1.Problem Statement

    The purpose of this project is to develop a series of systems model for traffic passing through a 4-way intersection, controlled by traffic light. We will assume that arrangement of traffic lights and road lanes is fixed and that the lights switch from red to green to amber in a regular repetitive pattern. Moreover, we assume that driver behavior is constrained by the road rules (we keep this part really simple) and the desire to avoid vehicle collisions.

Terminology

Terminologies are the first thing we should define before start the project. Because of the complexity of the intersection control system, terms can bring us better understanding of the properties.

• Cycle: one complete sequence of signal indications

• Phase: part of a cycle allocated to any combination of traffic movements receiving the right of way simultaneously during one or more intervals.

• Conflict points: the potential points in a cycle that is possible to make collision.

• Level of Service: is defined in terms of average stopped delay per vehicle for signalized intersection.

• Queue: the total number of vehicle waiting at the intersection

A sample Intersection

When considering about an intersection, we should consider the following subsystems:

• Control system: the control design subsystem, the facility subsystem, and the signal control subsystems.

• User system: includes pedestrians, drivers, and traffic engineers.

• Physical intersection: the geometric information, pavement information and the traffic information.

To design the systems model for traffic passing through a 4-way intersection, the core in this project is how to design the control system so that the drivers and pedestrians can perceive precise and reliable information, with maximized system capacity and safety.

Since this project is addressed on the logical design, it’s necessary to clarify the response system between road user and control system and the design concerns of control system. There are 7 kinds of basic control system for an intersection.

i)        No control

ii)       Guide signing only

iii)     Guide and warning signing

iv)     Yield control

v)      Stop Control

vi)     Signalization

vii)    Police officer

Considering the real world situation, we only discuss four cases in our system.

• No control

• Stop control: Stop sign is needed in one/both direction; the vehicle will pass according their arriving sequence, first in first out.

• Yield control: Yield sign is needed in minor direction, no control in major direction. Cars proceed with caution.

• Signal control: Signals are needed. For each direction, signal cycle and signal phase design is based on the traffic information.

2. Goals & Scenarios

Goals 1. The system must be safe.

• Scenario 1.1: The setting of phases should eliminate the conflict points to a reasonable extend.

• The straight traffics in orthogonal direction can’t pass the intersection together.

• The left turn traffic can’t pass the intersection at the same time with the straight traffic in opposing direction.

• Scenario 1.2 : The time setting of each phase should be reasonable.

• The setting of green phase length must be long enough for a single vehicle cross the intersection from static status.

• The setting of red phase length must be long enough for a single vehicle in opposite vehicle cross the intersection from static status.

• The setting of yellow phase length must be long enough for an approaching vehicle to notice.

• The setting of pedestrian light length must be long enough for a senior person to cross the intersection.

• Scenario 1.3 : The driver must perceive the traffic before action

• The driver should check the traffic on the same direction.

• The driver should check the traffic on the opposite direction.

• The driver should check the traffic on the orthogonal direction.

• The driver should check the traffic light.

• The driver should check the pedestrians.

• Scenario 1.4:The pedestrian must perceive the traffic before action.

• The pedestrian should check the traffic light.

• The pedestrian should check the traffic on orthogonal direction.

• The pedestrian should check the right turn traffic on same direction.

• The pedestrian should check the left turn traffic on opposite direction.

Goals 2. The system must be efficient.

• Scenario 2.1 :The timing for each phase should be long enough for cleaning the queue.

• Scenario 2.2 :The length of a cycle should inside a proper range.

• Scenario 2.3 :The computed capability should be optima.

Goals 3. The system must be economic.

• Scenario 3.1: The setting of phase should be compatible with the traffic volume.

• Scenario 3.2: The setting of traffic light should be compatible with traffic volume.

• Scenario 3.3: The sign system should be compatible with the traffic volume.

Goals 4. The system must be compatible with traffic law.

• Scenario 4.1: The control design should according to the current traffic law.

• Scenario 4.2: The users should be aware of the traffic law.

• The driver should be aware of the traffic law.

• The pedestrian should be aware of the traffic law.

