1 CES 341:Transportation Engineering and Planning Chapter 8 Traffic Analysis Techniques Asst. Prof. Dr. Mongkut Piantanakulchai Email: [email protected]

1

CES 341:Transportation Engineering and Planning

Chapter 8Traffic Analysis Techniques

Asst. Prof. Dr. Mongkut PiantanakulchaiEmail: [email protected]

CES 341 Transportation Engineering and

Planning

Chapter8: Traffic Analysis Techniques 2

8.1 Space-Time Relationships

Figure 8.1 Space-time diagram

t1

t2


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8.1 Space-Time Relationships

t1

t2

Note: Assume vehicle’s length is negligible


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8.1.1 Direct Graphical SolutionFig. 8.2 Location and size of double-track sections

Transit systemSingle track

15 km longTrain 10 min

interval dispatched from each end (W-E)

5 min layoversNeglect stop

time at stations

Uniform speed 45 km/h both directions

• Determine number and location of double-track sections, and the minimum length required for such sections in order for trains running as much as 2 min behind schedule to pass one another without delay


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8.1.1 Direct Graphical Solution Fig. 8.3 Train dispatch problem

Rail line 90 km long

7.5 km long double-track section located between 60-67.5 km from W end

A train leaves W end at 1:00 p.m. and travel E at constant speed of 45 km/h

The second train leaves from the E end at 1:30 p.m. and may travel at any speed up to 90 km/h

1) Determine earliest time the W-bound train can arrive at the W end of the line2) Determine the latest dispatch time (after 1:00 p.m.) that will allow the W-bound train to reach its destination without unnecessary delay


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8.1.2 Development of Analytical Solutions

Complicated space-time problems Space-time diagrams are used to

derive analytical solutions


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Example: Runway Capacity Analysis

Fig. 8.4 Time separation at runway threshold, vi ≤ vj

Fig. 8.5 Time separation at runway threshold, vi ≥ vj

jij vt

ijjij vvvt

11


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Example: Runway Capacity Analysis

iji j

ijmin tph

jiij ppp

minhC

1

Weighted average of interarrival time

where pij = probability of arrival pair i-j

Note: Assume arrivals only, no departuresMore details in CES 446 Port and Airport Engineering

If arrivals are independent

(10.2)

(10.3)

Capacity is expressed by

(10.1)


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8.1.3 Development of Simulation Models

More complicated problems Space-time diagrams are used to develop

simulation models Behavior of system in a step-by-step manner


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Example: Block Signal Control System for Rail Line Objective: To protect

train collisions and other hazards such as broken rails

System consists of• Electronically

insulated section of tracks = blocks

• Train detection system: to determine if a train is in a particular block (the block is occupied)

• Signal system (warn or control)

System of blocks and aspects (combination of signal lights)


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Example: Block Signal Control System for Rail Line

Fig. 8.6 Block signal control systems


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Example: Block Signal Control System

0.75 km long blocks Three-block, four aspect system

•RR –stop and proceed at 7.5 km/h prepared to stop

•RY – proceed at 30 km/h, prepare to stop at next signal

•GY – proceed at 60 km/h

•GG – proceed at full speed


Planning


Example: Block Signal Control System

•A train traveling at 45 km/h, passes a point A, which is located at a block boundary, at 11:00 a.m.

•Five min and 30 s later, a second train passes this point traveling at 90 km/h in the same direction

•Both trains are 0.375 km long

Describe the motion of the second train, determine the time that the rear of second train passes point B, located 4.875 km beyond point A


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Time-space diagram of the first train


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Signal indication after the first train


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Trajectory of the second train according to block signals


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Trajectory of the second train (front) according to block signals


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Trajectory of the second train (front&rear) according to block signals


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8.14 Non-trajectory Space-Time Diagrams

Display information about traffic states (speed, flow rate, density) as well as vehicle trajectories

