Breaking into traffic at an intersection

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Breaking into traffic at a 'T' intersection involves calculating the time required for a driver to complete a turn and accelerate to match the speed of oncoming vehicles. This requires understanding the mean time interval between vehicles in cross traffic and assessing how often this interval allows for a safe turn. A probability distribution can be applied to model the likelihood of finding a suitable gap in traffic. Key variables affecting the mean time between vehicles include traffic density, speed limits, and time of day. Analyzing these factors can help predict the likelihood of successfully entering the intersection.
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I was given a very open ended question stating...

"How Long will it take to break into a line of traffic at a 'T' intersection"

I need some sort of start like a theory that includes this kind of thing. We have been studying probability this term so i need something to do with a probabilty distribution to solve this or something along those lines...

Just any help really would be greatly appreciated.
 
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For a driver to turn into cross traffic, there needs to be some interval of time in which the driver can complete a turn (left or right) and accelerate to match the speed of the traffic.

One would have to determine the mean time (interval) between vehicles in the cross-traffic, and determine over some cumulative time, how often does the right interval between vehicles exceed the interval required for the turning vehicle to turn and match speed.

One has to determine the variables that affect the mean time between vehicles in the cross traffic.
 

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