Optimizing Coordinated Vehicle Platooning: An Analytical Approach Based on Stochastic Dynamic Programming

Platooning connected and autonomous vehicles (CAVs) can improve traffic and fuel efficiency. However, scalable platooning operations require junction-level coordination, which has not been well studied. In this paper, we study the coordination of vehicle platooning at highway junctions. We consider a setting where CAVs randomly arrive at a highway junction according to a general renewal process. When a CAV approaches the junction, a system operator determines whether the CAV will merge into the platoon ahead according to the positions and speeds of the CAV and the platoon. We formulate a Markov decision process to minimize the discounted cumulative travel cost, i.e. fuel consumption plus travel delay, over an infinite time horizon. We show that the optimal policy is threshold-based: the CAV will merge with the platoon if and only if the difference between the CAV's and the platoon's predicted times of arrival at the junction is less than a constant threshold. We also propose two ready-to-implement algorithms to derive the optimal policy. Comparison with the classical value iteration algorithm implies that our approach explicitly incorporating the characteristics of the optimal policy is significantly more efficient in terms of computation. Importantly, we show that the optimal policy under Poisson arrivals can be obtained by solving a system of integral equations. We also validate our results in simulation with Real-time Strategy (RTS) using real traffic data. The simulation results indicate that the proposed method yields better performance compared with the conventional method

A Comparison Of Energy Expenditure And Prediction Equations During Walking Or Running Corrected For One Mile In Normal Weight And Overweight African American, Asian, And Caucasian Adults And Cross-Validation Of The Equations

The prevalence of obesity is rapid across the world. Knowledge of the actual energy expenditure (EE) of walking and running can lead to a more precise exercise prescription which may lead to an obesity reduction or avoidance. Limited research has focused on EE during walking and running. Therefore, the aims of this study included developing ethnic based cross validated EE prediction equations for African American, Asian and Caucasian adults, and a multiple regression equation developed that included all three ethnic groups. Also, the energy expenditure among these three ethnic groups was compared. A total of 224 subjects, including 71 Caucasians, 68 African Americans and 85 Asians were recruited to test EE through indirect calorimetry. Analysis of variance (ANOVA) was used for over- all significance with post Hoc Scheffe test to compare EE in three groups (normal weight walkers, overweight walkers and runners). Multiple regression analysis was employed for EE prediction, and a dependent t-test and chow statistical test were used to cross-validate. The results shothat EE in runners was significantly higher than that in normal weight walkers in African Americans. When EE was expressed relative to body weight, similar difference was observed between walkers and runners in both African Americans and Asians. When EE was expressed relative to fat free mass, normal weight walkers expended less energy than runners, both among African Americans and Asians. Furthermore, EE in African Americans was significantly higher than that in Caucasians and in Asians. Three EE prediction equations were developed specifically for African Americans, Asians, and the three ethnic groups. Through cross-validation, all the three equations were valid and they were all recommended to apply for calculating EE during walking or running one mile. The overall prediction equation was: EE=0.978 bw-4.571 gender (m=1, f=2)+3.524 ethnicity (Caucasians=1, AA=2, Asians=3)+32.447 (r=0.77; see=12.5 kcalâ·mile-1)