable data management concepts to aid in the de-velopment of novel transportation science models and theories to understand emergency traffic. New col-laborative computer science research is proposed to probe innovative database concepts underlying networknon-equilibrium dynamics data and queries. New fundamental Computer Science research is proposed ondatabase support for time-variant graphs and flow networks. The researchers on this multi-disciplinary teamnot only have strong track records in both spatial databases and transportation science but they have alsoalready worked collaboratively for the past two years. This proposal complements individual projects of thePIs by stimulating multi-disciplinary research in science informatics.

Intellectual Merit: The proposed approaches to time-variant graphs and spatio-temporal database sup-port for flow networks significantly differ from the traditional approaches in the database literature. Thisproject is expected to result in III-CXT innovations in the following areas. First, graph-aggregates, a novelrepresentation of time-varying graphs, will be explored along with appropriate conceptual, logical and phys-ical data models. Second, database support for flow network operations, e.g. min-cut, and max-flow, willbe investigated. For example, we will examine I/O-scalability of alternative flow algorithms to large spatio-temporal graph datasets using implementations on common database server architectures as well as directimplementation using file systems. Third, the proposed database concepts will be designed and evaluatedin collaboration with domain scientists and professionals using grand challenge problems (e.g., emergencytraffic management) and datasets (e.g. large urban evacuation scenarios, population distributions, and flownetworks). We believe that the proposed research will significantly enhance domain scientists’ ability tounderstand and manage non-equilibrium network behavior, not only in Transportation Science, but also inmany other important domains including logistics, telecommunication networks, electric power grids, anddistribution networks for gas, water, etc.

Broader Impact: Education activities will include training of undergraduate students and graduate re-searchers. Teaching materials (e.g., slides, software prototypes) to facilitate incorporation of research resultsin courses and classroom activities will be prepared. This project will broaden the participation of underrep-resented groups at many levels. The research team includes women graduate students and one PI has a trackrecord of participation in summer institutes involving undergraduate students from historically black collegesand universities. Results will be submitted for publication and presentation at relevant peer-reviewed CS andtransportation science conferences and journals. Periodic meetings will increase collaboration among re-searchers in computer science and transportation science, and facilitate technology transfer to emergencyplanners. If successful, the results with benefit society by reducing evacuation time, which may save livesand reduce exposure of vulnerable populations in the face of man-made and/or natural disasters.

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1 Introduction

Transportation science [47] seeks to understand the dynamics of traffic in general through the analysis oftraffic flows, reasons for bottlenecks, and the wide range of travelers’ behavioral choices. One importantarea of transportation science is emergency traffic management. Emergencies caused by natural or man-made disasters can result in atypical demands on a transportation network, resulting in severe congestion.For example, Figure 1 shows the massive traffic jam [85] and loss of human lives [86] that occurred onHighway after hurricane Rita [96] hit the Gulf Coast of the US in 2005. Traffic equilibrium models that

(a) Hurricane Rita (b) Evacuation traffic (c) Accidents during evacuation

Figure 1: Houston-Galveston evacuation for hurricane Rita resulted in miles of traffic jam, human suffering,and loss of life. (Best viewed in color, Source: National Weather Services [96], Dallas News [85], NationalGeographic News [86])

are commonly used in transportation science may not be applicable in emergency traffic management. Akey challenge of transportation science is to develop the necessary framework and tools to understand non-equilibrium traffic dynamics toward better management of emergency traffic. This task is extraordinarilylabor-intensive, because of the tremendous data volumes involved, the semantic gap between transportationscience theory and current database management systems, and the spatio-temporal graph nature of the data.

The goal of this proposal is to begin building data management tools and techniques to facilitate analysisand use of spatio-temporal graph datasets to further the understanding of non-equilibrium dynamics, anddevelopment of better management practices for emergency traffic. We propose to explore a set of conceptsand develop a set of tools to (a) provide a mapping between the concepts in transportation science and currentdatabase management systems, (b) conveniently represent common queries from transportation scientistsamd emergency traffic managers, and (c) efficiently process common queries. The proposed tasks representsignificant new computer science challenges due to the spatio-temporal nature of the datasets. For example,new representations need to be developed to efficiently store and manage time-variant properties such asconnectivity over long time periods. New I/O-aware query processing strategies need to be investigated toefficiently answer transportation flow-network operations such as max-flow [19].

Our multi-disciplinary team consists of computer scientists and transportation scientists, and is well-qualified to carry out the proposed tasks. Dr. Shashi Shekhar has expertise in spatial data modeling andspatial network analysis and was elected an IEEE Fellow for his contributions to spatial database [104, 105]storage methods [106, 108, 109], data mining [56, 110, 112], and geographic information systems. Dr.Henry Liu has a significant track record in transportation research, particularly related to the proposed tasks,namely evacuation traffic management [70, 72, 73, 75], analytical transportation network modeling [7, 8, 35,71, 72, 74, 77, 123], and traffic simulation and control [16, 17, 63, 76, 78, 79, 80]. The team has a history ofcollaboration. The evacuation route planning algorithms [80] developed by Dr. Shekhar’s group have beeneffectively used in Dr. Liu’s research on adaptive feedback control models for the management of networktraffic flow. In addition, the PIs have close collaboration [118] with the Emergency Traffic Managers at the

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Minnesota Department of Transportation and transportation scientists at the Center of Transportation Studies(see letters of support). These practitioners will participate in the verification and validation of the proposedwork.

