We could evaluate the safety of a control system by counting the number of conflicting desired movements at the local level. We could then compare systems by safety as well as by performance and hence evaluate the claim that certain types of traffic circles are safer than intersections [Flannery and Datta 1996].
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One Ring to Rule Them All:
The Optimization of Traffic Circles
Aaron Abromowitz Andrea Levy
Russell Melick
Harvey Mudd College Claremont, CA
Advisor: Susan E. Martonosi
Summary
Our goal is a model that can account for the dynamics of vehicles in a traffic circle. We mainly focus on the rate of entry into the circle to determine the best way to regulate traffic. We assume that vehicles circulate in a single lane and that only incoming traffic can be regulated (that is, incoming traffic never has the right-of-way).
For our model, the adjustable parameters are the rate of entry into the queue, the rate of entry into the circle (service rate), the maximum capacity of the circle, and the rate of departure from the circle (departure rate). We use a compartment model with the queue and the traffic circle as compart-ments. Vehicles first enter the queue from the outside world, then enter the traffic circle from the queue, and lastly exit the traffic circle to the outside world. We model both the service rate and the departure rate as dependent on the number of vehicles inside the traffic circle.
In addition, we run computer simulations to have a visual representation of what happens in a traffic circle during different situations. These allow us to examine different cases, such as unequal traffic flow coming from the different queues or some intersections having a higher probability of being a vehicle destination than others. The simulation also implements several life-like effects, such as how vehicles accelerate on an empty road but decelerate when another vehicle is in front of them.
In many cases, we find that a high service rate is the optimal way to maintain traffic flow, signifying that a yield sign for incoming traffic is most effective. However, when the circle becomes more heavily trafficked,
The UMAP Journal 30 (3) (2009) 247–260. c!Copyright 2009 by COMAP, Inc. All rights reserved.
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Figure 1. A simple traffic circle. Traffic circles may have more than one lane and may have a different number of intersections.
a lower service rate better accommodates traffic, indicating that a traffic light should be used. Thus, a light should be installed in most circle im-plementations, with variable timing depending on the expected amount of traffic.
The main advantage of our approach is that the model is simple and allows us to see clearly the dynamics of the system. Also, the computer simulations provide more in-depth information about traffic flow under conditions that the model could not easily show, as well as enabling visual observation of the traffic. Some disadvantages to our approach are that we do not analyze the effects of multiple lanes nor stop lights to control the flow of traffic within the circle. In addition, we have no way of analyzing singular situations, such as vehicles that drive faster or slower than the rest of the traffic circle, or pedestrians.
Introduction
Traffic circles, often called rotaries, are used to control vehicle flow through an intersection. Depending on the goal, a traffic circle may take different forms; Figure 1 shows a simple model. A circle can have one or more lanes; vehicles that enter a traffic circle can be met by a stop sign, a traffic light, or a yield sign; a circle can have a large or small radius; a circle can confront roads containing different amounts of traffic. These features affect the cost of the circle to build, the congestion that a vehicle confronts as it circles, the travel time of a vehicle in the circle, and the size of the queue of vehicles waiting to enter. Each of these variables could be a metric for evaluating the efficacy a traffic circle.
Our goal is to determine how best to control traffic entering, exiting, and traversing a traffic circle. We take as given the traffic circle capacity, the
arrival and departure rates at each of the roads, and the initial number of vehicles circulating in the rotary. Our metric is the queue length, or buildup, at each of the entering roads. We try to minimize the queue length by allowing the rate of entry from the queue into the circle to vary. For a vehicle to traverse the rotary efficiently, its time spent in the queue should be minimized.
We make the following assumptions:
• We assume a certain time of day, so that the parameters are constant.
• There is a single lane of circulating traffic (all moving in the same direc-tion).
• Nothing impedes the exit of traffic from the rotary.
• There are no singularities, such as pedestrians trying to cross.
• The circulating speed is constant (i.e., a vehicle does not accelerate or decelerate to enter or exit the rotary).
• Any traffic light in place regulates only traffic coming into the circle.