Problem 11-17 (Static) The National State Bank is trying to make sure that they have enough tellers to handle the Friday afternoon rush of workers wanting to cash their paychecks. They are only concerned with the last hour of the day from 4:00 to 5:00 p.m. It takes 5 minutes per customer to be processed by the tellers. The average customer arrivals are shown in the table below. TIME 4:00-4:05 4:05-4:10 4:10-4:15 4:15-4:20 4:20-4:25 4:25-4:30 4:30-4:35 4:35-4:40 4:40-4:45 4:45-4:50 4:50-4:55 4:55-5:00 5:00-5:05 Total CUSTOMERS ARRIVING 5 6 8 10 12 16 12 10 6 4 2 0 93 The bank currently has eight teller stations, and all are staffed during the Friday afternoon rush hour. a. What is the current maximum output at the bank during rush hour? Current maximum output the bank customers per hour b. Can the bank process all the customers by 5:00 P.M.? process all the customers by 5:00 PM.
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- Problem 11-19 (Algorithmic) All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has three screening stations available, and the facility manager must decide how many to have open at any particular time. The service rate for processing passengers at each screening station is 3 passengers per minute. On Monday morning the arrival rate is 5.2 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. When the security level is raised to high, the service rate for processing passengers is reduced to 2 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning. Note: Use P0 values from Table 11.4 to answer the questions below. The facility manager's goal is to limit the average number of passengers waiting in line to 10 or fewer. How…The following build-up diagram tracks the number of customers for a single-server queueing system (e.g., an ATM machine) from 10:00am to 10:15am on a certain day. The number of customers shown in the chart includes both those in service and waiting in line. Build-up diagram # of Customers in system (in service + waiting) 3 2 1 0 10:00 10:01 10:02 10:03 10:04 10:07 10:09 We will call the customer who arrived the earliest during this time span the first customer, the customer who arrived the second earliest the second customer, etc.. The service discipline is first-come-first-served (FCFS). According to the diagram, how long did the second customer have to wait (in minutes) before he can enter service?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?
- (10 Points) Eat well is a small drive through fast food restaurant, staffed by anefficient employee John, is located in a super mall area. Customers arrive at thecounter at an average of one every 15 minutes, and the customer arrival followsa Poisson distribution. John takes at most 10 minutes to process each foodorder.a) What is average number of customer being served at any time?b) The expected number of customers waiting to be served.c) Compute the average time customer wait in the system.d) Compute the average time customer wait in the line.e) What percentage of time is John Idle?B. Draw and explain the flow charts of the Arrival Event and Service Completion Event.Customer arrive at one-window drive in bank according to Poisson distribution with mean 10 per hour. Service time per customer is exponential with mean 5 minutes. There are three spaces in front of the window, including the car being served. Other arriving cars can wait outside these three spaces. A. What is the probability that an arriving customer can enter one of these three spaces? B. What is the probability that an arriving customer is expected to wait outside the three spaces. C.How long is an arriving customer expected to wait before starting service.
- The store opens at 8 am. Customers will arrive at Poisson rate λ = 10 per hour. (i) At what time do you expect the first customer to arrive? (ii) Given that the second customer arrived after 8.10 am, what is the expected arrival time of the first customer? (iii) After serving the third customer, the sales clerk takes a 10-minute break at 8.20 am. Upon his/return, he finds that the fourth customer has arrived. What is the probability that the customer has been waiting for more than 3 minutes?The time from when a patient is discharged from NorthShore Hospital to the time the discharged patient’s bed isready to be assigned to a new patient is referred to as thebed assignment turnaround time. If the bed turnaroundtime is excessive, it can cause problems with patient flowand delay medical procedures throughout the hospital. Thiscan cause long waiting times for physicians and patientsthus creating customer dissatisfaction. The admissions RNhas assigned a patient care associate to measure the bedturnaround time for a randomly selected bed each morning,afternoon, and evening for 30 days. Following are the bedturnaround time sample observations:a. Develop an x-chart to be used in conjunction with anR-chart using 3 limits to monitor the bed turnaroundtimes and indicate if the process is in control usingthese charts.b. Is the hospital capable of consistently achieving bedturnaround times of 120 minutes 15 minutes withoutimproving the process?Problem 15-31 (Algorithmic) Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 10 calls per hour. The arrival rate is 16 calls per hour.
- 13. Movie Tonight is a typical video and DVD movie rental outlet for home viewing customers. During the weeknight evening, customers arrive at Movies Tonight at the average rate of 1.25 customers per minute. The checkout clerk can serve an average of two customers per minute. Assume Poisson arrivals and exponential service times.What is the probability that no customers are in the system?What is the average number of customers waiting services?What is the average time a customer waits for service to begin?Do the operating characteristics indicate that the one-clerk check out system provides an acceptable level of service?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…The time from when a patient is discharged from North Shore Hospital to the time the discharged patient’s bed is ready to be assigned to a new patient is referred to as the bed assignment turnaround time. If the bed turnaround time is excessive, it can cause problems with patient flow and delay medical procedures throughout the hospital. This can cause long waiting times for physicians and patients thus creating customer dissatisfaction. The admissions RN has assigned a patient care associate to measure the bed turnaround time for a randomly selected bed each morning., afternoon, and evening for 30 days. Following are the bed turnaround time sample observations: Day Day Bed Turnaround Times (min) 1 1 127 135 167 144 151 2 2 140 155 122 135 119 3 3 112 128 97 118 131 4 4 223 135 154 187 150 5 5 181 155 160 172 166 6 6 103 158 145 124 149 7 7 146 135 167 150 178 8 8 104 122 115 137 129 9 9 136 158 137 148 156 10 10 145 163 106 139 170 11 11 84 146 125 98…