2 Domain Science Challenges and Proposed Work

2.1 Domain Science Challenges

Transportation science [47] is a multi-disciplinary field that requires expertise from different domains. Thedifficulty, but also fascination, of this professional practice derives from the intrinsic complexity of trans-portation systems, which have both physical and behavioral elements. The physical elements in the systems(e.g., vehicles, infrastructure, etc.) are governed by the law of physics. On the other hand, the mechanismsunderlying the functionality and the performances of these physical elements are often connected to thetraveler’s behavioral choice. Traditionally, user equilibrium [122], meaning that all travelers use the least in-convenient routes and no individual can unilaterally improve his/her travel, has been the center of behavioralchoice modeling. A vast amount of literature on user equilibrium is available and we refer readers to [97]for more details. It is assumed in user equilibrium concept that travelers have perfect information aboutroad conditions. This is generally true for commuters because they can learn the recurrent congestion fromtheir day-to-day travels. However, this assumption is not applicable when the congestion is non-recurrent.In particular, when an extreme event occurs, and transportation network conditions become dynamic anduncertain, the user equilibrium assumption cannot be applied. Thus one of the greatest challenges in trans-portation science is how to manage traffic with time-varying transportation network, especially in disastersituations.

(a) Night-time Population (b) Day-time Population

Figure 2: Night-time and day-time population distributions in the Twin Cities, Minnesota. Night-time pop-ulation is based on Census 2000. Day-time population is based on Census 2000 and employment Origin-Destination estimate from the Minnesota Department of Employment and Economic Development, 2002

Recent events [54, 68] have clearly spelled out the range of potential large-scale natural and manmadethreats that confront major metropolitan regions throughout the world. Emergency evacuation, the massmovement of people from disaster-impacted areas to safer ones in a timely manner, has been studied andpracticed for decades aiming to mitigate the disastrous consequences. It is undisputable that during evac-uation, the ground transportation system plays a central role. How can transportation networks be betterprepared in advance and managed in real time to deal with emergency evacuation in a comprehensive, logi-cal, and effective manner? Interestingly, despite a long history of evacuation study in the transportation field,

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most of the work has focused on emergency transportation planning [9] from various perspectives, such astraffic management policies [117], origin-destination (OD) trip estimations [41, 83, 84], and behavior analy-sis [6, 40, 51, 92]. Moreover, due to the distinctive features of different types of disasters, specific planningmodels have been developed for different evacuation scenarios, including nuclear power plant crisis [81],hurricane, flooding, and fire, etc. [36, 39, 52, 58, 98, 119, 120].

Recently, the realization that these emergency events are highly unpredictable has led traffic planners todevelop scenarios and attendant actions: ”If this is scenario X, then follow plan x”. For example, alternateevacuation route and plans may be used during a work day and night time due to differences in populationdistribution (See Figure 2). Other evacuation scenarios may be defined based on event types (e.g., hurricanes,nuclear power plant accidents, Homeland Security threat types, etc.), event locations, time of incident, shelterchoices, etc. For detailed discussions regarding evacuation planning modeling, we refer to reviews by [3,114, 120]. Scenario-based approach is effective if (a) there is a small finite set of possible scenarios, and morecrucially (b), if it can be predicted how the evacuees will travel, with and without travel advisories. However,during evacuations, some travelers may not follow the recommended routes and, furthermore, none of theplans assumed may be appropriate since there are an innumerable number of alternative scenarios. Hence,there is a tremendous interest in emergency management agencies to look for ways to manage evacuationtraffic more efficiently and effectively in real-time.

2.2 Proposed Domain Science Research

The proposed domain research aims to develop an integrated framework for real-time dynamic traffic man-agement under emergency evacuation using Model Reference Adaptive Control (MRAC) [5, 29, 70, 95],as depicted in Figure 3. To cope with the dynamic and uncertain nature of evacuation traffic, the proposed

Adjustment

Controller

Control Strategy Generator

actual

referencecorrection

Parameter

Traffic Monitoring System

SystemObjective

Reference ModelPrescriptive

Descriptive Micro−Simulation

(Real World)

Figure 3: Model Reference Adaptive Control for Evacuation Traffic Management

framework adopts the traffic management paradigm ”observe, evaluate, control and advise, cyclically andfrequently” so that the dynamic nature of evacuation can be captured and the unpredictable features of theproblem alleviated by adaptive control. In the MRAC framework, a Traffic Monitoring System, e.g., traf-fic sensor network on urban highways which measures congestion levels as illustrated by Figure 4, takesobservation measurements from real world traffic, a Prescriptive Reference Model estimates the optimalfuture states for use by the feedback control system, which consists of a Control Strategy Generator andDescriptive Micro-Simulator.

Strategies are generated to control and advise the traffic towards the optimal states to achieve certainSystem Objectives designated by traffic management authorities. Examples of objectives include minimiz-ing evacuation time, maximizing evacuation rate by optimal use of transportation network. The procedureneeds to be conducted cyclically and frequently, in a rolling horizon fashion, similar to the scheme usedin on-line demand- responsive traffic signal control [43]. The rolling horizon approach repetitively utilizesthe latest traffic data available from the last rolling period and provides a system optimal solution for thepredetermined time horizon. This framework is in contrast to traditional evacuation models, which onlyinclude the descriptive traffic assignment or simulation model for the testing of fixed evacuation plans (for

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Figure 4: Sensor networks periodically report time-variant traffic volumes on Twin Cities highways (Bestviewed in color, Source: Mn/DOT)

example, [25, 50, 82]; to name but a few). Our preliminary analysis [70] using traffic simulation showsthat the adaptive control approach can significantly reduce the evacuation clearance time, thereby reducingeconomic costs and loss of life.

To the best of our knowledge, we are the first to apply the MRAC framework to the emergency trafficmanagement problem. During evacuation adaptive control is needed for dynamic real time traffic manage-ment because it involves a level of complexity not present in normal traffic scenarios. Drivers’ behavioralchoice cannot be modeled as user optimal, since the travelers’ first concerns are neither to choose the shortestroutes nor reach the traffic equilibrated (in the sense of network equilibrium) because such events are veryrare. The primary goal of evacuees is to leave impacted areas at the earliest time. Therefore, conventionaltransportation network models based on user equilibrium may not be effective. In evacuation scenarios, onlythe following general short-term characteristics may be stated with some confidence: traffic tends to moveaway from the incident.

