CE431 - Topic 7.2 Fratar Model PDF

TRIP DISTRIBUTION FRATAR MODEL FRATAR MODEL Also known as Growth Factor Model It is a method used in trip distribution to forecast travel demand between different zones based on existing patterns. It is typically used for updating trip matrices by adjusting for future growth in popu...

TRIP DISTRIBUTION FRATAR MODEL FRATAR MODEL Also known as Growth Factor Model It is a method used in trip distribution to forecast travel demand between different zones based on existing patterns. It is typically used for updating trip matrices by adjusting for future growth in population, employment, or other factors affecting travel demand. ASSUMPTIONS Proportional Growth: The number of trips between zones will grow proportionally to changes in population, employment, or other factors. Fixed Trip Patterns: The general pattern of trips between zones remains consistent over time; the distribution is assumed not to change dramatically. Balanced Matrix: The model ensures that the total number of trips originating from a zone equals the number of trips arriving at that zone. Limited Data Changes: It works best when major structural changes in transportation or land use are not expected. FRATAR MODEL FORMULA The number of trips between two zones is the average of the trips from point A to B, and point B to A SAMPLE PROBLEM A study area consists of four zones (A, B, C, and D). An O-D survey indicates that the number of trips between each zone is as shown in Table 12.17. Planning estimates for the area indicate that in five years the number of trips in each zone will increase by the growth factor shown in Table 12.18 and that trip generation will be increased to the amounts shown in the last column of the table. Determine the number of trips between each zone for future conditions SAMPLE PROBLEM SAMPLE PROBLEM 1.2 1.1 400 A B 10 100 0 300 D C 300 1.3 1.4 SAMPLE PROBLEM SAMPLE PROBLEM SAMPLE PROBLEM SAMPLE PROBLEM SAMPLE PROBLEM SAMPLE PROBLEM *Growth factor must be as close to unity (1.0), and must fall within +-5% (0.95 to 1.05) SAMPLE PROBLEM 1.04 0.96 428 A B 14 124 1 372 D C 430 0.94 1.04 ACTIVITY (1/2 CROSSWISE YELLOW PAPER OR BOND PAPER) GROUPS 1&2 : TRIPS AB &BA GROUPS 3&4 : TRIPS AC &CA GROUPS 5&6 : TRIPS AD & DA GROUPS 7&8 : TRIPS BC & CB GROUPS 9&10 : TRIPS CD & DC SAMPLE PROBLEM MODE CHOICE Mode Choice Mode choice is that aspect of the demand analysis process that determines the number (or percentage) of trips between zones that are made by automobile and by transit. Mode choice models attempt to replicate the relevant characteristics of the traveler, the transportation system, and the trip itself, such that a realistic estimate of the number of trips by each mode for each zonal pair is obtained. Factors Influencing Mode Choice Trip Purpose - The reason for the trip (e.g., commuting, leisure, shopping) can significantly affect the chosen mode. Travel Time - The perceived time required to use a specific mode plays a vital role in decision-making. Cost - Financial considerations, including fuel, fares, and parking fees, heavily influence mode choice. Convenience - The ease of accessing a mode, including factors like proximity to stops or availability of services, impacts the selection process. Traveler Characteristics - Attributes such as income, age, car ownership, and personal preferences shape how individuals choose their travel modes. Types of Mode Choice Models Direct Generation Models Trip End Models Trip Interchange Models Logit Models Direct Generation Models This method assumes that the attributes of the system are not relevant. Factors such as time, cost, and convenience are not considered. They do not rely on trip generation or distribution steps. Mode shares are determined from these variables without detailed interaction between zones or trips. They are simpler and often used for quick analysis in small-scale projects. Example: Direct Generation Models Determine the number of transit trips per day in a zone which has 5000 people living on 50 acres. The auto ownership is 40% of zero autos per household and 60% of one auto per household. Example: Direct Generation Models Determine the number of transit trips per day in a zone which has 5000 people living on 50 acres. The 500 auto ownership is 40% of zero autos per household and 60% of one auto per household. 250 Example: Direct Generation Models 500 trips/day 250 Trip End Models These models consider the characteristics of the trip's origin or destination. They evaluate factors like land use, population density, or employment at the ends of a trip. Mode choice is determined based on the trip purpose and characteristics of the zones but does not directly consider the interaction between the origin and destination. Example: Trip End Models The total number of productions in a zone is 10,000 trips/day. The number of households per auto is 1.80, and residential density is 15,000 persons/square mile. Determine the percent of residents who can be expected to use transit. Example: Trip End Models 45 27 Trip Interchange Models In this method, system level-of-service variables are considered, including relative travel time, relative travel cost, economic status of the trip maker, and relative travel service. An example of this procedure is illustrated using the QRS method which takes account of service parameters in estimating mode choice. The QRS method is based on the following relationship: Trip Interchange Models: Example To illustrate the application of the QRS method, assume that the data shown in Table 12.21 have been developed for travel between a suburban zone S and a downtown zone D. Determine the percent of work trips by auto and transit. An exponent value of 2.0 is used for work travel. Median income is $24,000 per year. Trip Interchange Models: Example To illustrate the application of the QRS