•  Scenario 4.3: The sign design should according to the current traffic law.

Goals 5. The system must be feasible.

• Scenario 5.1:The control design should be compatible with the sign system.

• Scenario 5.2:The control design should be compatible with the road geometries.

• Scenario 5.3:The LOS of the designed intersection can’t below grade f.

3.Use cases

3.1.Identify Actors

• Drivers

• Pedestrians

• Signal System

• Physical Intersection/ roadway

• Laws

3.2.Define Users

User 1: Pedestrians

Requirements:

1.      Safety: when the pedestrian is crossing the street, no car

2.      Perceivable: the information of when to walk and when to stop is perceivable to the pedestrian.

3.      Comfortable: the allowable time for walk is long enough to cross

User 2: Driver

Requirements:

1        Safety: the number of conflicting points is as small as possible.

2        Perceivable: the signals are perceivable and clear to the driver.

3        Comfortable: the allowable time for walk is long enough to cross the street.

User 3: Signal System

Requirements:

1.      Safety: the system has the least possibility of traffic accidents.

2.      Efficiency: The capacity of the intersection is maximized.

3.      Economy: The total investment of this system is minimized.

4.      Advanced requirement*:

a. Environmental consideration: air pollution, vibrations pollution, light pollution.

b. Regional consideration: the influence to the up flow traffic and down low traffic.

3.3.Initial Use Case Modeling

The use cases represent system goals or system functions.

Since we consider the safety, efficiency and economy of the system, the behavior of driver drives through an intersection can be divided into 3 parts:

1. Driver’s action: go straight ahead or turning left or right

2. Driver’s preservation:  watch the traffic lights, the traffic in other lanes and the pedestrians, etc.

3. System function: cycle length and phase setting.

3.4.System boundary

The driver, other traffic, pedestrian and other obstacles, and traffic lights are all external systems.

Use case (1): Cycle length setting.

Description: The cycle length setting should improve the capability of the intersection.

Primary Actor: Roadway, Law.

Preconditions: The roadway geometries and traffic data are known, drivers always follow the traffic law.

Flow of events:

(1)   Collect daily traffic volume.

(2)   Limited the cycle length in 50 seconds to 90 seconds according to the daily traffic volume.

Post–conditions: traffic data is known, and the cycle length is limited.
 

Use case (2): Phase setting

Description: The phase setting should improve the capability of the intersection.

Primary Actor: Roadway, Law.

Preconditions: The roadway geometries and traffic data are known, drivers always follow the traffic law, and the cycle length is known.

Flow of events:

(1)   Decide the number of signal phases.

(2)   Decide the time setting for each phase.

Post–conditions: Traffic cycle length and detailed phase setting are given.
  

Use case (3): Watch the traffic lights.

Description: The driver should be able to perceive the traffic light information.

Primary Actor: Driver, signal system.

Preconditions: The traffic signal system is available and stable; drivers always follow the traffic law.

Flow of events: 

(1)   The traffic lights are perceivable.

(2)   The driver has correct understanding of the traffic light.

Post–conditions: the driver is clear about the current signal status and has enough expectation of the possible change.

Use case (4): Watch traffic traveling in the same direction.

Description: The phase setting should improve the capability of the intersection.

Primary Actor: Driver Roadway, Law.

Preconditions: The roadway geometries and traffic data are known; drivers always follow the traffic law.

Flow of events: 

(1)   Watch the traffic in the same lane.

(2)   Watch the traffic in the other lanes.

Post–conditions: Perceive the traffic in the same direction and find a proper 

Use case (5): Watch for oncoming traffic.

Description: The driver should perceive the oncoming traffic before do any proceed action.

Primary Actor: Driver, Roadway, Law.

Flow of events:

(1)   Watch the oncoming (includes the traffic in orthogonal direction) straight traffic.

(2)   Watch the oncoming (includes the traffic in orthogonal direction)  left-turn traffic.

(3)   Watch the oncoming (includes the traffic in orthogonal direction)  right-turn traffic.

