Optimal Control for Congestion Pricing: Theory, Simulation, and Evaluation

Pushkin Kachroo, Saumya Gupta, Shaurya Agarwal, Kaan Ozbay

Research output: Contribution to journalArticlepeer-review


This paper presents a mathematical framework for dynamic congestion pricing. The objective is to calculate an optimal toll using the optimal control theory. The problem consists of tolled lanes or routes and alternate non-tolled lanes or routes. The model is developed using a traffic conservation law, the queuing theory, and fundamental macroscopic relationships. A logit model is used for establishing the relationship between the price and the driver's choice behavior. We design a cost function and then use Hamilton-Jacobi-Bellman equation to derive an optimal control law that uses real-time information to determine an optimal tolling price. Simulations are performed to demonstrate the performance of this optimal control congestion-pricing algorithm.

Original languageEnglish (US)
Pages (from-to)1234-1240
Number of pages7
JournalIEEE Transactions on Intelligent Transportation Systems
Issue number5
StatePublished - May 2017


  • Optimal control
  • chattering
  • congestion pricing
  • logit
  • saturation function

ASJC Scopus subject areas

  • Automotive Engineering
  • Mechanical Engineering
  • Computer Science Applications


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