At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 1208 veh/h, and at the booth, drivers take an average of 10 seconds to pay their tolls. Both the arrival and departure rates can be assumed to be exponentially distributed. How would the average queue length, time in the system change if a fifth toll booth were opened? Queue Analysis - Numerical • M/M/N - Average length of queue - Average time waiting in queue - Average time spent in system A = arrival rate pm 11 P/N 10 1 NIN (1-p/NF P+0 1 2 i=P+Q = departure rate M/M/N - More Stuff - Probability of having no vehicles 1 P₁ = p p² + n! N(1-p/N) - Probability of having n vehicles p" Po P₁ =! forn SN n! P₁ = p"P NNN! - Probability of being in a queue Pop PAN= NIN(1-p/N) A = arrival rate p=²p/N<1.0 for n Σ Ν = departure rate

At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 1208 veh/h, and at the booth, drivers take an average of 10 seconds to pay their tolls. Both the arrival and departure rates can be assumed to be exponentially distributed. How would the average queue length, time in the system change if a fifth toll booth were opened? Queue Analysis - Numerical • M/M/N - Average length of queue - Average time waiting in queue - Average time spent in system A = arrival rate pm 11 P/N 10 1 NIN (1-p/NF P+0 1 2 i=P+Q = departure rate M/M/N - More Stuff - Probability of having no vehicles 1 P₁ = p p² + n! N(1-p/N) - Probability of having n vehicles p" Po P₁ =! forn SN n! P₁ = p"P NNN! - Probability of being in a queue Pop PAN= NIN(1-p/N) A = arrival rate p=²p/N<1.0 for n Σ Ν = departure rate

Traffic and Highway Engineering

5th Edition

ISBN:9781305156241

Author:Garber, Nicholas J.

Publisher:Garber, Nicholas J.

Chapter6: Fundamental Principles Of Traffic Flow

Section: Chapter Questions

Problem 26P: The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to bePoisson...

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