A bus route is 15 miles long The average traveling speed on

A bus route is 15 miles long The average traveling speed on the bus route during peak period is 20 mph. There are 4 buses seeing the route. Determine the expected passenger waiting time at bus stops. Determine whether or not the available number of buses is adequate to satisfy the hourly demand of 150 passengers if a single bus can carry 40 passengers. If traffic signal retiming increases the travel speed to 25 mph, how many buses would you recommend for the hourly demand of 150 passengers> Recommend a strategy to encourage public transportation usage in urban areas.

Solution

(a) The bus route is 15 miles long. The average speed of the bus is 20 mph. Therefore , the time taken by a bus to cover 15 miles is 15/20 = 3/4 = 0.75 hour = 45 minutes. Let x minutes be the time gap betweebn 2 buses. Then, the 2nd bus, 3rd bus and the 4th bus leave x minutes, 2x minutes and 3x minute after the 1st bus. Then, the 1st bus must come back x minutes after the 4th bus leaves, i.e. after 4x minutes after it first left. Since the 1st bus will take 45 minutes for the return journey also, it will come back 90 minutes after it first left. Then 4x = 90 so that x = 90/4 = 22.5 minutes.

(b) There are 4 buses in an hour. Each bus carries 40 passengers. Then 4 buses will carry 160 passengers. Thus, in an hour 160 passengers can travel.Since,there are 150 passengers only per hour, 4 buses are adequate for this level of traffic.

(c) I(f the traffic signals change in the manner so that the average speed of the bus increases to 25 mph, then the journey of 15 miles can be completed in 15/25 = 3/5 = 0.6 hour or 36 minutes. Since the bus takes 36 minutes for the onward as well as return journey, the 1st bus will come back in 72 minutes after it first left. The traffic level being 150 passengers per hour, the number of passegers in 72 minutes will be (72/60)* 150 = 180. The capacity of each bus being 40, 4 buses will still be needed as these will carry 160 passengers and the 1st bus which comes back will cary the balance 20 passengers. Only the waiting time will come down.

(d) If the journey by public transport ismade comfortable, convenient and hassle free, and the waiting time plus the time taken by the public transport is comparable to other means of transport,more people will be encouraged to use public transport especially if the costof public transport is lower that that of other means. An education about savings in fuel cost , lessening of pollution and congestion will be added advantages.