"Space Mountain", a classic attraction at Disneyland Park, attracts many tourists to take a ride. Each ride can take tourist at a rate of 5 persons/min. The park is opened at 9:00 AM. Based on daily observations, it is found that the tourist arrival rate is 8 persons/min during 9:00 AM - 12:00 PM, 5 persons/min during 12:00 PM - 3:00 PM and 2 persons/min after 3:00 PM. Apply a D/D/1 queuing model to calculate what is the maximum number of tourists waiting in the queue? (Round to the nearest integer and fill in the blank with a number only.) 12 12 Tourist # D/D/1 180 360 Time (min)
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- There is a single gate at an entrance to a recreational park where arriving vehicles must stop to pay their tickets. The park opens at 8:00AM, at which time vehicles begin to arrive at a rate of 480 veh/hr. After 20 minutes the arrival flow rate declines to 120 veh/hr, and it continues at that level for the remainder of the day. If the service time is 15 seconds per vehicle, and assuming D/D/1 queuing, determine the Length of Queue at 8:1OAM. Note: Round off your answers to the nearest whole number. Only include the numeric value of your answer without the unit (i.e. 22).There is a single gate at an entrance to a recreational park where arriving vehicles must stop to pay their tickets. The park opens at 8:00AM, at which time vehicles begin to arrive at a rate of 480 veh/hr. After 20 minutes the arrival flow rate declines to 120 veh/hr, and it continues at that level for the remainder of the day. If the service time is 15 seconds per vehicle, and assuming D/D/1 queuing, determine the Longest Vehicle Queue. Note: Round off your answers to the nearest whole number. Only include the numeric value of your answer without the unit (i.e. 22).There is a single gate at an entrance to a recreational park where arriving vehicles must stop to pay their tickets. The park opens at 8:00AM, at which time vehicles begin to arrive at a rate of 480 veh/hr. After 20 minutes the arrival flow rate declines to 120 veh/hr, and it continues at that level for the remainder of the day. If the service time is 15 seconds per vehicle, and assuming D/D/1 queuing, determine the time that the queue will dissipate. Answer must be in this format: *:**AM, minute time must be rounded off to the nearest whole number (i.e. 8:50AM)
- Vehicles begin to arrive to a parking lot at 7:00 AM at a rate of 2000 veh/hour, but the demand reduces to 1000 veh/hour at 7:30 AM and continues at that rate. The ticketing booth to enter the parking lot can only serve the vehicles at 1000 veh/hour until 7:15 AM, after which the service rate increases to 2000 veh/hour. Assuming D/D/1 queuing, draw a queuing diagram for this situation. Find: a) the time at which the queue clears, b) the total delay, c) the longest queue length, and d) wait time of the 500th and 2000th vehicles to arrive to the parking lot (assuming FIFO conditions)?Vehicles arrive at an entrance to a recreational park. There is a single gate (at which all vehicles must stop), where a park attendant distributes free brochures. The park opens at 8:00 AM. At which vehicles begin to arrive at a rate of 480 veh/h. After 20 minutes, the arrival flow rate declines to 120 veh/h and corrtinues at that level for the remainder of the day. If the time required to distribute the brochure is 15 seconds, and assuming D/D/1 queuing (a) draw the queuing diagram (b) describe the operational characteristics of the queue (maximum queue length, maximum queuing time, average queuing time per vehicle etc.)The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to be Poisson with a mean of 30 veh/h. It takes an average of 1.5 min for the necessary tickets to be bought for occupants of each car. 6-23 (a) What is the expected length of queue at the ticket gate, not including the vehicle being served? (b) What is the probability that there are no more than 5 cars at the gate, including the vehicle being served? (c) What will be the average waiting time of a vehicle?
- Vehicles arrive at the carpark of an airport. Vehicles have to queue at the single entrance gate of the carpark at 9:00 AM. The arrival rate is constant at 240 veh/hr. However, between 9:00 and 9:40 AM, the parking ticket machine at the entrance works slowly due to a malfunction, and consequently, each vehicle spends 30 seconds to take the parking ticket. After 9:40 AM, the problem is solved and vehicles spend only 10 seconds at the gate to take the ticket. In how many minutes does the queue dissipate? Select one: a. 60 b. 70 c. 75 d. 80Vehicles arrive at an entrance to a recreational park. There is a single gate (at which all vehicles must stop), where a park attendant distributes a free brochure. The park opens at 8:00 A.M., the average arrival rate be 240 veh/h and Poisson distributed (exponential times between arrivals) over the entire period from park opening time (8:00 A.M.) until closing at dusk. If the time required to distribute the brochure is 10 seconds, the distribution time varies depending on whether park patrons have questions relating to park operating policies, assuming M/M/1 queuing. a.) Compute the average length of queue (express in veh), b.) Average waiting time in the queue (express in min/veh), c.) and average time spent in the system(express in min/veh)SEAT WORK: EA4 Queving theory: D/D/1 Vehicles arrive at an entrance to a recreational park. There is a single gate (at which all vehicles must stop), where a park attendant distributes a free brochure. The park opens at 9:00 A.M., at which time vehicles begin to arrive at a rate of 470 veh/h. After 20 minutes, the arrival flow rate declines to 115 veh/h, and it continues at that level for the remainder of the day. If the time required to distribute the brochure is 14 seconds, and assuming D/D/1 queuing, describe the operational characteristics of the queue.
- delay? 4. The gate entrance to a park opens at 9:00 A.M. At 9:00 A.M. there are 32 vehicles in the queue waiting to enter. Vehicles continue to arrive (from 9:00 A.M. onward) at a rate of X(t) = 4.2-0.05t (with X(t) in veh/min and t in minutes after 9:00 A.M.). The gate attendant processes vehicles at a rate of u(t) = 3 + 0.3t [with u(t) in veh/min and t in minutes after 9:00 A.M.]. Assuming D/D/1 queuing, what is the maximum queue length and total vehicle delay from 9:00 A.M. onward? A.20 mph nohorCompute the peak hour factor if the hourly volume of traffic is 1882 veh/hour and the highest 15-min volume is 790. Round off to two decimal places.Vehicles arrive at the entrance of the new extension of NLEX. There is a single toll gate at which all vehicles must stop where a toll attendant distribute a trip ticket. The toll opens at 6:00AM at which vehicles begin to arrive at the rate of 8 vehicles per minute. After 20 minutes, the arrival flow rate declines to 2 vehicles per minute and it continues at that level for the remainder of the day. If the time required to distribute the trip ticket is 15 seconds, determine the time the queue dissipates.