# F if computer breakdown time costs rs 125 per day and

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f. If computer breakdown time costs Rs. 125 per day and the mechanic is paid Rs. 30 per day then compute the total cost per day. 8. A foreign bank is considering opening a drive-in window for customer service. Management estimates that customers will arrive for service at the rate of 12 per hour. The teller, whom it is considering to staff the window, can serve customers at the rate of one every three minutes. Assuming Poisson arrivals and exponential service, find a. Utilisation of teller b. Average number of customers in the system c. Average waiting time in the line d. Average waiting time in the system 8. Customers arrive at a one-window drive according to a Poisson 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 one. Other vehicles have to wait outside this space. Calculate:

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a. Probability that an arriving customer can drive directly to the space in front of the window. b. 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. 9. At a public telephone booth in a Post office arrivals are considered to be Possion with and average inter-arrival time of 12 minutes. The length of a phone call may be assumed to be distributed exponentially with an average of 4 minutes. a. What is the probability that a fresh arrival will not have to wait for the phone? b. What is the probability that an arrival will have to wait more than 10 minutes before the phone is free? c. What is the average length of queues that form time to time? 10. A maintenance service facility has Poisson arrivals rates, negative exponential service times, and operates on a first-come first-served queue discipline. Breakdowns occur on an average three machines per day with a range from zero to eight. The maintenance crew can service on an average six machines per day with a range from zero to seven. Find the : a. utilization factor of the service facility, b. Mean time in the system c. Mean number in the system in breakdown or repair d. Mean waiting time in the queue e. Probability of finding two machines in the system and f. Expected number in the queue.
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