A key challenge in the domain research is to design robust MRAC methods for dealing with potentiallyunstable nature of emergency traffic as illustrated in Table 1. A visual comparison of Figure 1(b) and leftpart of Table 1 shows that emergency traffic may resemble level of service F which exhibits highly variableunstable flow [11, 24].

The proposed research development will focus on the following components: Not only the uncertaintyof traffic flow under evacuation comes from evacuee’s behavioral choice on routes, as we discussed above,it also comes from the short spacing and frequent lane changes happened in the evacuation. Both these twotypes of uncertainties pose great challenges in MRAC design. The proposed research development will focuson the following components:

A prescriptive reference model: This component produces simultaneously the target or desired trafficstates and perfect control to achieve such states. This reference model represents the desired response of thetraffic under evacuation, based on the designated system objective (e.g., minimize total evacuation time, ormaximize evacuation rate) from the traffic management authorities. In an evacuation scenario, a traveler’sbehavior is highly uncertain and only a short-term (a few minutes) traffic forecasting is reliable enough; butthat is all that may be used for a closed-loop feedback control approach. It should also be noted that in caseof evacuation, strict traffic controls, e.g., traffic guidance and control at major intersections, are not onlyfeasible but also desirable. For the management authorities, the goal may be to reduce the total clearancetime so as to minimize the total fatalities and property losses. While from the individual evacuee’s point ofview, he or she may need effective traffic guidance and control to reach the safe areas as quickly as possible.

A descriptive real world model: The descriptive model will adopt a control strategy (instead of a fixed”plan”) for evacuation; by strategy, we mean a real-time traffic assignment procedure that provides, cyclically

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and frequently, a set of routes and traffic control advisories based on feedback of the current observed state.We propose to use a microscopic traffic simulation model as a ”real world” representation for the testing andevaluation of this research.

Design of the feedback control system: This process is based on the difference of desired traffic statesbetween the reference model and the current prevailing traffic states collected from the traffic monitoringand sensing system. For MRAC, the adaptation law searches for parameters such as ”the response of theemergency traffic and transportation network under adaptive control becomes the same as that of the refer-ence model”, i.e., the objective of the adaptation is to make the tracking error converge to zero [113]. Forexample, suppose we receive the information that an intersection has a heavy traffic during evacuation. Thiswould result in the feedback control system coordinating the traffic light to alleviate the congestion.

Table 1: Levels-of-Service Criteria for Freeways (Source: [11, 24])Level of Density Avg. Speed MSFc

Servicea (PC / mi / ln)b (mph)A ≤ 12 - -B ≤ 20 ≥ 50 1,000C ≤ 30 ≥ 47 1,400D ≤ 42 ≥ 42 1,700E ≤ 67 ≥ 30 2,000

Level of Service F F ≤ 67 ≥ 30 d

a Degree of congestion classified by speed, travel time, freedom of maneuver, and safetyc Maximum service flow rate per lane under ideal conditionsb (Passenger Car / Mile / Lane), d Highly variable, unstable

Based on the above discussion, we propose the following research tasks.Task TS1: Formulation of Reference Models: We plan to investigate the model formulations based on dif-

ferent traffic flow fidelities with application to emergency evacuation under different spatio-temporal scales.Due to the computational time constraint, trade-off needs to be made between the model fidelity and scal-ability since higher fidelity traffic models will usually require longer computational time. Under this task,formulation of both a low traffic flow fidelity, large spatio-temporal scale model and high-traffic flow fidelity,small spatio-temporal scale model will be investigated.

Task TS2: Estimation of Reference Models: We plan to explore the potential solution algorithms for themodels specified in task 1, to achieve a balance between solution accuracy and efficiency. Close collaborationbetween transportation scientists and computer scientists is needed to design an efficient algorithm and itssupporting data structure.

Task TS3: Robust Adaptive Controller Design: This includes the development of a feedback controllerand its parameter adjustment mechanism. How to design a robust controller for the traffic control at junctionpoint and how to adjust the controller parameters are research issues. Furthermore, we will also study thestability and responsiveness of the resulting controller and its adjustment mechanism.

Task TS5: Model Validation and Verification: We plan to integrate microscopic traffic simulation [87,89] for the model validation and verification. A traffic simulator serves as a platform that can emulatedifferent evacuation scenarios and provides performance measures for evacuation traffic management. A keychallenge is to address convergence and robustness issues of the model.

Computational and Data Management Needs: The expected domain contributions are to: 1) advancethe scientific understanding of the behavior of non-equilibrium traffic, particular under emergency evacu-ation; 2) enhance dynamic transportation network models by considering the characteristics of evacuationtraffic and integrating feedback control theory; and 3) provide a suite of conceptual, analytical, and sim-ulation models that are expected to function as real-time on-line tools for evacuation traffic management.

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However, these domain contributions are not possible without inter-disciplinary research in computer sci-ence to develop appropriate spatio-temporal database reprepresentations and query processing algorithms tomake decisions in a timely manner due to the tremendous data volume and semantic gap between transporta-tion science concepts and the concepts supported by current database systems. For example, MRAC andother models of emergency traffic use time-variant flow-network [2] operations like min-cut and max-flow[19], which are not supported by current databases.

While CS/III expertise is needed in different areas of our research, a specified area of need is towarddesigning the solution algorithm to the reference model and its associated data structure in such a waythat high efficiency can be achieved without great sacrifice of model accuracy. The MRAC framework isdesigned for real-time evacuation traffic management, the reference model must be responsive and ableto provide a target state in reasonable time. Therefore the computational accuracy and efficiency of thereference model is critical to the success of the proposed framework. To this end, heuristic algorithms areneeded to balance accuracy and efficiency since the direct application of existing linear programming basedsolution methods from the operations research community [15, 38, 48, 53, 64, 65] are simply not feasibledue to the large computational time requirements. Our prior CS/III work on the Capacity Constrained RoutePlanner (CCRP, [80]) identifying high capacity evacuation routes, provides a good starting point for thedesign of computationally efficient heuristic algorithms. Though this method proved to be computationallymore efficient and scalable than the previous linear programming based methods, it did not account fortime variation in network properties which could compromise solution quality. Hence, an approach whichconsiders the temporal variations of the transportation network needs to be developed.

