9 - Chapter5-Queuing Theory

# 9 - Chapter5-Queuing Theory - Queuing Theory TTE 4004 Recap...

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Unformatted text preview: Queuing Theory TTE 4004 9/30/11 Recap – Traffic Flow Models Why do we need traffic models? To quantify and examine the microscopic behavior of vehicles Model requirements? Discrete Random What do we use for vehicle arrival? What do we use for headways? Recap – Poisson Distribution P ( n ) = probability of exactly n vehicles arriving in a time interval t λ = average arrival rate (veh/unit time) n = # of vehicles arriving in a specific time interval t = selected time interval (duration of each counting period (unit time)) ! ) ( ) ( n e t n P t n λ λ- = Equation for Poisson dist. is: (Eq. 5.23) Recap – Negative Exponential P(h ≥ t) = probability that the headway is greater than or equal to a given time q = volume (veh/hr) t = time that we are comparing our headway to Attendance Quiz The time headways between successive vehicles on a section of highway are exponentially distributed and 60% of the headways are 13 seconds or greater. If you decide to count traffic in 30 second intervals, estimate the probability that you count exactly four cars in an interval. ! ) ( ) ( n e t n P t n λ λ- = First, find flow: t = 13 sec 0.6 = exp(-q × 13 / 3600) q = 141.46 veh/hr Then, find probability that we count exactly 4 cars in an interval q = 141.46 veh/hr q = 0.03929 veh/sec λt = 0.03929 × 30 = 1.17883 veh P(4) = [1.17883^4 × exp(-1.17883)] / 4! = 0.02475 2.5 % ! ) ( ) ( n e t n P t n λ λ- = Introduction - Queuing Why is examination of queuing important? Because queuing leads to delay Motorists do not like delay Delay is the important factor in determining the “level of service” for at intersections Major implications for design purposes Generally have to compromise between accommodation of queuing and construction costs The Basic Queuing Process Customers requiring service are generated over time by an input source These customers enter the queuing system...
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9 - Chapter5-Queuing Theory - Queuing Theory TTE 4004 Recap...

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