Contour diagram can be used to display region with similar traffic state values


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8.14 Non-trajectory Space-Time Diagrams

Figure 8.11 Speed contours


Planning


8.2 Queuing Analysis

Figure 8.12 Queuing System


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8.2.1 Queuing Theory Fundamentals

Figure 8.13 Arrival function for airport runway

Figure 8.14 Arrival and departure functions for airport runway


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8.2.1 Queuing Theory Fundamentals

Figure 8.14 Queuing diagram features

Figure 8.14 Queuing diagram, smooth curve approximation


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8.2.2 Queue Discipline

First-in, first-out (FIFO) Last-in, first-out (LIFO) Random service Priority service


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Relationship of Delay (w(t)) and Queue Length (Q(t)) of Individual at Time t

tQ

tw

W(t) = Waiting time (Delay) of an individual at time t

Q(t) = Queue length at time t

rateservice


Planning


8.2.3 Stochastic Queuing Models

Deterministic queuing models – arrival and service rate are deterministic (known as some function)

Stochastic queuing models • constant long term arrival and service rates

• short-term random fluctuations around the average rates

• arrival rate may exceed service rate for short time intervals and queues will form


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Stochastic Queuing Models

M/D/1

M/M/1

ArrivalsExponentiallyDistributed

ServiceDeterministic(No random variation)

One Channel

Inter-arrival times followNegative Exponential Distribution


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M/D/1

12

2

12

1

2

t

w

Q

system in thespent

timeaveraget

time waitingaveragew

length queue averageQ

intensitytraffic

rateservice

ratearrival


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M/M/1

1

1

2

t

w

Q

system in thespent

timeaveraget

time waitingaveragew

length queue averageQ

intensitytraffic

rateservice

ratearrival


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General relationships

1

wt

tQ


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8.2.4 Transportation Applications of Queuing Theory

Server opens after arrivals beginArrival rate temporary exceedsconstant service rate

Service rate varies Server temporarily shut down


Planning


8.2.5 Queue Density, Storage, and Spillback

Density (vehicles per unit distance) Occupancy – fraction of time vehicles

are over the detector Objectives of studying queue density

•Locating queues and bottlenecks in traffic

•Determine the length of the queue and space needed for queue storage, control the queue spillback to upstream section


Planning


Example Problem 8.1

Morning peak traffic upstream of a toll booth is given in the table

The toll plaza consists of three booths, each of which can handle an average of one vehicle every 6 s.

Using queuing diagram, determine the maximum queue, the longest delay to an individual vehicle, and the total delay


Planning


Example Problem 8.1

Time period 10 min volumeCumulative

volume

7:00-7:10 200 200

7:10-7:20 400 600

7:20-7:30 500 1100

7:30-7:40 250 1350

7:40-7:50 200 1550

7:50-8:00 150 1700


Planning

Chapter8: Traffic Analysis Techniques 358-21

300 veh/min, D(t)

Cumulative volume, A(t)

D(t)>A(t) {Show A(t), No queues}


Planning


8.3 Network Analysis

Network•Nodes : Usually points of facilities intersect

•Origins or destinations of trips (source or sink nodes)

•Decision points

•Links : Usually road or railway segments Link characteristics

•Link costs: Distance, travel time, generalized costs (weighted sum of several costs)


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Network Elements


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Example networkMinimum path algorithm, step 1


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Minimum path algorithm, step 2


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Table 8.1 Link-cost array

Node

Node

1 2 3 4 5 6

1 -1 8 -1 2 -1 -1

2 8 -1 4 -1 2 -1

3 -1 -1 -1 -1 -1 3

4 2 -1 -1 -1 -1 -1

5 -1 2 -1 3 -1 10

6 -1 -1 3 -1 10 -1


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Documents

1 CES 341:Transportation Engineering and Planning Chapter 8 Traffic Analysis Techniques Asst. Prof. Dr. Mongkut Piantanakulchai Email: [email protected]