PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5, Problem 52P
To determine
The time at maximum queue length.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Question 1
In studying traffic flow at a highway toll booth over a course of 60 minutes, it is
determined that the arrival and departure rates are deterministic, but not
uniform. The arrival rate is found to vary according to the function of A (t) = 1.8
2
+0.25t -0.0030t. The departure rate function is u(t) =1.4 + 0.11 t. In both of
these functions, t is in minutes after the beginning of the observation and X(t)
and u(t) are in vehicles per minutes.
(i) When will the queue that forms be cleared?
(ii) What time does the maximum queue length occur and what will be the
corresponding queue length?
(iii) Determine the total delay
(iv) Estimate the average time delay per vehicle
After observing arrivals and departures at a highway toll booth over a 60-minute time period, an observer notes that the arrival and departure rates (or service rates) are deterministic, but instead of being uniform, they change over time according to a known function. The arrival rate is given by the function, ?(?) = 2.2 + 0.17? − 0.0032?^2, and the departure rate is given by ?(?) = 1.2 + 0.07?, where t is in minutes after the beginning of the observation period and ?(?) and ?(?) are in vehicles per minute. Determine the total vehicle delay at the toll booth and the longest queue, assuming D/D/1 queuing.
Two cars P and Q are moving in a racing
track continuously for two hour. Assume
that no other vehicles are using the track
during this time. The expressions relating
the distance travelled d (in km) and time t (in
hour) for both the vehicles are given as
P: d = 60t
Q: d = 60t²
Within the first one hour, the maximum
space headway would be
Chapter 5 Solutions
PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
Ch. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10P
Ch. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - The arrival rate at a parking lot is 6 veh/min....Ch. 5 - Prob. 16PCh. 5 - At the end of a sporting event, vehicles begin...Ch. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Vehicles begin arriving at a single toll-road...Ch. 5 - Vehicles begin to arrive at a toll booth at 8:50...Ch. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - Vehicles begin to arrive at a parking lot at 6:00...Ch. 5 - At a parking lot, vehicles arrive according to a...Ch. 5 - Prob. 28PCh. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Vehicles arrive at a recreational park booth at a...Ch. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - A truck weighing station has a single scale. The...Ch. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - Vehicles leave an airport parking facility (arrive...Ch. 5 - Vehicles begin to arrive at a parking lot at 7:45...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - Prob. 45PCh. 5 - Prob. 46PCh. 5 - Prob. 47PCh. 5 - Prob. 48PCh. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - Prob. 51PCh. 5 - Prob. 52PCh. 5 - A theme park has a single entrance gate where...Ch. 5 - Prob. 54PCh. 5 - Prob. 55P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Similar questions
- A highway has directional arrival rate of 30 [veh/min] and capacity of 40 [veh/min]. At time t = 0 [min], an accident occurs and stops all traffic. At t = 20 [min], the accident is cleared, and the highway returns to its original capacity. What are the values of lambda (1) and mu (µ) at t= 30? a b At what time does the queue clear? Present your answer to the nearest minute.arrow_forward1. Assume you are observing traffic in a single lane of a highway at a specific location. You measure the average headway and average spacing of passing vehicles as 3 seconds and 150ft, respectively. What is the average speed of the traffic stream? Note: you can use two methods to conduct the calculation. 2. Assume the speed and density at a freeway location follows a linear relationship. You observe traffic flow rate of 2250 vehicles/hour at 45 mph and 3000 vehicles/hour at 30 mph. What are the jam density, free flow speed (max speed), and capacity of this freeway location? How about the density and speed (i.e., the critical density and the critical speed) at the capacity?arrow_forwardA parking garage has a single processing booth where cars pay for parking. The garage opens at 6:00 A.M. and vehicles start arriving at 6:00 A.M. at a deterministic rate of Ȝ(t) = 6.1 − 0.22t where Ȝ(t) is in vehicles per minute and t is in minutes after 6:00 A.M. What is the maximum constant departure rate (from 6:00 A.M. on) needed to ensure that the queue length does not exceed 10 vehicles? Answer in veh/min. final answer: 8.21arrow_forward