3 Computer Science Challenges and Proposed Work

Transportation science is in need of understanding the dynamic nature of emergency traffic environmentduring an evacuation. Previous strategies that utilized specific plans for pre-determined evacuation scenar-ios may not be robust to unanticipated events during evacuation. The proposed MRAC framework doesnot assume specific evacuation scenarios and adjusts the traffic controls (e.g., highway ramp meters, roadintersection control traffic lights) to cope with particular traffic conditions in a transportation network. TheMRAC framework presented CS/III challenges of modeling the network dynamics and scalable flow networkoperations (e.g., finding high capacity evacuation routes) to address the issues of tremendous data volumeand semantic gap between current databases and transportation science. We address the first challenge byproposing time-variant graphs to represent spatial road network where the edge properties are time-dependenton the state of the traffic (Section 3.2). We address the second challenge of scalable flow network operation(e.g., high capacity evacuation routing) by proposing database support for flow networks that represent avail-able edge capacities based on the current traffic volume to identify high-capacity evacuation routes (Section3.3).

3.1 Computer Science Framework and Challenges

Framework: The proposed CS research will focus on novel database capabilities to support spatio-temporal graph datasets without reinventing core database functionalities as shown in Figure 5. We expectthe system to be useful for scientists and engineers from various domains. Transportation scientists willbe able to make use of the system to better understand and analyze network dynamics, even under non-equilibrium conditions. In addition, the proposed database will provide support to applications tools such asthe capacity constrained route planner (CCRP) [80] and MRAC (Section 2). Emergency managers can makeuse of the database to identify the existing traffic conditions and make informed decisions about evacuationroute planning based on network conditions. They will be able to pose queries to gather information on theeffects of various modes of transportation, routes, and destination choices as illustrated in Table 2 for queries

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and Flow NetworkSpatio−Temporal Graph Extension

Emergency Managers Transportation Scientists

Applicationse.g. MRAC, CCRP

Choice ofMode, Route, DestinationQueries on

non−equilibrium networkdynamics

Questions to understandsource−destination pairmax−flow, nearest

Queries like min−cut,

Extensible Database Core

Figure 5: Framework of the Computer Science Proposed Research

related to shortest time travel routes or evacuation capacity of a transportation network. One significantquery is to find the maximum flow (maxflow) in the network, i.e., the largest volume of traffic that can movethrough the network per unit time without exceeding the available capacity.

Related work and their limitations: Most modern extensible database management systems [20, 21,45] consist of a platform and extensions that add significant new semantic capabilities to the database system,one of the most popular extension being the spatial ones. For example, spatial attachments with names suchas cartridge, datablade or spatial option and supported by Oracle, ESRI and IBM respectively [22, 23, 34]have existed for some time. Irrespective of the platform that supports it, these extensions have contributedconsiderably in enhancing the processing capabilities and productivity of database systems as a whole andtheir significance is widely acknowledged despite the ongoing debates on the merits of various platforms.Although spatial database blades have been popular in the scientific and business communities, none of theexisting products support the spatio-temporal graphs. The recent release of Oracle (version 10g) includes anetwork data model to store and maintain connectivity of link-node network and supports basic features suchas shortest path [90]. The Network Analyst extension of ArcMap from ESRI supports a network geodatabaseand provides basic algorithms (e.g., shortest path, service area, closest facility, etc.) [32]. These productsand academic literature on graph databases [10, 30, 32, 104, 109] do not adequately address time varianceof spatial networks and flow network databases, which is crucial in the analysis of non-equilibrium networkdynamics. The work proposed here addresses this aspect of spatial databases and proposes research in thearea of spatio-temporal graph databases, with a special focus on supporting emergency traffic management.This architecture also enables the re-use of core databases and studies from almost 30 years of research indatabases and data engineering.

Summary of Computer Science Challenges and Approaches: While efficient and effective techniquesfor spatial graph analysis, including shortest path computation and route evaluation [1, 27, 46, 55, 57, 59,60, 61, 91] have been studied, some pertinent challenges in the context of emergency traffic management stillneed to be addressed. One challenge comes from the time-dependence of the spatial network. For examplein emergency traffic management, travel times on the road segments and the road network structure are time-variant. Thus, their queries may ask for time-variant properties such as shortest travel-time or evacuationcapacity at different times of a day as shown in Table 2. Graph databases that represent spatial networksneed to represent the temporal nature of the networks.

Another important and orthogonal aspect that needs to be addressed is the capacity constraints of theroad networks in comparison with the size of the population that would need to use the network. Example

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Table 2: Example Queries with Time-variance and Flow NetworksStatic Time-Variant

Graph Which is the shortest travel time path Which is the shortest travel time path(No capacity from Minneapolis downtown to airport? from Minneapolis downtown to airportconstraints) at different times of a work day?

(Section 3.2)Flow Network What is the capacity of Twin-Cities What is the capacity of Twin-Cities

freeway network to evacuate freeway network to evacuateMinneapolis downtown? Minneapolis downtown at different(Section 3.3) times in a work day? (Section 3.3)

queries may include estimation of the capacity of the transportation system to evaluate an area of interest ata given time or at different times in a day as as shown in Table 2. Although flow network algorithms [2, 19],have been proposed to handle capacities and demands on graph edges, these have been studied in a mainmemory environment. There is a great need for research that evaluates algorithms and storage and accessstructures in a database environment.

3.2 Proposed Approach to Time-Variant Graphs

A time-variant graph is a graph whose edge and node properties and topological structure are time depen-dent. For example, traffic volume on urban highways varies over the time of a day (as illustrated in Figure 4),which leads to a variation in travel time and capacity available for evacuation. Thus, in emergency planning,the underlying spatial network is time-dependent and hence time-variant graphs may be needed to representthem. In addition to network parameter values, the network topology can also change with time due to theunavailability of certain road segments during some periods of time due to repair or natural calamities. Fig-ure 6(b) shows a submerged road segment during hurricane Rita making it unavailable during the evacuation.A spatio-temporal network will include the time-variations of a spatial network.

