Q.1 In the figure below, departures are presented in the time axis, Cycle length=100s At the beginning of green, 10 vehicles queued at the approach of a single lane road. 16 vehicles arrived at the approach during green interval. Determine the saturation headway, saturation flow rate, start-up lost time and capacity of the approach?
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- A stop sign is installed in one of the road intersection. Rate of arrival at a stop sign is 300 veh/hr and the average waiting time at the stop sign is 10 sec. per vehicle. If both arrivals and departures are exponentially distributed, determine the average queue length (in vehicles).The uniform arrival and uniform service rates observed on an approach road to a signalized intersection are 20 and 50 vehicles/minute, respectively. For this signal, the red time is 30 s, the effective green time is 30 s, and the cycle length is 60 s. Assuming that initially there are no vehicles in the queue, the average delay per vehicle using the approach road during a cycle length (in s, round off to 2 decimal places) isThe average queue length at the intersection of the two roads with a stop sign is 4 vehicles. If the arrival rate of vehicles at the stop sign is 300 veh/hr, determine the service rate of the road in veh/hr. Assume both arrival and departure rates are exponentially distributed.
- A stop sign is installed in one of the road intersection. Rate of arival at a stop sign is 300 veh/hr and the average waiting time at the stop sign is 10 sec. per vehicle. If both arrivals and departures are exponentially distributed, determine the average queue length (in vehicles). Answer in whole number.Cars have a long queue at a stop sign. If the total time delay queueing is one min., compute the traffic intensity if the service rate of the road is only 360 veh/ hr. Assume both arrival and departure rates are exponentially distributed.Transportation Engineering Roll No. - 69 do the numerical part 2. Explain with the help of sketches various types of highway intersections. The 15 minute design traffic volume on cross road 1 and 2 during peak hour are observed as 180+R.No. and 150+R.No. vehicles per lane respectively. If the amber times required are 4 and 3 seconds respectively for two roads, design the signal timing by trial cycle (or exact) method. Assume average time headway of 2.5 sec during green phase. CO3
- A volume of 320 veh/h. Assume that the vehicle arrivals are Poisson distributed. What is the probability that the headway between successive vehicles will be less than 10 seconds. choices: 62.70%, 58.90%, 56.30%, 60.00%The cumulative arrival and departure curve of one cycle of an approach lane of a signalized intersection is shown in the adjoining figure. The cycle time is 50 s and the effective red time is 30 s and the effective green time is 20 s. What is the average delay? Cumulative --- Arrival A Cumulative arrival or departure (No. of vehicles) TO 30 #1 Departure7. Queue Theory: At the end of a sporting event, vehicles begin leaving a parking lot at 2(1) = 12 - 0.25t and vehicles are processed at u(t) = 2.5 + 0.5t (t is in minutes and 2(t) and u(t) are in vehicles per minute). Assume D/D/1 determine: Time when queue clears and total vehicle delay.
- Question 4 Vehicles begin to arrive at a border gate at 06h50 with a deterministic arrival rate of λ (t) = 5.2 - 0.01t (λ is in vehicles per minute and t in minutes after 06h50). However, the gate opens at 07h00 and serves vehicles at a rate of μµ(t) =3.3 + 2.4t (with t in minutes after 07h00 and u in vehicles per minute). Once the service rate reaches 10 vehicles per minute, it stays at that level for the rest of the day. ● ● Illustrate the operational characteristics of the vehicle queue-delay on a (cumulative) vehicle-Time graph. When will the queue that forms be dissipated? What will be the maximum queue length? Determine the total delay.1) 1) A section of highway has the following flow-density relationship: q-50k-0.156k² What is the capacity (maximum flow) of the highway section, the space mean speed at capacity, and the density when the traffic flow on the highway is at one-quarter of its capacity? 2) An observer has determined that the time headways between successive vehicles on a section of highway are exponentially distributed (arrival of vehicle is Poisson distribution) and that 60% of the headways between vehicles are 13 seconds or greater. If the observer decides to count traffic in 30-second time intervals, estimate the probability of the observer counting exactly four vehicles in an interval.An observer notes that an approach to a pretimed signal has a maximum of eight vehicles in a queue in a given cycle. If the saturation flow rate is 1440 veh/h and the effective red time is 40 seconds, how much time will it take this queue to clear after the start of the effective green (assuming that approach capacity exceeds arrivals and D/D/1 queuing applies) (in seconds)? Round off the final answer to whole number