- The arrival function and departure functions at a traffic facility are given below: Arrival function, A(t) = 8t+0.95t2 • Departure function, D(t) = 2t+1t2 where, t = time in minutes. Determine the value of t (in minutes) at which the queue length is the maximum.arrow_forwardExample - Floating car method The data collected from speed and delay studies by floating car method on a stretch of urban road of length 3.5 km, running North-South are given below. Determine the average values of volume, journey speed and running speed & SMS of the traffic stream along either direction. Trip Direction of Journey trip time No. 1234S00 5 6 7 8 N-S S-N N-S S-N N-S S-N N-S S-N Total stop No. of delay vehicles Min-Sec Min-Sec overtaking 6-32 7-14 6-5 7-40 6-10 8-00 6-28 7-30 1-40 1-50 1-30 2-00 1-10 2-22 1-40 1-40 4552 M N N M 3 2 2 3 No. of vehicle overtaken 733L5252 1 No. of vehicles from opposite direction 268 186 280 200 250 170 290 160arrow_forwardQuestion 1 a) The spot speeds and headways of vehicles are measured by two loop detectors on a single lane at location Y on a freeway. A sample of the observations is given below: Vehicle no. ii. 1 2 345 Travel time between loops (seconds) 0.90 0.81 0.92 0.75 1.03 nex nyt q Headway between vehicles (seconds) 3.60 3.14 4.00 3.50 3.72 9 = = =/=/30 S= i. If the loop detectors are spaced 20 meters apart, estimate the space mean speed and flow of the traffic stream. If it is known that the jam density (k;) on this section is 105 vehicles/km per lane, and that a linear speed-density relationship holds, what would you estimate the free-flow speed of the section to be? -110 Ehi narrow_forward
- Write the distribution of vehicle headway which is known as the negative exponential distribution. ( Traffic Engineering )arrow_forward4. The observations from a moving car method are given in the table below. The column (1) shows the number of vehicles overtaken by the test vehicle, (2) show the number overtaking the test vehicle, (3) shows the number of vehicles moving against traffic stream, (4) is the travel time with the traffic (s), and (4) is the travel time against the traffic (s). Assuming linear speed-density relation, what is the maximum flow, speed, and density the following following stretch can take. Show the details of the calculation. (1) (2) (3) | (4) (5) 5 119 618 422 268 26 12 389 213 188 24 9 401 226 396 2 55 410 274 255 26 9 374 226 396arrow_forwardSuppose that only 30% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible. What is the probability that, of 12 randomly chosen drivers coming to an intersection under these conditions? a. Less than 8 drivers will come to a complete stop. P(X<8)?. b. What is the probability of (5< X< 10)?arrow_forward
- The average speed of vehicles on an expressway is being studied. a. Suppose observation on 50 vehicles yielded a sample mean of 65 km/hr. Assume that the standard deviation of vehicle speed is known to be 6 km/hr. Determine the two-sided 99% confidence intervals of the mean speed. b. In part (a), how many additional vehicles' speed should be observed such that the mean speed can be estimated to within + 1 km/hr with 99% confidence? C. Suppose John and Mary are assigned to collect data on the speed of vehicles on this expressway. After each person has separately observed 10 vehicles, what is the probability that John's sample mean will exceed Mary's sample mean by 2 km/hr? d. Repeat part (c) if each person has separately observed 100 vehicles instead?arrow_forward(b) Consider a stop-controlled intersection between a major and a minor street shown in the figure below. Traffic on the major street is arriving in a random manner (Poisson distributed vehicle arrivals) and passes through the intersection unimpeded, without having to stop. Traffic on the minor street must wait at the stop sign and can enter the major street only when there is a minimum headway tm = 2.5 seconds (gap) in the major street. Suppose that the flow rate on the major street is Q= 200 vehicles per hour, and only one vehicle can enter the major street during each acceptable gap. Estimate the maximum number of vehicles per hour that can be accepted to the major street (which is also the capacity) of the minor street approach. Major Street Minor Streetarrow_forwardThe number of traffic accident that occur on particular stretch of road during a month follows a Poisson distribution with a mean of 7. Find the probability of observing exactly three accidents on this stretch of road next month. H.W2/ In the entrance of car parking, the vehicle arrival in each counting period of 100 sec. is shown in table below, check whether the arrival distribution of vehicle can be assumed random or not. Vehicle per 100 sec. Frequency 0 60 1 28 2 16 3 8 24 0arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Structural Analysis (10th Edition)Civil EngineeringISBN:9780134610672Author:Russell C. HibbelerPublisher:PEARSON
Principles of Foundation Engineering (MindTap Cou...Civil EngineeringISBN:9781337705028Author:Braja M. Das, Nagaratnam SivakuganPublisher:Cengage Learning
Fundamentals of Structural AnalysisCivil EngineeringISBN:9780073398006Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel LanningPublisher:McGraw-Hill Education
Traffic and Highway EngineeringCivil EngineeringISBN:9781305156241Author:Garber, Nicholas J.Publisher:Cengage Learning
Structural Analysis (10th Edition)
Civil Engineering
ISBN:9780134610672
Author:Russell C. Hibbeler
Publisher:PEARSON
Principles of Foundation Engineering (MindTap Cou...
Civil Engineering
ISBN:9781337705028
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Cengage Learning
Fundamentals of Structural Analysis
Civil Engineering
ISBN:9780073398006
Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:McGraw-Hill Education
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning