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(c) Consider a section of a four-lane freeway (two lanes in each direction) as shown below. The freeway typically carries 2571 veh/hr during the morning peak period. An accident occurs at 8:00 AM at Point A, blocking the entire freeway in that direction. Fifteen minutes after the accident, one lane is cleared and traffic begins to flow again past point A. Assuming a triangular fundamental diagram as shown below, use shock wave analysis to answer the following questions: Flow (veh/hour) (1) Where is the end of the queue at 8:15 AM? (2) When (at what time) are the vehicles on the freeway last forced to stop by the queue? (3) What is the maximum size of the queue? (4) What is the maximum distance of the end of the queue from the accident site? *, (k₂) 4000 3000 2000 At Time t = 8:00 AM 1000 (*) H At Time t = 8:15 AM x₂ (k₂) (₂) 정 q= 50 k = 30 veh/mi P x₂ (k₂) uk = 60 mph (₂) 9 1- B H Flow-density relationship (one lane) when k Sk when k, sk Sk k-ke k,-k (k₂) B x₂ (k₂) (30, 1800) qe = 1800 veh/hour x, (k₂) P 7747 x₂ (k₂) k = 150 veh/mi 100 150 200 250 300 Density (veh/mi) (₂) 15 miles 1x₂ (k₂) 15 miles Flow (veh/hour) 4000 3000 2000 1000 x₂ (₂) P H x₂ (k₂) (k₂) x₂ (k₂) A ke = 60 veh/mi 50 100 A u= 60 mph x (₂) F 1x₂ (k₂) B Flow-density relationship (two lanes) (60, 3600) qe = 3600 veh/hour x₂ (k₂) k = 300 veh/mi 150 200 250 Density (veh/mi) 300

(c) Consider a section of a four-lane freeway (two lanes in each direction) as shown below. The freeway typically carries 2571 veh/hr during the morning peak period. An accident occurs at 8:00 AM at Point A, blocking the entire freeway in that direction. Fifteen minutes after the accident, one lane is cleared and traffic begins to flow again past point A. Assuming a triangular fundamental diagram as shown below, use shock wave analysis to answer the following questions: Flow (veh/hour) (1) Where is the end of the queue at 8:15 AM? (2) When (at what time) are the vehicles on the freeway last forced to stop by the queue? (3) What is the maximum size of the queue? (4) What is the maximum distance of the end of the queue from the accident site? *, (k₂) 4000 3000 2000 At Time t = 8:00 AM 1000 (*) H At Time t = 8:15 AM x₂ (k₂) (₂) 정 q= 50 k = 30 veh/mi P x₂ (k₂) uk = 60 mph (₂) 9 1- B H Flow-density relationship (one lane) when k Sk when k, sk Sk k-ke k,-k (k₂) B x₂ (k₂) (30, 1800) qe = 1800 veh/hour x, (k₂) P 7747 x₂ (k₂) k = 150 veh/mi 100 150 200 250 300 Density (veh/mi) (₂) 15 miles 1x₂ (k₂) 15 miles Flow (veh/hour) 4000 3000 2000 1000 x₂ (₂) P H x₂ (k₂) (k₂) x₂ (k₂) A ke = 60 veh/mi 50 100 A u= 60 mph x (₂) F 1x₂ (k₂) B Flow-density relationship (two lanes) (60, 3600) qe = 3600 veh/hour x₂ (k₂) k = 300 veh/mi 150 200 250 Density (veh/mi) 300

Traffic and Highway Engineering
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 21P
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(c) Consider a section of a four-lane freeway (two lanes in each direction) as shown below. The freeway typically carries 2571 veh/hr during the morning peak period. An accident occurs at 8:00 AM at Point A, blocking the entire freeway in that direction. Fifteen minutes after the accident, one lane is cleared and traffic begins to flow again past point A. Assuming a triangular fundamental diagram as shown below, use shock wave analysis to answer the following questions: (1) Where is the end of the queue at 8:15 AM? (2) When (at what time) are the vehicles on the freeway last forced to stop by the queue? (3) What is the maximum size of the queue? (4) What is the maximum distance of the end of the queue from the accident site? At Time t = 8:00 AM *(k,) B A 15 miles At Time t = 8:15 AM i, (k,) *, (k,) *,(k,) *, (k,) , (k,) A miles Flow-density relationship (one lane) Flow-density relationship (two lanes) 4000 4000 when k <k. (60, 3600) q. = 3600 veh/hour k-k. 1- 3000 when k, sk<k, 3000 k; -k. 2000 (30, 1800) qc = 1800 veh/hour 2000 uf = 60 mph 1000 /u = 60 mph 1000 k, = 150 veh/mi kc = 60 veh/mi k, = 300 veh/mi 50 100 150 200 250 300 0. 50 100 150 Density (veh/mi) 200 250 300 Density (veh/mi) k. = 30 veh/mi Flow (veh/hour) Flow (veh/hour)
Transcribed Image Text:(c) Consider a section of a four-lane freeway (two lanes in each direction) as shown below. The freeway typically carries 2571 veh/hr during the morning peak period. An accident occurs at 8:00 AM at Point A, blocking the entire freeway in that direction. Fifteen minutes after the accident, one lane is cleared and traffic begins to flow again past point A. Assuming a triangular fundamental diagram as shown below, use shock wave analysis to answer the following questions: (1) Where is the end of the queue at 8:15 AM? (2) When (at what time) are the vehicles on the freeway last forced to stop by the queue? (3) What is the maximum size of the queue? (4) What is the maximum distance of the end of the queue from the accident site? At Time t = 8:00 AM *(k,) B A 15 miles At Time t = 8:15 AM i, (k,) *, (k,) *,(k,) *, (k,) , (k,) A miles Flow-density relationship (one lane) Flow-density relationship (two lanes) 4000 4000 when k <k. (60, 3600) q. = 3600 veh/hour k-k. 1- 3000 when k, sk<k, 3000 k; -k. 2000 (30, 1800) qc = 1800 veh/hour 2000 uf = 60 mph 1000 /u = 60 mph 1000 k, = 150 veh/mi kc = 60 veh/mi k, = 300 veh/mi 50 100 150 200 250 300 0. 50 100 150 Density (veh/mi) 200 250 300 Density (veh/mi) k. = 30 veh/mi Flow (veh/hour) Flow (veh/hour)
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