A bus route has stops at every intersection, 200 m apart. The speed of traffic and of the buses except for their stopping at bus stops is 30 km/h, but for every stop, buses lose a total of ts=20 seconds. Passengers are uniformly distributed along the route and walk to/from its stops at a speed of Vw= 4.8 km/h. a. How would a passenger's total travel time (consider only access to stops and travel on buses) change if every other stop was abandoned (i.e., the spacing between stops was increased from 200 m to 400 meters, if the average trip length on the line is: i) 4 km; ii) 6 km; and iii) 8 km? b. For what passenger trip length Lp will the total travel time remain the same?

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Question 4 Vehicles begin to arrive at a border gate at 06h50 with a deterministic arrival rate of λ (t) = 5.2 - 0.01t (λ is in vehicles per minute and t in minutes after 06h50). However, the gate opens at 07h00 and serves vehicles at a rate of μµ(t) =3.3 + 2.4t (with t in minutes after 07h00 and u in vehicles per minute). Once the service rate reaches 10 vehicles per minute, it stays at that level for the rest of the day. ● ● Illustrate the operational characteristics of the vehicle queue-delay on a (cumulative) vehicle-Time graph. When will the queue that forms be dissipated? What will be the maximum queue length? Determine the total delay.

The rate of arrival of vehicles at the expressway can be considered to be Poisson with a mean of 45 veh/hr, and the rate of service to vehicles can be assumed to be exponentially distributed with a mean of 1 min. (a) What is the average number of vehicles waiting to be served at the booth (that is, the number of vehicles in queue, not including the vehicle being served)? (b) What is the length of the ramp required to provide storage for all exiting vehicles 90% of the time? Assume the average length of a vehicle is 18 ft and that there is an average space of 10 ft between consecutive vehicles waiting to be served. (c) What is the average waiting time a driver waits before being served at the tollbooth (that is, the average waiting time in the queue)?