A graph representation of a network at three instants of time is shown in Figure 6(a), including temporalchanges in connectivity and edge properties (e.g. travel times). For example, the edge from node N3 to nodeN4 disappears at the time instant t=2 and reappears at t=3 and the travel time on the edge N2-N4 changes from2 time units at t=2, to 3 time units at t=3. Conventional graph algorithms cannot easily be applied to these

N2

N3 N4

[2]

[1]

[2]

t=3

N1 N2

N3 N4[4]

[3][2]

(a) Snapshots of a Network at time instants 1, 2, and 3 (b) Submerged road

N1

t=1

N1 N2

N3 N4[1]

[2]

[1]

[2]

t=2

Figure 6: Time-Variance of a Spatial Graph (Best viewed in color)

snapshot graphs to evaluate frequent queries without accounting for relationships among snapshots. Previousresearch in graph databases [28] performs computations over a snapshot of the network [49, 94], and do notconsider the interplay between the edge travel times and existence of edges or models graphs that do not varywith time [30, 31, 32, 104, 109, 115]. Traditionally, time-expanded networks [4, 26, 66, 93] have been used

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in transportation science to model spatio-temporal networks where the entire graph is replicated for everytime instant as shown in Figure 7(a). The time expanded graph in this case needed 7 copies of the entire

N3

N4 N4

N3

N2

N1 N1

N2N2 N2 N2 N2

N3

N4

N2

(a) Time Expanded Graph

N1

N3

t=6 t=7

N1 N2

N3 N41,

1,1,

2,2,28

8 ,4

(b) Time−aggregated Graph

2,2,3

t=5

N3 N3N3

N1 N1 N1 N1

N4 N4 N4 N4

t=1 t=2 t=3 t=4

Figure 7: Time-expanded Graph and Time-aggregated Graph

graph to depict the travel time of 4 units from node N3 to the node N4 at time instant 3. Time-expandedgraphs, though suitable for optimization algorithms that use linear programming, are not computationallyefficient. The changes in the network, especially the travel time variations, can be very frequent and formodeling such changes, the time-expanded networks could require a large number of copies of the originalnetwork. With traffic sensors reporting data every few seconds, for an urban transportation network with amillion nodes, the time-expanded network may have billions or trillions of nodes. Such large sized networksmay result in exorbitant storage and computation overheads.

Time-variant graphs raise many challenges for database research. First, due to their potentially large andevergrowing sizes, a storage-efficient representation is critical to reduce and possibly eliminate redundantinformation across different time-points. Second, new query language and logical data model conceptsneed to be investigated to represent and classify potentially new alternative semantics for common graphoperations such as shortest-path and connectivity. For example, a shortest path between a given pair ofnodes may have at least two interpretations, one for a given start time-point and the other for the shortesttravel-time for any start time in a given time interval. A third challenge is the design of efficient and correctquery processing strategies and algorithms since some of the commonly assumed graph-properties may nothold for spatio-temporal graphs. For example, consider the optimal substructure (a requirement for dynamicprogramming principle, [19]) for shortest paths in a graph. While each prefix path (path from a sourcenode to an intermediate node in an optimal path) is optimal in a static graph, it may not be optimal in aspatio-temporal graph due to potential wait at the intermediate node.

N1 N3N2

N1 N3N2 N1 N3N2

N1 N3 N1 N3

N1 N3

1 2 2

2 2 2

2

2 2

N2 N2

N2

t=1 t=3

t=4 t=5 t=6

t=2

Node

Edge

Legend

Travel time

Figure 8: Illustration of Lack of Optimal Substructure in Shortest Paths

A simple example is shown in figure 8 to illustrate the lack of optimal sub-structure. The figure shows anetwork with three nodes at six time instants. Edges are marked with the travel times. A journey that starts

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at t=1 at node N1 reaches the node N2 at t=2. Since the edge N2-N3 is not present at t=2, there is a waitat node N2 until t=5. The total travel time from N1 to N3 takes 6 time units. However, if the start time ismoved to t=3, the travel time is 4 time units, this being the shortest travel time. But, the prefix path (N1-N2)of this shortest travel time path is not optimal since it takes 2 time units. The shortest travel time from N1 toN2 is 1 time unit starting at t=1. The lack of an optimal substructure in the actual shortest paths may maketechniques such as dynamic programming and greedy strategies less effective.

Proposed Approach: We propose to explore a time-aggregated graph to meet the first challenge ofstorage efficient representation of spatio-temporal networks. Time aggregated graph collects the node/edgeattributes into a set of time series as illustrated in Figure 7(b) for the snapshots shown in Figure 6. Forexample, consider the edge N1-N2. Time aggregated graph attaches time-series (1,1,∞) to edge N1-N2 torepresent travel times of 1 unit during time-instants 1 as well as 2 and absence of edge N1-N2 during timeinstant 3.

Graph Aggregation: The temporal variation in the topology and parameter values can be representedusing aggregates as edge/node attributes in the graph used to represent the spatial network. The edges andnodes can disappear from the network during certain instants of time and new nodes and edges can be added.The time-aggregated graph keeps track of these changes through a time series attached to each node and edgethat indicates their presence at various instants of time. Preliminary results [44] show that time aggregatedgraph is promising, but need further investigation. For example, spatial properties need to be represented inthe time aggregated graph, which might add to the effectiveness of the model and may lead to the formulationof efficient algorithms. In addition, handling time granularity and different temporal scales is an issue thatneeds to be addressed. An effective way to represent different scales in the model needs to be developedsince in emergency planning, every scenario can demand different granularity. For example, an evacuationin preparation for an impending hurricane can take multiple days whereas a bomb threat might demand amuch faster response that needs to be completed in minutes or hours. Handling all granularities uniformlywill result in degraded performance and less convenience.

