Question

Left turn bay capacity =9 cars. LT Arrival rate = 8 veh/min. LT Red Interval =70 seconds. Left. 1 turn green arrow timed for 8 cars. Dont went to spill over into adjacent lane more then 10% of the time. Is turn bay length adequate

Answer 1

We are given

LT arrival rate = 8veh/min = .1333veh/sec

1 left-turn arrow is timed for 8 LT vehicles.

Since arrival rate is .1333 veh/sec, 8 vehicles will arrive in 8/.1333 = 60 seconds

So left turn green time = 60seconds, left-turn red time = 70 seconds

storage length of the LT bay = 9 vehicles

We want queue to be withing 1.1*9 i.e 9.9 vehicles

So we want to queue to be within the "turnbay storage length" 90% of the time.

So the probability that 10 vehicles arrive during the LT red time should be at max 10% i.e 0.01

So lets calculate the probably of 10 vehicles arriving in the left-turn red time

For a Poisson Distribution, we know that

Probability of n vehicles arriving in time t = P(n) = (qt)ⁿ * e^-qt/n!

where q = flow in veh/sec = .1333

t = 70 seconds, n = number of vehicles = 10

So probability of 10 vehicles arriving in 70 seconds = (.1333*70)¹⁰ * (2.71828^-.1333*70)/10! = .1222

This probability is greater than 10%

So Turn bay Length is NOT ADEQUATE

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