Preconditions: The driver has perceived the signal information

Use case (6): Watch out for pedestrians and other unexpected obstacles.

Description: The driver should try to avoid the collision of pedestrian and vehicle.

Primary Actor: Driver, Pedestrian, Law.

Preconditions: The driver has already perceived the traffic signals and other traffic.


Post–conditions: The signal information and traffic information are ready. 
  

Use case (7): Drive straight ahead.

Description: Driver should be able to drive the vehicle straight ahead.

Primary Actor: Driver, other traffic, law.

Precondition: The signal information and pedestrians’ information is perceived.

Flow of events: 

(1)   Judge if the integrated information allows driving.

(2)   Execute under the limitation of Law.

Post–conditions: The driver drives the car pass the intersection

Use case (8): Turn right.

Description: The phase setting should improve the capability of the intersection.

Primary Actor: Driver, Roadway, Law.

Preconditions: The traffic signal system is available and stable; drivers always follow the traffic law, the driver has perceived the signal information and traffic information in all direction.

Flow of events:

(1)   If the traffic light is green and the gap is large enough when there is yield control.

(2)   Turn right with proper execution.

Post–conditions: The driver drives the car pass the intersection.

Use case (9): Turn left.

Description: The phase setting should improve the capability of the intersection.

Primary Actor: Driver, Roadway, Law.

Preconditions: The traffic signal system is available and stable; drivers always follow the traffic law, the driver has perceived the signal information and traffic information in all direction.

Flow of events:

(1)   If the traffic light is green and the gap is large enough when there is yield control.

(2)   Turn left with caution.

Post–conditions: The driver drives the car pass the intersection.

3.5.Initial Use Case Diagram

Our initial use case diagram has four actors and six use cases.

Initial Use Case diagram

Activity Diagrams

4.Use case relationship diagram

5.System Requirements

5.1.Safety Requirements

1. Control system should avoid collision in the intersection
2. Time phasing should be reasonable for all directions and pedestrians
3. Drivers and pedestrians should perceive traffic before action

5.2.Performance Requirements

1. The timing for each phase should be long enough for cleaning the queue
2. The computed capability should be optimal

5.3.Compatibility Requirements

1. The setting of phase should be compatible with the traffic volume
2. The setting of traffic light should be compatible with traffic volume
3. The sign system should be compatible with the traffic volume and law
4. The control design should according to the current traffic law
5. The users should be aware of the traffic law
6. The control design should be compatible with the sign system
7. The control design should be compatible with the road geometries
8. The LOS of the designed intersection can’t below grade f

6.Simplified Model of System Behavior

    System has the following main subsystems:

• Controller System

• Controller Interface (Traffic Light)

• Intersection

• User System (Cars and pedestrians)

Simplified model of system behavior diagram

7.Simplified Model of System Structure

The signalized intersection system includes four main subsystems: traffic lights, environment, driver. However, the whole system can only work under the coordination of user, environment and facilities.

Simplified Model of System Structure

8.Logical Design

Signal Timing

    Signal timings describe the set of parameters defining the operation of signalized intersection. From an analytical perspective it involves the definition of the sequence by which the various movement at an  intersection is served  as well as the time duration of service for each movement.

    The process of Identifying the sequence of service is called phasing and it precedes all other signal timing steps. Then the cycle length is estimated and and green times are allocated to each phase according to the relative magnitude of traffic flows served in each phase. The latter part also includes the allocation of phase change intervals (yellow and all red). Certain constraints must be checked to ensure the safe and efficient processing of vehicles and pedestrians at an intersection.

Signal Phasing

    Phasing is the sequence by which the various movements of both vehicles and pedestrians are being served at a signalized intersection. The objective of phasing is the minimization of the potential hazards arising from the conflicts of vehicular and pedestrian movements, while maintaining the efficiency of flow through the intersection. Typical conflicts are 

1. Left turning vehicles conflict with opposing through traffic as well as with pedestrian

2. Right turning vehicles conflict with pedestrians

Increasing the number of phases promotes safety but hinders efficiency because it results in increasing delays. Delay increases because

1. Start-up lost times

2. Phase change intervals increase

3. Minimum phase duration requirements have to be met

The following figure shows two, three and four phase signal operation

    If heavy Left-Turning volumes are present on both intersecting streets, a four-phase operation is preferred. Actuated controllers are able to modify the cycle length as well as the durations of of green to better serve the actual demand. The flexibility of these systems results in more efficient service of traffic and and in the minimization of delays. Actuated controllers perform best at isolated locations and during off-peak times.

