Erdős’s Unit Distance Problem

Recently, electric vehicles (EV) have gained much attention as a potential enabling technology to support CO2 emissions reduction targets. Relative to their internal combustion vehicle counterparts, EVs consume less energy per unit distance, and add the benefit of not emitting any carbon dioxide in operation and instead shift their emissions to the existing local fleet of power generation. However, the true success of EVs depends on their successful integration with the supporting infrastructure systems. Building upon the recently published methodology for the same purpose, this paper presents a “systems-of-systems” case study assessing the impacts of EVs on these three systems in the context of Abu Dhabi. For the physical transportation system, a microscopic discrete-time traffic operations simulator is used to predict the kinematic state of the EV fleet over the duration of one day. For the impact on the intelligent transportation system (ITS), the integration of EVs into Abu Dhabi is studied using a multi-domain matrix (MDM) of the Abu Dhabi Department of Transportation ITS. Finally, for the impact on the electric power system, the EV traffic flow patterns from the CMS are used to calculate the timing and magnitude of charging loads. The paper concludes with the need for an intelligent transportation-energy system (ITES) which would coordinate traffic and energy management functionality.

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An improved FPT algorithm for the flip distance problem

Information and Computation ◽

10.1016/j.ic.2021.104708 ◽

2021 ◽

pp. 104708

Author(s):

Qilong Feng ◽

Shaohua Li ◽

Xiangzhong Meng ◽

Jianxin Wang

Keyword(s):

Fpt Algorithm ◽

Distance Problem ◽

Flip Distance

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Evaluating the Safety of Shared-Use Paths

Transportation Research Record Journal of the Transportation Research Board ◽

10.1177/0361198105193900112 ◽

2005 ◽

Vol 1939 (1) ◽

pp. 99-106 ◽

Cited By ~ 1

Author(s):

Lisa Aultman-Hall ◽

Jeffrey LaMondia

Keyword(s):

Sample Size ◽

Event Rate ◽

The Self ◽

Travel Patterns ◽

Unit Distance ◽

Safety Concerns ◽

Crash Rates ◽

Incident Rate

The project described in this paper involved the design of a survey of shared-use path safety for use at three facilities in Connecticut in the fall of 2002 and the summer of 2003. The objective was to collect self-reported information on collision and fall events and on travel exposure so that crash rates could be developed. The analysis of the self-reported events and travel patterns provides complementary data that are not available from other sources but are needed to address safety concerns on these facilities. The strengths of this approach include the collection of underreported minor events and the ability to estimate travel exposure and thus allow the estimation of crash rates per unit distance. The sample size of 684 was sufficient only for the development of aggregate crash rates, which suggest that skaters have the highest rates, followed by bicyclists and then pedestrians. The bicycle event rate was three times that of pedestrians, while the rate for skaters was more than six times that for pedestrians. Falls were more frequently reported than collisions, and they were more often associated with an injury. The overall incident rate for each of the three individual facilities was the highest for the path with the highest user volume and highest percentage of skaters and cyclists.

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A Maxmin Distance Problem

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3426562 ◽

1972 ◽

Vol 94 (2) ◽

pp. 155-158 ◽

Cited By ~ 7

Author(s):

R. Aggarwal ◽

G. Leitmann

Keyword(s):

Minimum Distance ◽

Terminal State ◽

Initial State ◽

Closed Set ◽

Distance Problem

The problem of maximizing the minimum distance of a dynamical system’s state from a given closed set, while transferring the system from a given initial state to a given terminal state, is considered. Two different methods of solution of this problem are given.

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