Query Language: A query language needs to represent common queries. Conceptually, snapshot viewsmay be easier for users and we plan to provide an API (get Graph(time)) to extract the snapshot views outof time aggregated graphs. A key challenge is to define a complete set of logical operators for the time-aggregated graph. A representative set of operators is listed in Table 3. In snapshot view, the operators returnthe results with respect to the graph at the given instant of time and aggregated-view-operator results areevaluated on the time-aggregated graphs. For example, the snapshot operator getEdge(node1,node2,time)returns the edge properties for the edge from node n1 to node n2, such as edge identifier (if any) and the edgeparameters at the given time. Table 3 also shows the difference in the behavior of the logical operators forsnapshot and aggregated views. While the operator getEdge(node1,node2,time) returns the edge properties atthe given time, the corresponding time-aggregate operator get edge presence series(node1,node2) extractsthe time series of the edge

properties in addition to the edge identifier (if any). The general framework will be to provide an exten-sible query language rather than a customized set of queries for the specific domain application. This wouldextend the usefulness of the model beyond spatial networks.

Query Processing: The time aggregated graph with the proposed query operators will be used to processqueries pertaining to the domain applications. In evacuation planning, finding evacuation routes is the keystep. For a small group of evacuees, this can be formulated as a shortest path problem in the time-aggregatedgraph. The algorithm needs to consider the availability of the required edges and nodes at the appropriatetime instants. If the shortest route and the shortest route travel time are time-dependent, shortest path com-putation can be performed for a given start time or it can find the least travel time path over the entire timeperiod of interest. If the optimal substructure property does not always hold in the shortest paths, designtechniques other than dynamic programming need to be explored. The strategy may reduce potential waitsat intermediate nodes by postponing the start of the journey to the maximum extent allowed by the edge

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Table 3: Examples of logical operators with and without ’time’ dimensionOperator Snapshot Time-aggregate

get get(node,time) get node Presence series(node)getEdge getEdge(node1,node2,time) get edge Presence series(node1,node2)

get node Presence get node earliest Presence(node,time) get node Presence series(node)get edge Presence get edge earliest Presence(node1,node2,time) get edge Presence series(node,node2)

get Graph get Graph(time) get Graph()

availabilities. Search space may be pruned through comparison of start times and end times of candidatepaths.

Task TG1:Datatypes and Query Operators: We plan to explore various data types and query operatorsto represent the time-aggregated graphs. We will design a set of query operators to develop an algebra closedunder the operations. This language will enable users to frame queries to retrieve routes and attributes fromthe time aggregated graph.

Task TG2:Query Processing Algorithms: We will explore algorithm design techniques that are specifi-cally suited for spatio-temporal graphs. The algorithms will be developed to compute frequent route queryresults, even if optimal sub-structure property does not hold for all shortest paths.

Task TG3: Extension of algorithms for top k results: We expect that the support for some applications(e.g., CCRP, [80]) can be improved if a generalized shortest path algorithm can return top k results. Forexample, performance or evacuation route finding in emergency planning can be improved if scheduling isdone simultaneously over a set of paths, rather than a single path. We will develop algorithms that can retrievek shortest paths or shortest paths over k successive time instants. We will explore the relative performanceof overlapping paths with respect to disjoint paths in the set.

Task TG4: Storage and Access methods: We will study and compare the performances of various disk-based data structures for the storage of the time aggregated graphs. We will also develop indexing methodsto provide efficient access to the time aggregated graphs. Extensibility of existing access methods likeCCAM [109] will be studied for time aggregated graphs.

Task TG5: Spatial Properties in Time Aggregated Graph: We will investigate various methods to in-corporate spatial attributes in time aggreagated graphs and exploit these in increasing the computationalefficiency of query processing algorithms.

Task TG6: Verification and Validation: We will verify the performance of the time-aggregated graphsand algorithms using road network data of the Twin Cities Metro area in Minnesota. The validation of theproposed model and algorithms will be done in collaboration with transportation scientists and emergencyplanning personnel.

3.3 Spatio-temporal Database Support for Flow Networks

A flow network [2] is a directed graph where each edge has a maximum capacity, such that the amount of flowalong an edge does not exceed its capacity. In addition, the amount of flow into a node equals the amount offlow out of it, except source and sink. In transportation science, a traffic network may be modeled as a flownetwork where the flow is equivalent to the number of vehicles per unit time going through a road segment.Capacity of a highway network for evacuation purposes may be modeled using flow-network operationssuch as min-cut or max-flow to estimate lower bounds on evacuation time. Applicability of flow networks isnot limited to road networks, it also covers drinking water distribution networks, electrical circuits [18], gaspipelines, and computer networks [67] with data packets. Spatio-temporal graph database support is crucialbecause most flow networks consist of very large number of elements and highly dynamic attributes.

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However, most current databases [32, 90, 91, 109] lack support for flow networks. Current implementa-tions of flow network algorithms [2, 19, 37, 116] using the capacity attribute rely on loading the entire graphin main memory. For example, suppose that an emergency planner calculates a maximum flow using Ford-Fulkerson’s algorithm [37]. Without database support for the flow network, an application software needs toload the entire flow network into the main memory to perform the calculation. However, the tremendous andgrowing size of the time-variant flow network may be much larger than available main memory due to theon-going collection of time-history as discussed in section 3.2.

Challenges: Database support for flow networks is challenging due to the following reasons. First, thereis a lack of understanding of performance issues in processing flow operations, e.g., min-cut, max-flow, indatabase environments. How do available network-flow algorithms (e.g. Ford-Fulkerson [19, 37], Minimumcost flow [19], Edmonds-Karp [19], Relabel-to-Front [2], the Circulation problem [19], and Capacity Con-strained Route Planner [80]) [2, 19, 37, 116] perform in database environments? Consider a mixed query todetermine capacity of a transportation network to evacuate a circle of one mile radius around a sports sta-dium. What are efficient ways to process mixed queries involving flow-network operations as well as otherspatial or spatio-temporal operations? Can network-flow algorithms take advantage of database conceptslike indexing, transitive closure, etc.?

