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- Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.In the production shop of a company, the breakdown of the machines is found to be Poisson distributed with an average rate of 3 machines per hour. Breakdown time at one machine cost 400 birr per hour to the company. There are two choices before the company for hiring the repairmen. One of the repairmen is slow but cheap, the other is fast but expensive. The slow cheap repairman demands 200 birr per hour and will repair the broken down machines exponentially at the rate of 5 per hour. The fast expensive man demands 300 birr per hour and will repair machines exponentially at an average rate of 6 per hour. Which repairman should be hired?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?
- Let a queuing system have the Kendall model (M/M/1) : (GD/infinity/infinity). Assume A < µ. Does W, for the service discipline FIFO equal W, for the service discipline SIRO? O I have no idea. no yes It cannot be determined.The common measures of a queuing system's performance include: O probability that the service facility will be idle, average queue length, and probability that the waiting time will exceed a specified duration. average time each customer spends in the system, probability that the service system will be idle, and average time each customer spends in the queue. average queue length, maximum time a customer may spend in the queue, and the utilization factor for the system. average time each customer spends in the system, maximum queue length, and probability of a specific number of customers in the system. maximum queue length, maximum time a customer may spend in the queue, and average queue length.A copier is able to operate for an average of 200 hours between repairs, and the mean repair time is two hours. Determine the availability of the copier.
- The average time between the arrivals of the taxis arriving at the airport to pick up passengers has an exponential distribution, with an average of 10 minutes. a) What is the probability that a passenger will wait for the taxi less than 15 minutes? b) What is the probability that a passenger will wait for the taxi between 20 and 30 minutes? Solve using the cumulative distribution function H1A proposal has been presented to the government of Newfoundland and Labrador that would build a new section of highway which would provide improved access for residents of a remote coastal area near Bonavista. The highway would be 16 kilometres in length. The initial proposal called for 7 toll booths, each staffed by an employee. But a subsequent proposal recommended replacing the employees with machines. Many factors must be considered because the intended employees are unionized. However, one of the government's concerns is the effect that replacing the employees with machines will have on the times the drivers spend in the system. Customers will arrive to any one toll booth at a rate of 9 per minute. In the exact-change lanes with employees, the service time is essentially constant at 5 seconds for each driver. With machines, the average service time would still be 5 seconds, but it would be exponential rather than constant, because it takes time for the coins to rattle around in…Currently, Commercial Banks have 1 unit of ATM machines to meet customer needs. It is known that there is an average of 12+x customers in the system. Then it is also known that the average time spent by someone in the system is 10 minutes. Assume that the system follows M/M/1. The Commercial Bank operational manager is considering whether it is necessary to add 1 unit of ATM machine. What are your considerations? To strengthen the consideration, compare the queue length, queue length, and utilities before and after adding an ATM machine? Note: x denoted by the last number of my ID Number.Example, if my ID number is 2602296545, then the number used are “5”
- Consider a bank with two tellers. An average of 2 customers per hour arrive at the bank and wait in a single línea for an idle teller. The average time it takes to serve a customer is triangular (x1=1, y1=0), (x2=4, y2=2/3) Assume that inter-arrival times and services time is exponential. Develop the service (ST) equation? a. Y=2x-22/6B. Y=2x-22/3C. Y=22/3x-2/3D. Y=2x-3/22Currently, Commercial Banks have 1 unit of ATM machines to meet customer needs. It is known that there is an average of 15 customers in the system. Then it is also known that the average time spent by someone in the system is 10 minutes. Assume that the system follows M/M/1. The Commercial Bank operational manager is considering whether it is necessary to add 1 unit of ATM machine. What are your considerations? To strengthen the consideration, compare the queue length, queue length, and utilities before and after adding an ATM machine?41) Burger Cart April has a popular burger cart where an average of 12 customers per hour arrive to buy a burger. April can serve an average of 20 customers per hour. Layla runs a coffee stand across the street from April. As Layla looks over at April's burger cart, what is the probability she will see 3 customers at the cart (in line or being served)? Group of answer choices 0.4219 0.0156 0.7500 0.0117 0.0720 0.1055 0.2500 42) Burger Cart The average time required to serve a customer = _______ minutes. Group of answer choices 2.50 minutes 1.67 minutes 3.00 minutes 20.00 minutes 4.00 minutes 5.00 minutes 2.00 minutes