PCE15-M – Queuing, Safety, Service & Traffic Studies, Slides of Transportation Engineering

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PCE15-M

PRINCIPLES OF

TRANSPORTATION ENGINEERING

Queueing Theory, Highway

Safety and Accident Analysis,

Service Rates and Traffic

Studies

OUTLINE

I. Queueing Theory

II. Highway Safety and Accident

Analysis

a. Accident rates for 100 million vehicle

miles of travel for a segment of

highway

b. Accident rates per million entering

vehicles for an intersection

c. Severity ratio

III. Service Rates

IV. Traffic Studies

a. Basic Intersection Design Principle

b. Intersection Design Elements

c. Methods of Control of Intersection

d. Analysis of Unsignalized Intersections

e. Analysis and Design of Roundabouts

or Rotondas

f. Traffic Signal Control

Arrival Rate (λ) - The rate at which vehicles arrive at a queue Departure Rate (μ) - The rate at which vehicles leave the queue point

• or Service Rate Traffic Intensity (ρ) - The ratio of the arrival rate to the departure rate Queue Length - The number of vehicles waiting in line Waiting Time - The time each vehicle spends in the queue

QUEUING THEORY

Types of Queue

• Oversaturated queue are those arrival rate is greater than the service rate
• Saturated queue are those arrival rate is less than the service rate

Under-saturated infinite queues when both arrivals and service times are exponentially

distributed and there is one channel. For example, when the road is under repair on one

lane.

QUEUING THEORY

• D / D / 1 Due to the regularity of both arrivals and departures, it is more convenient to analyze a D/D/ 1 queuing system graphically. Arrivals and departures are easily represented by straight lines with the slopes corresponding to their rates.
• M / D / 1 The M/D/ 1 queuing system assumes that the arrivals of vehicles follow a negative exponential distribution, a probability distribution characterized by randomness.

QUEUING THEORY

a. Average length of queue

m =

b. Average waiting time

w =

c. Average time spent in the system

i =

• M / M / 1 The M/M/ 1 queuing system assumes negative exponential for both arrival and departure distributions.

QUEUING THEORY

a. Average length of queue

m =

b. Average waiting time

w =

c. Average time spent in the system

i =

Sample Problem A freeway has three lanes in each direction and has a maximum flow of 100 veh/min. It is operating at 50 veh/min. A collision occurs, blocking the two lanes and restricting the flow of the third lane to 25 veh/min. The freeway has a constant speed of 60 veh/hr and its three-lane jam density is 60 veh/m. The incident is completely cleared in 30 minutes and traffic returns to normal as soon this happened. a. Determine the length of queue 20 mins after the collision b. Determine the longest vehicle queue. c. In how may minutes will the queue dissipate? d. How may vehicles were affected by the accident? e. Compute the total delay due to the accident. f. What is the average delay per vehicle.

QUEUING THEORY

HIGHWAY SAFETY AND ACCIDENT ANALYSIS

Accident rates for 100 million vehicle miles of travel is a crucial metric in highway safety analysis. It helps in understanding the frequency of accidents relative to the amount of travel on a specific highway segment.

HIGHWAY SAFETY AND ACCIDENT ANALYSIS

Severity Ratio: :

Severity Ratio =

• f : fatal
• i : injury
• p : property damage

HIGHWAY SAFETY AND ACCIDENT ANALYSIS

Importance of Accident Rates :

• Safety Assessment : Helps identify high-risk areas.
• Resource Allocation : Guides where to focus safety improvements.
• Performance Measurement : Evaluates the effectiveness of safety interventions.

HIGHWAY SAFETY AND ACCIDENT ANALYSIS

Data Collection and Analysis :

• Crash Data : Collecting accurate crash data is essential.
• Traffic Counts : Measuring traffic volumes accurately.
• Geospatial Analysis : Mapping accident locations to identify patterns.

SERVICE RATES

Service rates refer to the speed at which a system can serve or process arriving entities, such as vehicles in a traffic system or customers in a queue.

SERVICE RATES

Service rates refer to the speed at which a system can serve or process arriving entities, such as vehicles in a traffic system or customers in a queue. Service rate is a crucial parameter in analyzing how efficiently resources are utilized, affecting wait times and congestion levels in transportation systems. It is usually expressed in units such as vehicles per hour or customers per minute.

SERVICE RATES

Service rates refer to the speed at which a system can serve or process arriving entities, such as vehicles in a traffic system or customers in a queue. Service rate is a crucial parameter in analyzing how efficiently resources are utilized, affecting wait times and congestion levels in transportation systems. It is usually expressed in units such as vehicles per hour or customers per minute.