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Signal Timing Optimization for Mixed Connected Automated Traffic Based on A Markov Delay Approximation

Ximin Yue, Yunlong Zhang, Zihao Li, Yang Zhou

TL;DR

This work develops a Markov-based analytical framework to approximate intersection delay in mixed traffic consisting of CAVs and HDVs. By embedding a Discrete-Time Markov Chain platoon model within a car-following/queuing-theoretic setting, it derives closed-form expressions for capacity and cycle-length optimization that capture differences in CAV and HDV arrivals and headways. The key contributions are a tractable DTMC-based capacity expression, a queueing-based delay model distinguishing CAV-led and HDV-led departures, and an explicit optimal cycle-length formula, all validated through numerical experiments. The results show that increasing CAV penetration reduces delay and that optimizing green time allocation can yield substantial gains, guiding traffic-signal design for emerging mixed-traffic environments.

Abstract

Connected Automated Vehicles (CAVs) offer unparalleled opportunities to revolutionize existing transportation systems. In the near future, CAVs and human-driven vehicles (HDVs) are expected to coexist, forming a mixed traffic system. Although several prototype traffic signal systems leveraging CAVs have been developed, a simple yet realistic approximation of mixed traffic delay and optimal signal timing at intersections remains elusive. This paper presents an analytical approximation for delay and optimal cycle length at an isolated intersection of mixed traffic using a stochastic framework that combines Markov chain analysis, a car following model, and queuing theory. Given the intricate nature of mixed traffic delay, the proposed framework systematically incorporates the impacts of multiple factors, such as the distinct arrival and departure behaviors and headway characteristics of CAVs and HDVs, through mathematical derivations to ensure both realism and analytical tractability. Subsequently, closed-form expressions for intersection delay and optimal cycle length are derived. Numerical experiments are then conducted to validate the model and provide insights into the dynamics of mixed traffic delays at signalized intersections.

Signal Timing Optimization for Mixed Connected Automated Traffic Based on A Markov Delay Approximation

TL;DR

This work develops a Markov-based analytical framework to approximate intersection delay in mixed traffic consisting of CAVs and HDVs. By embedding a Discrete-Time Markov Chain platoon model within a car-following/queuing-theoretic setting, it derives closed-form expressions for capacity and cycle-length optimization that capture differences in CAV and HDV arrivals and headways. The key contributions are a tractable DTMC-based capacity expression, a queueing-based delay model distinguishing CAV-led and HDV-led departures, and an explicit optimal cycle-length formula, all validated through numerical experiments. The results show that increasing CAV penetration reduces delay and that optimizing green time allocation can yield substantial gains, guiding traffic-signal design for emerging mixed-traffic environments.

Abstract

Connected Automated Vehicles (CAVs) offer unparalleled opportunities to revolutionize existing transportation systems. In the near future, CAVs and human-driven vehicles (HDVs) are expected to coexist, forming a mixed traffic system. Although several prototype traffic signal systems leveraging CAVs have been developed, a simple yet realistic approximation of mixed traffic delay and optimal signal timing at intersections remains elusive. This paper presents an analytical approximation for delay and optimal cycle length at an isolated intersection of mixed traffic using a stochastic framework that combines Markov chain analysis, a car following model, and queuing theory. Given the intricate nature of mixed traffic delay, the proposed framework systematically incorporates the impacts of multiple factors, such as the distinct arrival and departure behaviors and headway characteristics of CAVs and HDVs, through mathematical derivations to ensure both realism and analytical tractability. Subsequently, closed-form expressions for intersection delay and optimal cycle length are derived. Numerical experiments are then conducted to validate the model and provide insights into the dynamics of mixed traffic delays at signalized intersections.
Paper Structure (13 sections, 1 theorem, 33 equations, 9 figures, 1 table)

This paper contains 13 sections, 1 theorem, 33 equations, 9 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. CAPACITY DERIVATION FOR MIXED TRAFFIC
  3. Steady State Mixed Traffic Sequence Analysis
  4. Capacity Analysis
  5. DELAY APPROXIMATIONS AND ANALYTICAL MODEL
  6. Intersection arrival & departure behaviors and delay approximation
  7. Analytical delay models of the intersection
  8. Optimal cycle length
  9. NUMERICAL EXPERIMENTS AND ANALYSIS
  10. Numerical Experiments Settings
  11. Experiment results and analysis
  12. Optimal cycle length for mixed traffic
  13. CONCLUSION

Key Result

Proposition 1

Under our delay model, the total delay of mixed traffic with CAVs and HDVs at an isolated intersection is a monotonically increasing function of the cycle length $C$, where $C \in (0, \infty)$. Therefore, minimizing the cycle length reduces the total delay at the intersection.

Figures (9)

  • Figure 1: Illustative example of DTMC for mixed traffic platoon
  • Figure 2: Arrival and departure behavior of CAV-led platoon.
  • Figure 3: Arrival and departure behavior of HDV-led platoon.
  • Figure 4: Arrival and departure behavior of an HDV-led platoon.
  • Figure 5: Illustration of start-up delay of the HDV-led platoon
  • ...and 4 more figures

Theorems & Definitions (1)

  • Proposition 1