1) Consider a corridor of length l = 10 mi with demand = 100 users/mi/hr that is served by express and local buses. Both express and local buses run...

1) Consider a corridor of length l = 10 mi with demand λ = 100 users/mi/hr that is served by express and local buses. Both express and local buses run on the same scheduled headway of H = 10 min. There is a time loss associated with each transfer equal to ∆ = 5 min and a lost time per stop equal to ts = 30 sec/stop. The spacing of the local bus stops is Sl = 0.1 mi, and the spacing of the express bus stops is Se = 0.5 mi. Transit users walk at a speed of vw = 3 ft/sec, and the maximum speed of the buses is vmax = 30 mph. Assume that the cost for running a bus is cd = 50 $/mi traveled, and there are 2 local buses required per express bus dispatch (i.e., one for distributing passengers and one for collecting passengers).

(a) What is the cost per passenger associated with running the service, both local and express (i.e., agency cost)?

(b) What is the door-to-door travel time for the worst case passenger?

(c) What are the spacings for the local and the express service Sl and Se that minimize the door-to-door travel time for the worst case passenger?

(d) What is the minimum door-to-door travel time for the worst case passenger?

2) Trips originate along a 10 mile linear corridor that runs from the edge of a city (x = 0) to its central business district (x = 10) where everyone works, shops, or just wants to be. The schedule of train arrivals at the city is given and is such that every train carries the same number of people. We assume that schedules are published and passengers arrive just in time to avoid waiting. The number of people in each train at any location x, N(x), is equal to the density times the distance from the origin, N(x) = Dx. Demand is evenly distributed with density D = 100 people per mile. Travelers spend time to access their stations by walking, and once aboard each traveler endures an in-vehicle-delay of τ = 2 min for each stop experienced along the ride. The running speed of the train not including stops is v = 40 miles per hour, and passengers access the stations by walking along the corridor at va = 3 miles per hour.

Problem 2 Part A) Assume that stops are evenly spaced with spacing S (such that 10/S is aninteger value) and passengers walk to the nearest downstream station. In addition, assume that travelers suffer an extra τ/2 minutes of stop delay at the station they board and τ/2 at the station they alight. Assume that each traveler experiences time costs equal to the average traveler.

(a) Write an expression for the total passenger access cost in terms of S.

(b) Write an expression for the total passenger stopping delay cost in terms of S.

(d) Write an expression for the total passenger cost in terms of S using the expressions derived above.

(e) What is the value of S that minimizes the expression you wrote in (d) (relaxing for a moment the constraint that 10/S is an integer value)? Which value of S would you choose in reality (such that 10/S is an integer value)? What would then be the total passenger time?