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I High Performance Computing and Big Data I.1 High Performance Computing for Mobility (HPC4Mobility)

Jane Macfarlane, Lead Principal Investigator Lawrence Berkeley National Laboratory 1 Cyclotron Road Berkeley, CA 94780 E-mail: jfmacfarlane@lbl.gov

Bin Wang, LBL, Principal Investigator E-mail: wangbin@lbl.gov Prasad Gupte, DOE Technology Development Manager U.S. Department of Energy E-mail: prasad.gupte@ee.doe.gov Start Date: October 1, 2017 End Date: September 30, 2019 Project Funding (FY18): $250K DOE share: $250K Non-DOE share: $0

Project Introduction Traffic planners often use some instantiation of a static traffic assignment problem to estimate traffic states in their cities. To accommodate changes in the demand profile over an entire day, the problem might be broken up into time slots of interest and static traffic assignment solutions are run for each slot. Example time slots are early morning, morning rush hour, mid-day, evening rush hour, late evening. Because of the complexity of the network and the scale of the demand, these models often take many hours or perhaps even days to run. The purpose of this project is twofold: 1) leverage High Performance Computing capabilities to reduce the computing time associated with running these models on urban scale problems, and 2) examine the energy impact of urban-scale traffic by developing and implementing a scalable assignment model that optimizes for fuel consumption. The energy optimization function can then be compared to the typical travel time optimization that is traditionally used in traffic assignment models to determine real-world impact of considering fuel consumption in system level traffic control. The City of Los Angeles, CalTrans and the UCB Connected Corridor Program are providing the modeling expertise and feedback for this effort. HERE Technologies is providing urban-scale GPS device data to inform our modeling approach. This work will contribute to LBNL’s efforts to develop new processes, analytical tools, program designs, and business models to advance the state of the art in next-generation sustainable transportation solutions.

Objectives

The work proposed for this project will provide a simple but ambitious proof of concept that traffic assignment and optimization models can be efficiently implemented on HPC platforms. The goal of the project is to provide a computational framework capable of ingesting urban-scale demand data and produce an optimized network loading estimate from the data. The models will include traditional static user equilibrium, as well as a dynamic traffic assignment model capable of handling time varying components, e.g. network variations through the day, special events and other dynamic phenomena. The project will follow the steps outlined below.

1. Formulation of a processing pipeline to handle map data and demand data in an HPC setting. This involves creating a common mechanism for ingesting map data at scale on distributed platforms and implementing distributed models with varying demand data profiles. At the end of the work, the success of this step can be demonstrated by swapping two different models and two different demand data types at very little set up cost and running both at urban scale.

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2. Implementation of at least two models at urban scale, one static (i.e. user equilibrium or game theoretic extension), and one dynamic (i.e. dynamic traffic assignment capable of handling network state aware routing). These two models will be demonstrated at scale on the entire LA Basin or a similar large-scale network.

3. Derivation of an improved energy optimization function, that can be mathematically proven to converge with a unique solution, will be posed and integrated into the optimization code for travel assignment.

4. Benchmark data scenarios. The effort will be showcased by demonstrating HPC computing capabilities on a suite of demand data (provided to us by SCAG and in collaboration with LA Metro). With these different demand data files (for example corresponding to nominal days, weekends, special events, perturbations such as weather, fires etc.), the HPC platform will be used to demonstrate our computational abilities in scenarios conceived and reviewed with LA Metro.

Approach The approach was to begin with a traditional static traffic assignment model in which the routing for all origin and destinations are computed in parallel on high performance computing facilities. Convergence of the numerical methods rely on the solution of convex programs, or extensions of these. This step demonstrates the ability to parallelize the Frank Wolfe algorithm. Implementation of the traffic assignment problem on a large-scale network follows this initial demonstration. Introduction of a fuel optimization focus is then integrated into the implementation by modifying the optimization function to include data-driven models from real-world chassis dynamometer test data. The final step will be to address the dynamic traffic assignment problem through iterative static traffic assignment solutions with high performance simulation capabilities. A small and well researched part of the LA Basin, known as the Connected Corridor, that provides detailed demand data was selected as the initial demonstration area for a distributed traffic assignment solution. The road link/intersection network for this area of interest is show on the left. A Frank Wolfe algorithm is used for

implementing this particular traffic assignment problem when optimizing travel time. This code was further developed to include the energy optimization case. The proposed energy model is a combination of the CMEM fuel consumption model [1]. with a traditional BPR function. To ensure convergence, the speed – fuel consumption curve was slightly adjusted to make the curve convex which allows the gradient descent method to converge. This geospatial area represents 28,000 road links. A demand model of 100,000 Origin/Destination pairs from the SCAG demand profile are applied to this road network. Note that a static assignment does not deal with the dynamic behavior that results from network dynamics, it

simply assigns an O/D routing solution that minimizes travel time for all mobile entities so that no driver can unilaterally reduce his/her travel costs by shifting to another route. This is often referred to as the Nash Equilibrium . To extend our optimization focus further, we also included a notion of system optimization in context of these two different objectives. Consequently, four key cases are the subject of the investigation:

• Energy optimized at the system level • Energy optimized selfishly at the vehicle level • Travel time optimized at the system level • Travel time optimized selfishly at the vehicle level.

With these four cases implemented on a small-scale network the next step it to address larger scale road networks and dynamic assignment models.

