By Advisors Divya Kumar Amit Kumar Dr. Srinivas Peeta - - PowerPoint PPT Presentation

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Aug 14, 2023 451 likes •660 views

By Advisors Divya Kumar Amit Kumar Dr. Srinivas Peeta Introduction Objective & Scope Methodology Computational Results Summary 4 Step Transportation Planning Process Trip Generation Trip Distribution Mode

SLIDE 1

By Divya Kumar Advisors Amit Kumar

Dr. Srinivas Peeta

SLIDE 2

 Introduction  Objective & Scope  Methodology  Computational Results  Summary

SLIDE 3

 4 Step Transportation Planning Process

 Trip Generation  Trip Distribution  Mode Choice  Traffic Assignment

SLIDE 4

 Traffic Assignment

 Given: Network Structure, Origin-Desitination (O-D)

Demand, Link Performance Function

 Objective: To estimate the link / route flows and travel

times in a network

 Static Traffic Assignment – Mostly used for planning purposes  Dynamic Traffic Assignment

SLIDE 5

 Static Traffic Assignment

 System Optimal

 Minimizes travel time of system as a whole

 User Equilibrium (UE)

 Minimizes travel time of individual users

 More realistic and used in the planning process

SLIDE 6

 User Equilibrium (UE)

 Based on Wardrop’s first principle

 Definition of UE: “For each O-D pair, the travel times on all

used paths are equal, and less than or equal to the travel time experienced by a single vehicle on any unused path”

 Assumptions:

 All users perceive travel time identically and have full knowledge

f travel times on all possible routes

 All motorists unilaterally try to decrease their travel time  At equilibrium no motorist can experience a lower travel time by unilaterally changing routes.

SLIDE 7

 Solving for Static Traffic Assignment UE

 Link Based algorithm  Origin Based algorithm  Path Based algorithm

 Multi Path Algorithm (MPA)

SLIDE 8

 Objectives:

 Parametric Analysis  Sensitivity Analysis

 Scope:

 To identify the values of parameters of the algorithm that

will get the best performance of the algorithm

SLIDE 9

 Parametric Analysis

 Keep Scaling Factor & Demand Level Constant  Change # of Inner Iterations  For each Scaling Factor (0.8 – 1.6), run program for Inner

Iterations 1 – 10

 Record Ngap & Cpu Time for each Inner Iteration  Plot graph of Ngap vs. Cpu time of all Inner Iterations for each

Scaling Factor (0.8 – 1.6)

 Take best Inner Iteration (lowest Ngap & Cpu time) from each

Scaling Factor and plot into one final graph.

 Repeat for remaining Demand Levels

SLIDE 10

 Sensitivity Analysis

 For a given demand level, find the best combination of scaling factor

and inner iteration

 Ex. For Dem. Level 0.8 (ScF. 1.1, InIt 1) is the best

 For the Scaling Factor & Inner Iteration obtained in step 1, plot the

result of runs for all demand levels

 Ex.  Dem. Level 0.8 (ScF. 1.1, InIt 1) --Best  Dem. Level 1.0 (ScF. 1.1, InIt 1)  Dem. Level 1.2 (ScF. 1.1, InIt 1)

 Repeat process for other demand levels  Plot graph of Ngap vs. Cpu Time for best parameters for all demand

levels

0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 5 10 15 20 Ngap (Log Scale) Cpu Time (sec)

Best of Dem. Level 0.8

Dem0.8 Sf1.1 Init1 Dem1.0 Sf1.1 Init1 Dem1.2 Sf1.1 Init1

SLIDE 11

 Parametric Analysis  Sensitivity Analysis

SLIDE 12

0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10 100 1 2 3 4 5 6 7 8

Ngap Cpu time (Sec) Sc.Fac=1.1, Dem Lev=0.8

initer1 initer2 initer3 initer4 initer5 initer6 initer7 initer8 initer9 initer10

SLIDE 13

0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10 100 2 4 6 8 10 12 14

Ngap Cpu time (Sec) Demand Level = 0.8

Sf0.5Init3 Sf0.6Init2 Sf0.7Init1 Sf0.8Init1 Sf0.9Init1 Sf1.0Init1 Sf1.1Init1 Sf1.2Init1 Sf1.3Init1 Sf1.4Init1 Sf1.5Init3

SLIDE 14

0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 5 10 15 20 25 30 35 40

Ngap Cpu time (Sec) Demand Level = 1.0

Sf0.5Init3 Sf0.6Init2 Sf0.7Init1 Sf0.8Init1 Sf0.9Init1 Sf1.0Init1 Sf1.1Init1 Sf1.2Init1 Sf1.3Init1 Sf1.4Init1 Sf1.5Init3

SLIDE 15

0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 5 10 15 20 25 30 35

Ngap Cpu time (Sec) Demand Level = 1.2

Sf0.5Init3 Sf0.6Init2 Sf0.7Init1 Sf0.8Init1 Sf0.9Init1 Sf1.0Init1 Sf1.1Init1 Sf1.2Init1 Sf1.3Init1 Sf1.4Init1 Sf1.5Init3