   The following figure illustrates the operation of a four-phase scheme under actuated control.

9.Use Case/Task interaction matrix

Traceability

11.Measures of effectiveness

According to the analysis of system goals we can define our measure of system effectives in the following aspects:

• Safety: the total accident per year, the accident related cost per year, the number of deaths caused by the accident per year…

• Capacity: level of service of the intersection, the average delay per vehicle, the peak-hour capacity,…

•  Economy: the construction cost, maintenance cost, etc.

• Other considerations: noise pollution, sound pollution, vibration pollution, land use impact,…

The effectiveness measures are listed in the following table.

The difficulty in the trade-off process is that the measures are in different scales, and it’s difficult to unify them to one unit so that we can find the optimal alternative easily. However, we can use the concept of “weight” to compare the importance of these measures. Here, we list the proposed weight for each measure, but a more reasonable and precise decision of weights need further discussion

12.Trade-off analysis

With the consideration of available budgets and technician, even the possible land use constraints. The best alternatives should be some design plan with the maximum evaluation value.

We introduce a ranking system in this evaluation process, which is described as below:

•  Assume there are n alternatives.

•  Compare the value of one measure of each alternative, i=1,..n , the alternative with the best measurement value gets n-1 , the second best gets n-2 , … the worst get 0 .

• Get the weighted summation of the ranking values for each alternative.

• Pickup the alternative with the largest weighted summation value, subject to the budget constraints and technology constraints.

Then the formulation can be:

However, with concern about safety, we should apply some ‘minmax’ criterion into the trade-off procedure, e.g. suppose for each traffic condition the total ranking result is shown as the following table.

Then if we apply the minmax criterion here, we will choose alternative 1 or alternative under the assumption that all these 3 events happen with same probability.

If we assign the possibility as below:

Then we should choose alternative 1, because it has less possibility to be the worse case.

If we apply maxmax, then we should choose alternative 2.

13.Conclusions & Future work

Traffic system is a typical “system of system” . In this project, we can learn how to planning and analyze a complex system with the systematic, integrated process, find the inner relation between each components and design the system.

In a signal control intersection, the actors are far more than the driver himself, depends on the degree of complexity, much more actors interact with the system externally, such as signal system, pedestrians, other traffic, even roadway law and vehicle itself.

The decision of actors depends on the scale and depth of the system design. However, after fix the scale and depth of the problem, it’s become much easier to write down the goals and scenarios, user cases and system behavior, however, with the consideration of accordance all the time. Comparatively, the logical design is the most difficult part of this project. It shows the core of our understanding of the system design, and a clear and brief explanation is difficult to achieve. Also, trade-off system is another key point that is difficult to fulfill because of the lack of quantitative measures.

The system we designed actually is simplified to some extend. More extension can be done with the consideration of control method choice, signal setting details with system behavior, more specifications on user cases, etc.

We are glad to see our improvement in the system design of signalized intersection, but, without doubt, there’s a lot of space for us to explore for a more precise and more concrete system design.

14.Refrences

1. M. A. Austin and B. A. Frankpitt, “System Engineering Principles: Lecture notes for ENSE 621 and ENPM 641”, 1998.
2. M. A. Austin, “System Engineering Requirements, Design and Trade-off Analysis: Lecture notes for ENSE 622 and ENPM 642”, 2002.
3. William R. McShane, Roger P. Roess, “Traffic Engineering”, Prentice Hall, 1990.
4. C.S. Papacostas, P.D.Prevedouros, "Transportation Engineering & Planning", Prentice Hall, 2001
5. "Traffic Control Systems Handbook", US Department of Transportation, Federal Highway Administration, 1996