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In order to focus on pragmatic results that can impact city level government, existing infrastructure from another VTO supported program - Big Data Solutions for Mobility Planning – was leveraged and extended for this program. An urban scale simulation program that has been implemented on HPC, called Mobiliti, had previously built an infrastructure for ingesting large-scale demand models and urban-scale road networks. As a part of the Mobiliti simulation work an efficient network routing algorithm was also implemented. This ingestion infrastructure and the routing algorithms were integrated into a Frank Wolfe solution. The Mobiliti routing solution optimizes the compute time and is capable of identifying optimal routes through the network instead of approximate solutions, which are often used to reduce computational loads. With this infrastructure, a processing pipeline is in place for this project that provides ingestion of urban-scale demand profiles and networks and high-speed routing capabilities. Instead of optimizing the system based on the travel time, we extended existing algorithms for the traffic assignment problem (TAP) with new objective functions to incorporate vehicle fuel consumption. Specifically, we use a vehicle fuel consumption curve, i.e. fuel consumption rate vs. speed curve from the developed afore-mentioned data-driven CMEM [1] energy models. We conducted multiple experiments to investigate the patterns of the four different traffic assignment methods, i.e. time-based user-equilibrium (UET), time-based system-optimal (SET), fuel-based user-equilibrium (UEF) and fuel-based system-optimal (SEF). Preliminary visualization programs were developed to perform exploratory analysis on these four different cases. The procedures to solve this problem on the supercomputer Cori is as follows:

Results The figures below show the results of these optimizations. Links that represent the top 1000 flow values are shown with blue at the lower values and green/red as the higher values. Each optimization focus shows a variation in flow as a result of the optimization.

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Flow Impact Due to Different Optimization Solutions

Typically, cities are interested in optimizing travel time. Realizing that travel time optimizing is usually accomplished by selfish routing – e.g. a traveler will pick the travel time that is shortest for their own goal – we provide a view that is normalized to this particular perspective. The figures below show how travelers are impacted for each specific case in terms of distance traveled and travel time.

Distance Impact on Travelers Due to Different Optimization Solutions: Normalized to User Equilibrium

Travel Time The peaks in the figures represent travelers that experience no impact in these scenarios. The tails of the graphs show the percentage distance impact from their path if this were optimized for travel time only. Total vehicle miles traveled for each case is shown below with User Equilibrium that is optimized for fuel consumption results in the lowest vehicles miles traveled.

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Difference in Vehicle Miles Traveled with respect to User Equilibrium Travel Time Optimization

In addition to distance, travel time impacts were also determined and are shown in the figures below. As expected, travel time suffers if alternate optimization solutions are considered. Similar to the distance impacts, the peaks in the figures represent travelers that experience no impact in these scenarios. The tails of the graphs show the percentage travel time impact from their path if this were optimized for travel time only. Clear from this analysis is the complexity of the tradeoffs in transportation system optimization solutions.

Travel Time Impact with Respect to User Equilibrium Travel Time Optimization

Our next step was to extend this model to address a much larger, urban-scale model. A network and demand model that provides a foundation for research work at VTTI {ref} is being integrated into the infrastructure. This model is based on the HERE Technologies map that is a high-quality representation of the Los Angeles network. As this is being implemented, an alternate urban-scale network for the Bay Area was investigated.

The Bay Area network has 2 million road links and the traffic demand includes 22 million origin-destination pairs. The preliminary performance results of a total solving time of 45 mins, was implemented on the LBNL Cori supercomputer with a single computing node and 64 threads. The figure below indicates the highest flow links for a UET solution. An important note is that the compute time for this solution is significantly lower than any traffic assignment solutions at this scale. In fact, due to the computational loads current solutions break the problems into smaller time scale solutions and still might, in the best case, run in a compute time on the order of many hours. The figure at the left shows top 5000 Flow Links in a UET optimization scenario.

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To initiate a discussion of metrics associated with control of an urban-scale fleet, we also show the network usage for our four optimization cases. We wish to explore how optimization drives network use. This is important if we wish to consider how to best use our available network resources. Note that the larger scale urban network of the Bay Area, that contains bridges and reduces the connectivity among regions significantly changes the direction of impact on VMT. Once again demonstrating the complexity of tradeoffs in transportation system planning and optimization.

Metrics to Consider for Urban-Scale Fleet Level Optimization

Conclusions

The complexity of road network connectivity and demand modeling dynamics has long been the challenge for urban planners and urban modeling and simulation research. From a practical standpoint, first order estimates are currently being used to predict the energy impacts of emerging mobility solutions. For example, the impact of CAVs on VMT and energy footprint have been estimated based on census data and statistics of travel behavior. HPC, data science and advanced modeling, will allow DOE to develop the ability to perform more realistic and detailed computations. Such capabilities are essential, as the complexity of the transportation infrastructure cannot be aggregated and comprehensively modeled mathematically. As such local/regional, State, and Federal level will need to rely on models that can be considered at a granular level, yet still at scale. This initial work has shown the complexity of the tradeoffs associated with optimizing traffic assignment. With HPC, we are able to investigate scaled optimization scenarios with a compute time on the order of less than an hour of which will enable cities to reimagine their opportunities to offer their citizens and businesses better environments in which to live.

References [1] George Scora and Matthew Barth. Comprehensive modal emissions model (cmem), version 3.01. User guide. Centre for Environmental Research and Technology. University of California, Riverside, 2006.