SLIDE 16

0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 5 10 15 20 Ngap (Log Scale) Cpu Time (sec)

Best of Dem. Level 0.8

Dem0.8 Sf1.1 Init1 Dem1.0 Sf1.1 Init1 Dem1.2 Sf1.1 Init1 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 5 10 15 20 25 30 35 Ngap (Log Scale) Cpu Time (sec)

Best of Dem. Level 1.0

Dem0.8 Sf1.5 Init3 Dem1.0 Sf1.5 Init3 Dem1.2 Sf1.5 Init3 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 5 10 15 20 25 Ngap (Log Scale) Cpu Time (sec)

Best of Dem. Level 1.2

Dem0.8 Sf1.4 Init1 Dem1.0 Sf1.4 Init1 Dem1.2 Sf1.4 Init1

SLIDE 17

0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 5 10 15 20 25

Ngap (Log Scale) Cpu Time (sec) Best of All Dem. Levels

Dem0.8 Sf1.1 Init1 Dem1.0 Sf1.5 Init3 Dem1.2 Sf1.4 Init1

SLIDE 18

 The performance of the Multi Path Algorithm (MPA)

depends on Scaling Factor and # of Inner Iterations

 The best performance of MPA for demand level 1

was found at the scaling factor of 1.5

 The performance of the MPA is also sensitive to the

level of demand

 With the increase in demand level, the required Cpu

time to achieve convergence increases

SLIDE 19

By Divya Kumar Advisors Amit Kumar

 Introduction  Objective & Scope  Methodology  Computational Results  Summary

 4 Step Transportation Planning Process

 Trip Generation  Trip Distribution  Mode Choice  Traffic Assignment

 Traffic Assignment

 Given: Network Structure, Origin-Desitination (O-D)

Demand, Link Performance Function

 Objective: To estimate the link / route flows and travel

times in a network

 Static Traffic Assignment – Mostly used for planning purposes  Dynamic Traffic Assignment

 Static Traffic Assignment

 System Optimal

 Minimizes travel time of system as a whole

 User Equilibrium (UE)

 Minimizes travel time of individual users

 More realistic and used in the planning process

 User Equilibrium (UE)

 Based on Wardrop’s first principle

 Definition of UE: “For each O-D pair, the travel times on all

used paths are equal, and less than or equal to the travel time experienced by a single vehicle on any unused path”

 Assumptions:

 All users perceive travel time identically and have full knowledge

 All motorists unilaterally try to decrease their travel time  At equilibrium no motorist can experience a lower travel time by unilaterally changing routes.

 Solving for Static Traffic Assignment UE

 Link Based algorithm  Origin Based algorithm  Path Based algorithm

 Multi Path Algorithm (MPA)

 Objectives:

 Parametric Analysis  Sensitivity Analysis

 Scope:

 To identify the values of parameters of the algorithm that

will get the best performance of the algorithm

 Parametric Analysis

 Keep Scaling Factor & Demand Level Constant  Change # of Inner Iterations  For each Scaling Factor (0.8 – 1.6), run program for Inner

Iterations 1 – 10

 Record Ngap & Cpu Time for each Inner Iteration  Plot graph of Ngap vs. Cpu time of all Inner Iterations for each

Scaling Factor (0.8 – 1.6)

 Take best Inner Iteration (lowest Ngap & Cpu time) from each

Scaling Factor and plot into one final graph.

 Repeat for remaining Demand Levels

 Sensitivity Analysis

 For a given demand level, find the best combination of scaling factor

and inner iteration

 Ex. For Dem. Level 0.8 (ScF. 1.1, InIt 1) is the best

 For the Scaling Factor & Inner Iteration obtained in step 1, plot the

result of runs for all demand levels

 Ex.  Dem. Level 0.8 (ScF. 1.1, InIt 1) --Best  Dem. Level 1.0 (ScF. 1.1, InIt 1)  Dem. Level 1.2 (ScF. 1.1, InIt 1)

 Repeat process for other demand levels  Plot graph of Ngap vs. Cpu Time for best parameters for all demand

levels

 Parametric Analysis  Sensitivity Analysis

Ngap Cpu time (Sec) Sc.Fac=1.1, Dem Lev=0.8

Ngap Cpu time (Sec) Demand Level = 0.8

Ngap Cpu time (Sec) Demand Level = 1.0

Ngap Cpu time (Sec) Demand Level = 1.2

Best of Dem. Level 0.8

Best of Dem. Level 1.0

Best of Dem. Level 1.2

Ngap (Log Scale) Cpu Time (sec) Best of All Dem. Levels

 The performance of the Multi Path Algorithm (MPA)

depends on Scaling Factor and # of Inner Iterations

 The best performance of MPA for demand level 1

was found at the scaling factor of 1.5

 The performance of the MPA is also sensitive to the

level of demand

 With the increase in demand level, the required Cpu

time to achieve convergence increases

Thank You 