We illustrate these issues via a detailed example in context of the Edmonds-Karp algorithm [19]. Thisalgorithm is designed to find maximum flow in a flow network using a specific order of finding the augment-ing path. Its asymptotic CPU-complexity is O(VE2) [19], where V is the number of vertices and E is thenumber of edges in a given graph, and it is often used for sparse graphs such as transportation networks. Akey challenge is to characterize the I/O complexity of this algorithm. This algorithm consists of a loop withthree major steps: Step 1, an augmenting path is identified using a breath-first search. Step 2, path capacityis determined as the minimum capacity of edges in the augmenting path. which is already studied and wellimplemented as a transitive closure query in the database domain. Step 3, a reservation for current augment-ing flow is made by updating available flow capacity of each edge in the augmenting path. Implementationof this algorithm in a database environment raises many design decisions. For example, should one leverageavailable database facilities? Will it efficient to implement the first step of this algorithm involving breadth-first search using the transitive closure operations supported by many database management systems? Shouldsteps 2 and 3 be modeled as the relational algebra selection operation? Will database implementation of thesesteps benefit from suitable indexing methods? Since these steps operate on augmenting paths, will defining aroute abstract data-type in database environment with appropriate operations to model steps 2 and 3 improveI/O costs ? These database design decisions are not unique to Edmonds-Karp algorithm [19]. Similar issuesmay arise for other flow-network algorithms.

Second, time-variance poses novel challenges for flow network operations by introducing alternativeinterpretations of traditional operations. Consider a query to identify bottleneck capacity of a transportationnetwork (modeled as a minimum cut) shown in Figure 9 at two time instants T and T+1. The numbersassociated with various edges represent their capacities. At time T, the bottleneck (i.e., minimum cut) of thisnetwork is 2 for flows starting from node S towards destination node T as shown in Figure 9(a). At timeT+1, the bottleneck changes to 4 as shown in Figure 9(b). Thus, minimum-cut of this time-variant flow-network may be a function of time. A database may allow aggregate queries over time-variant network-flowproperties like min-cut. Figure 9(c) shows an example of a query to find an average among time variantmin-cuts with temporal range.

Time-variant properties of flow-networks may raise novel modeling and algorithmic challenges, similarto those discussed in section 3.2. Recall that shortest path has two interpretation due to time-variance basedon alternative departure time of immediate departure or anytime departure to reach destination by a certaindeadline. Are there similar alternative semantics for flow-network operations like min-cut and max-flow?Also recall that some well-known properties, e.g. optimality of prefixes of shortest paths, may not hold forall paths in time-aggregated graphs requiring reexamination of common shortest path algorithms. Will there

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S

333

1

31

T

S

T

(c) Query Example(b) at time T + 1(a) at time T

2

2

3

3

SELECT AVERAGE(MINCUT(node, edge(t)))FROM node, edgeWHERE t BETWEEN T AND T+1;

33

3

3

Figure 9: Two Min-cut graphs with time variant capacity and a query example

be similar issues for flow-network properties and common flow-network algorithms?Task FN1: Modeling Flow Network: We propose to investigate time-aggregated graphs as a model time-

variant flow networks. We also plan to characterize the computational structure of flow-network algorithmsto identify a small kernel of database concepts to facilitate efficient and scalable implementation in databaseenvironment.

Task FN2: Query Processing Algorithms: We will develop I/O-aware query processing strategies fora kernel set of flow-network operations, which can speed-up common network flow algorithms. We willevaluate current graph database storage and access methods [109] for improving I/O efficiency of the kernelset of flow-network operations.

Task FN3: Time Variant Flow Queries: We will investigate alternative semantics of flow-network op-erations due to time variance. We also plan to examine impact of time-variance on those properties offlow-networks, which are exploited by common algorithms. We plan to probe efficient query processingalgorithms for time-variant flow networks by finding ways to reduce redundant computation across differenttime-instants.

Task FN4: Software Prototyping: We will implement a library of time-variant flow-network data typesand operators. The library will be designed for use as a cartridge in extensible database environments in-cludes I/O-aware algorithms to meet the requirements of scalability for large urban emergency managementscenarios.

Task FN5: Validation and Verification: Scalability of proposed methods will be evaluated using exper-iments with benchmark datasets as well theoretical analysis with algebraic cost models. We will leveragebenchmarks data-sets from Minneapolis-St. Paul metropolitan area from our previous work (e.g., CCRP[80]) as well other datasets about large urban emergency traffic management applications to compare theproposed database support for flow network with existing memory-based approaches. Correctness of novelalgorithms for time-variant graphs and flow-network will be examined via analytical methods based onproofs.

4 Project Management Plan

This research project will be a collaboration involving researchers from two domains: computer scienceand transportation science. The PI, Dr. Shashi Shekhar, has high visibility in the area of spatial databasesand spatial data mining. He will provide the general leadership for the project, as well as expertise in thecomputer science research areas described in Section 3. He will track the progress of the project and ensurethe timely and accurate reporting of the project’s status to the NSF. Dr. Henry Liu will provide leadership inthe research in transportation science. A schedule of tasks is shown in Table 4 by years.