method, assume that the data shown in Table 12.21 have been developed for travel between a suburban zone S and a downtown zone D. Determine the percent of work trips by auto and transit. An exponent value of 2.0 is used for work travel. Median income is $24,000 per year. Trip Interchange Models: Example Trip Interchange Models: Example Logit Models This form considers the relative utility of each mode as a summation of each modal attribute. Then the choice of a mode is expressed as a probability distribution. The utility of each mode is: If two modes, auto (A) and transit (T), are being considered, the probability of selecting the auto mode A can be written as Logit Models Logit Models TRAFFIC ASSIGNMENT TRAFFIC ASSIGNMENT The final step in the transportation forecasting process Traffic assignment is used to predict the actual routes and traffic volumes on highways and streets This method takes the origin-destination (O-D) pairs from earlier forecasting steps and assigns each trip to a specific route, whether by car or transit. By summing up the routes across all segments, planners can estimate the average daily or peak- hour traffic volume for each route. This forecast helps determine the capacity andLET ’ S GO potential congestion levels on urban transportation networks. ! TRAFFIC ASSIGNMENT To carry out a trip assignment, the following data are required: (1) number of trips that will be made from one zone to another (this information was determined in the trip distribution phase), (2) available highway or transit routes between zones, (3) how long it will take to travel on each route, (4) a decision rule (or algorithm) that explains how motorists or transit users select a route, and (5) external trips that were not considered in the previous trip generation and distribution steps. TRAFFIC ASSIGNMENT 1. Diversion Curves 2. Minimum Path Algorithm 3. All-or-nothing Assignment 4. Capacity Restrain Assignment a. Incremental Method b. Iterative Method c. Equilibrium Assignment User Equilibrium System Optimization 5. Stochastic Method DIVERSION CURVES This method is similar in approach to a mode choice curve. The traffic between two routes is determined as a function of relative travel time or cost. Figure shown below illustrates a diversion curve based on travel time ratio. MINIMUM PATH ALGORITHM The minimum time path method assigns all trips to those links that comprise the shortest time path between the two zones. The minimum path assignment is based on the theory that a motorist or transit user will select the quickest route between any O-D pair. In other words, the traveler will always select the route that represents minimum travel time. The results can be depicted as a tree, referred to as a skim tree. All trips from that zone are assigned to links on the skim tree. Each zone is represented by a node in the network which represents the entire area being examined. To determine the minimum path, a procedure is used that finds the shortest path without having to test all possible combinations. MINIMUM PATH ALGORITHM List possible paths from root node going to other nodes You do not need to list all paths, especially if it is evident that it will not be the shortest Compare total travel time for each possible path; choose the paths with shortest travel time Draw the skim tree using the chosen shortest paths DETERMINING MINIMUM PATH Determine the minimum path for nodes 1, 5, and 3. Sketch the skim trees. 1 8 min 3 3 min 2 5 min in in 5m 7m 2 m in 1 5 6 min 4 DETERMINING MINIMUM PATH Root/Home: Node 1 SKIM TREE: To Node 2: To Node 4: 1-2 = 8 min 1-2-4 = 8 + 5 = 13 min 1 2 3 1-5-2 = 5 + 12 = 17 min 1-5-4 = 5 + 6 = 11 min To Node 3: To Node 5: 1-2-3 = 8 + 3 = 11 min 1-5 = 5 min 1-2-4-3 = 8 + 5 + 7 = 20 min 1-2-5 = 9 + 12 = 20 min 5 4 1-5-4-3 = 5 + 6 + 7 = 18 min DETERMINING MINIMUM PATH Root/Home: Node 3 SKIM TREE: To Node 1: To Node 4: 3-2-1 = 3 + 8 = 11 min 3-4 = 7 min 1 2 3 3-2-5-1 = 3 + 12 + 5 = 20 min 3-2-4 = 3 + 5 = 8 min To Node 2: To Node 5: 3-2= 3 min 3-2-5 = 3 + 12 = 15 min 3-4-2 = 7 + 5 = 12 min 3-4-5 = 7 + 6 = 13 min 5 4 DETERMINING MINIMUM PATH Root/Home: Node 5 SKIM TREE: To Node 1: To Node 3: 5-1 = 5 min 5-4-3 = 6 + 7 = 13 min 1 2 3 To Node 2: To Node 4: 5-2= 12 min 5-4 = 6 min 5-4-2 = 6 + 5 = 11 min 5 4 ALL-OR-NOTHING ASSIGNMENT ALL-OR-NOTHING ASSIGNMENT ADVANTAGES DISADVANTAGES Simple Assumes all traffic will Inexpensive pass through one path Results are easy Creates unrealistic flow to understand patterns ALL-OR-NOTHING ASSIGNMENT 100 CAPACITY RESTRAINT The number of trips assigned to each link is compared with the capacity of the link to determine the extent to which link travel times have been increased by the additional volume placed on the formerly empty link. Using relationships between volume and travel time (or speed), it is possible to recalculate the new link travel time. A reassignment is then made based on these new values. The iteration process continues until a balance is achieved, such that the link travel time based on the loaded volume does not change with successive assignments. INCREMENTAL METHOD Incrementally assign a portion of the trip exchanges (i.e. in chunks) between zone pairs while updating the travel times between increments New travel time = function of volume that is assigned thus far STEPS: 1. Find path tree for each zone 2. Assign a portion of the trip exchange matrix (usually 40, 30, 20, and 10 percent) to shortest paths 3. Update travel times after each increment 4. Repeat until all trips are assigned 5. Sum INCREMENTAL METHOD INCREMENTAL METHOD 40 40 7 = 10.32min 0 10 0 = 10 min 0 16 0 = 16 min INCREMENTAL METHOD 7 40 = 10.32min 30 10 30 = 11.5 min 0 16 0 = 16 min INCREMENTAL METHOD + 20 60 = 23.8 min 7 30 = 11.5 min 10 0 16 0 = 16 min INCREMENTAL METHOD 7 60 = 23.8 min + 10 40 10 = 14.74 min 16 0 = 16 min INCREMENTAL METHOD 14.74 0