Chicago O'hare International Airport reports that cars arriving at International Lot (D) demonstrates that the time between arrivals is 1.2 minutes and is exponentially distributed. Based on this information, the mean number of cars arriving per minute is about 0.83. True False
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- Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is three trucks per hour, and the mean service rate is six trucks per hour. Use the Single Server QueueExcel template to answer the following questions. Do not round intermediate calculations. Round your answers to three decimal places. What is the probability that the truck dock will be idle? What is the average number of trucks in the queue? truck(s) What is the average number of trucks in the system? truck(s) What is the average time a truck spends in the queue waiting for service? hour(s) What is the average time a truck spends in the system? hour(s) What is the probability that an arriving truck will have to wait? What is the probability that more than two trucks are waiting for service?Customers arrive at a one window drive according to a poison distribution with mean of 10 minutes and service time per customer is exponential with mean of 6 minutes. The space in front of the window can accommodate only three vehicles including the serviced ones. Other vehicles are have to wait outside this space. Calculate:a. A. probability that an arriving customer can drive directly to the space in front of the windowb. Probability that an arriving customer will have to wait outside the directed space c. How long an arriving customer is expected to wait before getting the service?Consider a bank branch that has three distinct customer arrival patterns throughout the day, as measured by average arrival rates (below). Morning (8:30 - 11:30): arrival 1 = 47 per hour. %3D Lunch (11:30 - 1:30): arrival 2 = 70 per hour. Afternoon (1:30 - 4:00): arrival 3 = 30 per hour. Regardless of the time of day, the average time it takes for a teller to serve customers is 3.17 minutes. Because of competition with other banks in the area, management has developed an internal goal to keep the average customer wait before service to be less than 4 minutes. With that in mind, answer the following: a. During the morning period, what is the minimum number of tellers that the bank needs to hire to achieve the 4-minute service goal mentioned above? [ Select] b. During lunch, what is the minimum number of tellers that the bank needs to hire to achieve the 4 minute service goal mentioned above? [ Select ] c. In the afternoon, what is the minimum number of tellers that the bank
- Car owners fill up when their tanks are exactly half full. At the present time, an average of 8.5 cars/hr arrive at a single-pump gas station. It takes an average of 3.68 minutes to service a car. Suppose that a gas shortage occurs and panic buying takes place. All car owners now purchase gas when their tanks are exactly 3/4 full. Since each car is putting less gas into the tank for each visit, the average service time has been reduced to 2.54 minutes. Assume that arrival and departure rates are both exponential. What is the difference in length of queue before and after the shortage scenario, in terms of vehicles? answer an absolute value, and in four decimal places.Discuss how the design of a waiting system can negatively affect customers?The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 12 minutes to land and clear the runway (following an exponential distribution). Planes arrive at the airport at the rate of one every 15 minutes. The arrival rate follows a Poisson distribution. A plane is considered to have entered the “system” once it has notified the airport that it is in the vicinity and wants to land. For purposes of this analysis, you can ignore the planes taking off. a) Determine the average number of planes that are in the system waiting to land. b) Find the average time a plane is in the system either waiting to land or landing. c) What is the probability that a plane approaching the airport will find at least two other that are already in the “system” that is waiting to land? d) Suppose that the cost assigned to a plane while it is waiting to land (in the stack) is $1,000…
- Explain what is a waiting line problem ?Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to nine. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The arrival rate is 0.06 machines per hour for each machine, and the service rate for each individual assigned to the repair operation is 0.5 machines per hour. Compute the operating characteristics if the company retains the single-employee repair operation. If required, round your answers to four decimal places. P0 = fill in the blank 1 Lq = fill in the blank 2 L = fill in the blank 3 Wq = fill in the blank 4 hours W = fill in the blank 5 hours Compute the operating characteristics if a second employee is added to the machine repair operation. If required, round your answers to four decimal places. P0 = fill in the blank 6 Lq = fill in the blank 7 L = fill in the blank 8 Wq = fill…A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. 3. Find the proportion of the time that the employee is busy. 4. Find the average number of people receiving and waiting to receive information. 5. Find the average number of people waiting in line to get information.
- A car mechanic, Carlos, can install new mufflers at an average rate of 3 every hour (following an exponential distribution). Customers needing this service arrive at the shop (following a Poisson distribution) on an average of 2 per hour. They are served on a first-in, first-out basis and come from the very large (almost infinite) population of possible buyers. Calculate the following operating characteristics of the service system: a. The probability there are no cars in the system. b. The average number of cars waiting in line. c. The average number of cars in the system. d. The average time a car spends waiting in line. e. The average time a car spends in the system.Customers arrive at a video rental desk at the rate of 14 per minute(Poisson).Each server can handle 4.668 customers per minute(Poisson). If there are 6 servers, determine the probability of 5 or fewer customers in the system. a. 0.03 b. 0.025 c. 0.049 d. 0.901How does an event improve the smooth queue management?