We will measure the success of this project in terms of (i) successful CS research in the area of spatio-temporal network modeling, (ii) the building of tools that incorporate these results for use by the trans-portation science researchers on the team, (iii) development of multi-disciplinary collaboration, and (iv) thesuccess in addressing emergency traffic planning problems in transportation science that were previously not

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Table 4: Schedule of project tasks by years

Transportation Science Time-variant Graphs Flow NetworksSection 2.2 3.2 3.3Year I TS1: Formulation of ref. model TG1: Datatypes & query operators FN1: Modeling flow network

TS2: Solution algo. to the ref. model TG2: Query processing algo. FN2: Query processing algorithmsDev. bldg. blocks for DB operations

Year II TS3: Adaptive control design TG3: Extension of algo. for top k paths FN3: Time variant flow queriesTG4: Storage and access methods FN4: Software prototyping

Year III TS4: Model validation & verification TG5: Spatial attr. in time aggr. graphs FN5: Validation & verificationTG6: Validation & verification

well-defined.The collaborative work between transportation science and computer science will allow for further un-

derstanding of the dynamic aspects in a transportation network. The unpredictable behavior by travelersduring an evacuation may be captured using our three proposed themes of study. First, our MRAC modelidentifies several strategies to observe and collect the data set, prescribe specific plans based on the currentobservations, employ the plans, and then re-examine the network in a cyclic manner. Second, novel databasestechniques for time-variant graphs to capture the state of the transportation network at every time interval.Finally, our third theme identifies a constraint based method upon flow networks to represent the vehicledensity over time. Our strategies can be applied to a various number of applications including emergencyevacuation planning, transportation networks, travel route plans, etc. As a benchmark, we plan to evaluateour strategies using the Twin-Cities, Minnesota metro transportation network. Also, we will utilize severaldomain scientists in the Minnesota department of transportation to verify and validate our findings.

5 Results from Prior Support

Shashi Shekhar has been the PI or Co-PI for research grants [99, 111], equipment grants [100, 101, 102]and a planning grant [103]. In the most relevant grant, ”Databases for Spatial Graph Management” (IRI-9631539, 8/1996-7/1999), the objective was to develop, evaluate and implement a set of network storage andaccess methods and network analysis algorithms. The project led to the development of the ConnectivityClustered Access Method (CCAM) [108, 109], based on a min-cut graph partitioning idea in contrast totraditional spatial indexing methods based on geometry and proximity. The Connectivity Clustered AccessMethod (CCAM) is a graph storage method based on graph connectivity where nodes of the graph areassigned to disk pages using a graph partitioning strategy. This project, in addition to providing an improvedunderstanding of access methods for spatial graphs, attracted the attention of several organizations in theindustry. The PI was invited by the Environmental Systems Research Institute [33, 34] (the largest GIScompany) to advise on the storage methods for spatial networks such as road maps. This project openedthe possibility of exploring graph partitioning in other areas, including declustering problems and join-indexbased join algorithms. It also led to min-cut hyper-graph partitioning algorithms which have applicationsin VLSI circuit partitioning [62]. The work on CCAM resulted in one Ph.D thesis, several journal papersand conference papers [69, 107, 108, 109]. The significant impact of CCAM was recognized by the IEEEComputer Society by a Technical Achievement Award (2007).

The PI’s most recent grant is “SEI: Spatio-temporal Data Analysis Techniques for Behavioral Ecol-ogy” (0431141, 8/2004-7/2006) [111]. The PI and his research team developed novel approaches to spa-tial association mining, namely co-occurrence mining and semi-supervised learning algorithms, a Gombedatabase, data digitization and entry tools, and a Gombe database search engine website [88] to query the

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database. The research resulted in 2 Ph.D. dissertations, journal articles [124, 125, 126], conference papers[12, 13, 14, 42, 121, 127, 128] and several manuscripts in review.

6 Broader Impact

Education and Workforce Development: This proposed work will benefit many audiences, includinggraduate students, undergraduate students, and emergency planners. A significant outcome of this researchproject will be the training and development of graduate level researchers. Ph.D. students supported throughthis project will interact with team members from diverse domains and learn valuable skills in interacting andcontributing to such teams. The research will provide projects for the Undergraduate Research OpportunityProgram at the University of Minnesota and undergraduate honors theses. Results from the research will beused to enhance the syllabi of graduate level courses in computer science (CSCI8715: Spatial Databases,M.GIS Colloqium) and transportation engineering (CE5214: Transportation Systems Analysis, CE8212:Advanced Travel Demand Modeling and Supply Analysis). In addition, the results from the research will beincluded as part of course materials in graduate level courses in computer science and transportation science.Our group has experience in working with the Minnesota Department of Transportation on their metro-areaevacuation planning project. The results of the current research are likely to be extremely useful for theemergency planners in the Twin-Cities metro area in Minnesota. Presentations will be organized to helpthe emergency planning personnel become familiarized with the database system and information retrieval.Ample opportunities will be provided to key personnel to interact with the researchers and provide input onkey issues they face in the field.

Broadening Participation of Underrepresented Groups: Our proposed education plans include par-ticipation in the Summer Institute of the Army High Performance Computing Research Center where theparticipants are mostly from historically black colleges and universities. In addition, the PI has supervisedmany women graduate students (e.g., 3 Ph.D. students) and minorities in a variety of forums. Also, a womanPh.D. student is currently working on this project. The PI and the co-PI are committed to recruiting studentsfrom underrepresented groups at all levels of undergraduate and graduate education.

Dissemination: The research results will be submitted for presentation in relevant forums such as IEEETransactions on Knowledge and Data Engineering, the ACM International workshop on GIS, the Inter-national Symposium on Spatial and Temporal Databases, the UCGIS Annual Conference on GeographicInformation Science, the Journal of Transportation Research Board, and the Journal of Urban Planning andDevelopment.

Benefits to Society: The proposed framework will reduce the vulnerability of the public in the eventof disasters that require evacuating large segments of populations to safety. The planning phase will allowemergency planners to develop evacuation plans for metropolitan areas. In addition, it will allow them tostudy alternative scenarios, e.g., those based on transportation modes (e.g., pedestrian, public transportation,private vehicles), weather conditions, network disruption etc. The operational phase will allow emergencymanagers to revise evacuation routes based on major disruptions (e.g., loss of major routes/bridges). As de-scribed in the letter from the Minnesota Department of Transportation, research on spatio-temporal networkswill also be useful in other domains such as logistics, telecommunication networks [67], electric power grids,and distribution networks for gas, water, etc.

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