6. The arrival of employees in a service station (canteen) follows Poisson distribution, and service times are exponentially distributed. The rate of arrivals averages 45 employees each hour, and an attendant can serve on an average 50 employees each hour. The employees are paid Rs. 8 per hour, and the attendants are paid Rs. 5 per hour. Find the optimum number of attendants to be placed in the service station.

6. The Garrett-Tompkins Company provides three copy machines in its copying room for the use of its employees. However, due to recent complaints about considerable time being wasted waiting for a copier to become free, management is considering adding one or more additional copy machines. During the 2,000 working hours per year, employees arrive at the copying room according to a Poisson process at a mean rate of 40 per hour. The time each employee needs with a copy machine is believed to have an exponential distribution with a mean of 4 minutes. The lost productivity due to an employee spending time in the copying room is estimated to cost the company an average of $40 per hour. Each copy machine is leased for $4,000 per year. Find the following values for this system: λ, μ, Cs, Cw. Then use the Excel template to determine how many copy machines the company should have to minimize its expected total cost per hour. List your result in the following table. : S 3 4 5 P E(TC) = E(SC) + E…

6. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive according to a Poisson process at a mean rate of 2 per minute. However, business is growing and management projects that the mean arrival rate will be 3 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 1 minute. Management has established the following guidelines for a satisfactory level of service to customers. The average number of customers waiting in line to begin service should not exceed 1. At least 90 percent of the time, the number of customers waiting in line should not exceed 3. a)Use the Excel sheet to determine how many tellers will be needed a year from now to completely satisfy these guidelines.

6. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive according to a Poisson process at a mean rate of 2 per minute. However, business is growing and management projects that the mean arrival rate will be 3 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 1 minute. Management has established the following guidelines for a satisfactory level of service to customers. The average number of customers waiting in line to begin service should not exceed 1. At least 90 percent of the time, the number of customers waiting in line should not exceed 3. (a) Use the Excel sheet to evaluate how well the guidelines will be satisfied a year from now if no change is made in the number of tellers.

During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Find: (a) The average number of customers waiting for service if 5 clerks are used.   (b) The minimum number of clerks needed to keep the average waiting time in the system to under 5 minutes.   (c) If clerk cost is $40 per hour and customer waiting time represents a “cost” of $30 per hour, how many clerks can be justified on a cost basis? Please show work.

The following data has been collected on the number of customers seen to arriveto a museum in a succession of 5-minute intervals: 5, 1, 3, 7, 5, 5, 6, 7, 5, 7, 4, 8, 1,5, 2, 3, and 5. Estimate the squared coefficient of variation of the arrival process. Ifthis data was known to come from a Poisson process, what would be your estimateof l, the rate of customer arrivals?

The arrival rate of patients at a hospital counter follows Poisson distribution with a mean of 25 per hour. The service rate of the treatment to patients also follows Poisson distribution with a mean of 45 per hour.a) What is the probability of having 0 patients in the system (P 0 )?

4) Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs come in at a mean rate of three per eight- hour day (assume Poisson). Determine:1. The average number of customers awaiting repairs.2. System utilization.3. The amount of time during an eight-hour day that the repairman is not out on a call. 4. The probability of two or more customers in the system.

Many banks and post offices have switched from having a line at each teller or clerk to a single waiting line cordoned off by a set of ropes or chains. Examine this change by considering the following two cases: A. Case 1. Customers arrive at a bank at an average rate of 80 per hour and form a single line. There are five tellers, and the average service time is 3.0 minutes for each teller. Assuming exponential interarrival and service times, how long is the average wait in line? B. Case 2. Customers arrive at a teller's window at a rate of 16 per hour. There are five tellers so that the total arrival rate is 80 per hour. There is separate line at each window (with no switching between lines). As in Case 1, the average service time for each teller is 3.0 minutes. How long is the average wait in line? C. Comment on the results of Cases 1 and 2. What additional factors might affect waiting times in a real banking situation?