Hybrid model predictive control based dynamic pricing of managed lanes with multiple accesses

Tan, Zhouliang; Gao, H. Oliver

doi:10.1016/j.trb.2018.03.008

Cited by 16 publications

(16 citation statements)

References 21 publications

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“…Lou et al developed a self-learning toll calculation algorithm that searches for the optimal toll based on the approaching demand, learned willingness to pay, and the estimated TTs ( 19 ). Tan and Gao suggested toll pricing methods based on model predictive control, which considers different origin-destination (OD) pairs in toll calculation ( 20 ). Zhu and Ukkusuri proposed a distance-based algorithm that finds the optimal toll via an R-Markov Average Reward Technique-based reinforcement learning algorithm ( 21 ).…”

Section: Literature Reviewmentioning

confidence: 99%

Evaluation of Alternative Methods for Dynamic I-95 Express Lane Pricing

Mitrovic

Stevanovic

Glavić

2020

Transportation Research Record

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Developing dynamic toll algorithms is a major task for express lanes (EL) policy makers. The majority of pricing methods applied in the field utilize traffic data collected at several points along an EL segment to estimate traffic conditions (mainly traffic density) and calculate tolls. While travel time (TT) data can directly capture field conditions and users’ delay on a segment, such data are rarely utilized to calculate tolls for EL users. The literature suggests minor utilization of TTs in EL toll calculations, but not as the main target performance measure. More importantly, there is a need to look at performance of EL tolls from a multi-criteria perspective where the goal is not only to maintain certain level of service on the ELs. To address these topics, this study tests alternative toll calculation methods that rely mainly on TT data and compare their performance with the currently utilized toll calculation algorithm on I-95 EL in South Florida, U.S. In addition, this study proposes an evaluation framework which includes five different criteria to select the best-performing algorithms: 1. policy, 2. efficiency, 3. capacity utilization, 4. cost recovery, and 5. reliability. Results of the study show that a TT-based algorithm, which is less sensitive than conventional methods, performs similarly to a density-based algorithm, and that a travel time savings (TTS)-based algorithm maintains speeds on the ELs more efficiently than the alternative methods. Future research should apply and validate similar methods on other EL cases around the country.

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Section: Literature Reviewmentioning

confidence: 99%

Evaluation of Alternative Methods for Dynamic I-95 Express Lane Pricing

Mitrovic

Stevanovic

Glavić

2020

Transportation Research Record

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“…Yang et al ( 2 ) solve for optimal tolls for each entrance and exit by assuming that, if a traveler enters the managed lane, they do not exit it until their destination. Zhu and Ukkusuri ( 3 ) and Tan and Gao ( 12 ) make similar assumptions in their pricing models and use a binary logit model to determine lane choice. Pandey and Boyles ( 4 ) use VOT distributions to model lane choice by comparing utilities over a set of routes called decision routes.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Binary logit route choice models used in the literature ( 2 , 3 , 12 ) assume that travelers do not exit the managed lane from when they enter until the end of the corridor. The diverge nodes located on the managed lanes are no longer considered as decision points.…”

Section: Routing Modelsmentioning

confidence: 99%

Comparing Route Choice Models for Managed Lane Networks with Multiple Entrances and Exits

Pandey

Boyles

2019

Transportation Research Record

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Developing an appropriate route choice model for managed lanes with multiple entrances and exits is critical for the success of managed lane planning and operations. This research focuses on route choice models for managed lane networks with stochastic and time-varying tolls and travel times. In the model, a traveler receives real-time information about the tolls and travel times upon arrival at each diverge node and makes a dynamic lane choice decision that minimizes the total expected cost. The online route choice model is formulated as a Markov decision process and solved using a backward recursion algorithm. The model is compared against four other routing models: a binary logit model, a model based on decision routes, a model that chooses paths a priori, and a model with routes chosen randomly. The study also models irrational driver behavior with parameters like driver’s inclination toward making optimal lane choices and preference for certain lanes. Findings show that the expected costs from the routes chosen using the decision route model from the literature are close to the optimal cost with an average percentage error of 0.93%. The binary logit model is shown to have a high average error of 50% in the expected cost when a driver is assumed to behave rationally, but the same model shows optimal prediction for certain irrational driver behaviors. The proposed routing model forms a basis for future work in the area of managed lane pricing and planning.

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“…Several dynamic pricing algorithms have been explored in the literature that optimize tolls under varying assumptions on driver behavior. These include methods using stochastic dynamic programming [32], hybrid model predictive control (MPC) [27,28], reinforcement learning (RL) [20,36], and approximate dynamic programming [19]. While these algorithms do well against existing heuristics, they make some or all of the following restricting assumptions, which we relax:…”

Section: Introduction 1background and Motivationmentioning

confidence: 99%

“…Restricted access for travelers: travelers do not exit the managed lane once they enter till their exit is reached [32,36] and that they only consider the first entry point as the decision point for the lane choice decision [27] 2. Fully observable system: toll operators have access to measurements of traffic density throughout the network for optimizing tolls [19,20,27,32,36] 3. Ignored traveler heterogeneity: a single vehicle class is considered with a single origin and destination [19,32,36] 4.…”

Section: Introduction 1background and Motivationmentioning

confidence: 99%

Deep Reinforcement Learning Algorithm for Dynamic Pricing of Express Lanes with Multiple Access Locations

Pandey,

Wang,

Boyles

2019

Preprint

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This article develops a deep reinforcement learning (Deep-RL) framework for dynamic pricing on managed lanes with multiple access locations and heterogeneity in travelers' value of time, origin, and destination. This framework relaxes assumptions in the literature by considering multiple origins and destinations, multiple access locations to the managed lane, en route diversion of travelers, partial observability of the sensor readings, and stochastic demand and observations. The problem is formulated as a partially observable Markov decision process (POMDP) and policy gradient methods are used to determine tolls as a function of real-time observations. Tolls are modeled as continuous and stochastic variables, and are determined using a feedforward neural network. The method is compared against a feedback control method used for dynamic pricing. We show that Deep-RL is effective in learning toll policies for maximizing revenue, minimizing total system travel time, and other joint weighted objectives, when tested on real-world transportation networks. The Deep-RL toll policies outperform the feedback control heuristic for the revenue maximization objective by generating revenues up to 9.5% higher than the heuristic and for the objective minimizing total system travel time (TSTT) by generating TSTT up to 10.4% lower than the heuristic. We also propose reward shaping methods for the POMDP to overcome undesired behavior of toll policies, like the jam-and-harvest behavior of revenue-maximizing policies. Additionally, we test transferability of the algorithm trained on one set of inputs for new input distributions and offer recommendations on real-time implementations of Deep-RL algorithms. The source code for our experiments is available online at https://github.com/venktesh22/ExpressLanes_Deep-RL.

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Hybrid model predictive control based dynamic pricing of managed lanes with multiple accesses

Cited by 16 publications

References 21 publications

Evaluation of Alternative Methods for Dynamic I-95 Express Lane Pricing

Evaluation of Alternative Methods for Dynamic I-95 Express Lane Pricing

Comparing Route Choice Models for Managed Lane Networks with Multiple Entrances and Exits

Deep Reinforcement Learning Algorithm for Dynamic Pricing of Express Lanes with Multiple Access Locations

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