Answer Happy

In this Mini-Project, you are to design an urban bus route in a simplified context. We could take as a reference a typical route serving the city of Barcelona. Consider that the route will cover a distance of D = 12 km, which needs to be served in both directions. The cruising speed for buses in the city of Barcelona, with non-exclusive bus lanes and including delays at traffic signals is v = 16 km/h. The time lost per stop, including the deceleration and acceleration processes and the opening/closing of doors, can be assumed to be of L = 30 s/stop. The timeduring which doors are open at each stop depends on the boarding and alighting demand, and it has been observed that it takes r=4s for each passenger to board and r' = 1.5 s for each alighting passenger. Passengers use the two doors (i.e. front and rear) for boarding and alighting, so that boarding passengers need to wait for the passengers to alight before they can board. Regarding the operating agency costs, the unitary cost per vehicle-kilometer travelled is €v = 2 €/veh km, while the prorated hourly cost of each vehicle (including drivers' cost) is € = 40 €/veh. h. The agency is planning to serve the route with vehicles with a capacity of C = 75 pax. Consider a layover time of TH = 30 min, at each terminal (i.e. at both end stops of the route) to account for drivers' rest time and vehicle cleaning. Furthermore, the results of a demand estimation study predict a demand for the route of q = 2000+ 1000(dd/31) pax/h in each direction (so that the total demand for the line is 2q), where dd is the day of the month of your birthday (i.e. your birthdate is dd/mm/yyyy). In addition, the access speed of customers to stops is estimated to be vs = 2.5 km/h (i.e. access by walking with delays due to street crossings), and the average trip length results to be l = 4 km (i.e. one third of the total route length). Finally, the average value of time considered for passengers travelling within the city of Barcelona is estimated to be Br = 11 €/h. In turn, the value of time of passengers waiting at stops is two times this (i.e. Bw = 2B7 = 22 €/h). Part A Assume that you are in the planning stage of the bus route. Determine the following decision variables by optimizing the trade-off between users' and agency cost: (You are to work analytically with the different variables and parameters, and just substitute them by their numerical value as the last step). a) The average stop spacing, s. b) The average bus headway, h". Consider that the operating agency limits the headway to h 6 min, because lower headways create bus congestion at stops. So, if h* < 6 min, take h = 6 min. c) The required number of vehicles to serve both directions of the route, M. d) The average bus occupancy, O*. e) The expected commercial speed of the bus route, ve. f) The average customer door-to-door trip time (including access, wait and in vehicle travel time). g) The average customer "extra" time (i.e. this is the average customer door-to-door trip time minus the unavoidable line-haul time, l/v h) The total user extra costs per unit time (i.e. Zu* – Br2q1/v). i) The total agency costs per unit time, ZA*. j) The required fare, F-, if the system was to be operated without subsidies.