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Class_43.mode_choice

# Class_43.mode_choice - The Pennsylvania State University...

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Unformatted text preview: The Pennsylvania State University The Pennsylvania State University Department of Civil and Environmental Engineering CE 321: Highway Engineering Class # 43 – Mode Choice Spring 2008 Mode Choice Mode Choice Mode Choice/Split Analysis allows the planner to determine the magnitude of travel by individual modes. Mode Choice Models Mode Choice Models The choice of mode is a decision that is akin to the probability of doing something or not doing something. A model that will estimate probabilities based on measurable variables is needed. Logit Model (maximizes utility value) Utility, a microeconomic term, can be defined as the capacity to satisfy wants. Logit Model Logit Model Uim = Σ bmk zimk i Uim = specifiable portion of utility of alternative m for traveler i; bmk = coefficient estimated from data for mode/destination alternative m corresponding to mode/destination or traveler characteristic k; zimk = traveler or mode/destination characteristic k for mode/destination alternative m for traveler i. Logit Model Logit Model Pim = ∑e s e U im U sm Pim = probability that traveler i selects alternative m. Uim = specifiable portion of utility of alternative m for traveler i; Mode Choice Example Mode Choice Example Mode choice utility model from small urban area is shown below: Where DL = automobile­drive­alone; SR = automobile­ shared­ride; B = bus. Between a residential area and an industrial complex, 4000 workers depart for work during peak hour. Cost of driving automobile is \$4.00 with a TT of 20 minutes – the bus fare is \$0.50 with a TT of 25 minutes. If the shared­ride options always consists of two travelers sharing costs equally, how many workers will take each mode? UDL = 2.2 – 0.2(costDL) – 0.03(TTDL) USR = 0.8 – 0.2(costSR) – 0.03(TTDL) UB = ­0.2(costB) – 0.01(TTB) Modal Choice Example Modal Choice Example UDL = 2.2 ­ 0.2 (4) ­ 0.03 (20) = 0.8 USR = 0.8 ­ 0.2 (2) ­ 0.03 (20) = ­0.2 UB = ­0.2 (0.5) – 0.01 (25) = ­0.35 Modal Choice Example Modal Choice Example PDL = e0.8 / [e0.8 + e­0.2 + e­0.35] = .594 PSR = .819 / 3.749 = 0.218 PB = 0.705 / 3.749 = 0.188 2380 drive alone 870 share ride 750 bus Multiplying probabilities by 4000 gives: Extended Example Reflecting Gas Extended Example Reflecting Gas Price Increase Because of gas prices increases, cost of drive alone travel increases by \$2.00 Is there an increase cost for sharing a ride? Extended Example Reflecting Gas Extended Example Reflecting Gas Price Increase Because of gas prices increases, cost of drive alone travel increases by \$2.00 Is there an increase cost for sharing a ride? YES; assume half cost of DR as before. Is there a cost increase for transit? Extended Example Reflecting Gas Extended Example Reflecting Gas Price Increase Because of gas prices increases, cost of drive alone travel increases by \$2.00 Is there an increase cost for sharing a ride? YES; assume half cost of DR as before. Is there a cost increase for transit? YES; assume fare increases from 50 cent to 55 cents New Mode Shares New Mode Shares UDL = 2.2 ­ 0.2 (6) ­ 0.03 (20) = 0.4 USR = 0.8 ­ 0.2 (3) ­ 0.03 (20) = ­0.4 UB = ­0.2 (0.55) – 0.01 (25) = ­0.36 Mode shares: PDL = 0.52 (old = 0.59) PSR = 0.23 (old = 0.22) PB = 0.25 (old = 0.19) Importance of Logit Model Importance of Logit Model Estimates mode shares at disaggregate level – the individual traveler Modelincludes affect of variables we might want to change to influence mode share Travel time Cost of transit Cost of auto travel Other variables typically included: Demographics of travelers Frequency or waiting time of transit service Route Choice Route Choice Result is traffic flow (vehicles per hour) on specific highway routes. Route choice is function of travel times and traffic flow. Need relationship between route travel time and route traffic flow (highway performance function). Highway Performance Function Highway Performance Function Route travel time Free-flow travel time 0 Traffic flow User Equilibrium User Equilibrium Assume travelers select route between origins and destinations based on route travel times only. Assume travelers know travel times that would be encountered on all possible routes between origin and destination. Travelers will select the route that minimizes personal travel time. Route Choice Example Route Choice Example Two routes connect a city and a suburb. See speed limit and route length data below. Studies show that total TT on route 1 increases two minutes for every additional 500 vehicles added. Minutes of TT on route 2 increase with the square of the number of vehicles (1000’s). Determine user equilibrium travel times. Route 1 2 Speed Limit (mph) 60 45 Length (miles) 6 3 Route Choice Example Solution Route Choice Example Solution Free­flow travel times: Route 1 – 6 miles / 60 mph = 0.1 hr. = 6 min. Route 2 – 3 miles / 45 mph = 0.0667 hr. = 4 min. t1 = 6 + 4x1 Performance Functions t2 = 4 + 4x22 t1, t2 = average travel time on routes 1 & 2 (min) x1, x2 = traffic flow on routes 1 & 2 (1000’s vph) Route Choice Example Solution Route Choice Example Solution Note: At flows above q’, route 2 is congested enough that route 1 is a viable option. ...
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