Operating travel speed on an 8kmlong bus line with h 12 min

Operating (travel) speed on an 8-km-long bus line with h = 12 min is V_o = 16 km/h. Terminal time at each end is 6 min (sigma_t, = 12 min). Bus preferential treatments are considered to improve the operation. But they would require a certain level of investment. The company will make the investment if it can reduce the number of buses by one due to these improvements. What is the minimum value of V_0 that would allow saving one bus if the total terminal time at both ends should not be less than T_r = 0.15 T, and the headway remains 12 min?

Solution

Question is based on quening theory (waiting lines)

Traffic intensity = average arrival rate / average service time

Time speed by train in the station = waiting time + service time

Average expected no of trains in the queue system

Ls= average arrival rate / ( average service time - average arrival rate )

Expected length of non-empty queue is given by

Lb = average service time / (average service time- average arrival time)

Kindly use it for solving the question.

you have to put values in the formulae given above.