Applications are scanned in a two step process with two resources. The processing time at the first resource is 9.1 minutes and for the second resource it is 12 minutes The first resource has 2 workers and the second resource has 4 workers. Instruction: Round your answer to three decimal places. What is the capacity of this process in terms of applications per hour? applications per hour
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- Consider a bank where potential customers arrive at rate of 60 customers per hour. However, because of limited space, one out of every four arriving customers finds the bank full and leaves immediately (without enteringthe bank). Suppose that the average number of customers waiting in line in the bank is 3.5. How long will a typical entering customer have to wait in line? (Hint: In Little’s formula, l refers only to customers who enter the system.)Customers enter the camera department of a store at an average rate of six per hour. The department is staffed by one employee, who takes an average of six minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. (Use the Excel spreadsheet Queue Models.) a-1. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)? Note: Round your answer to 2 decimal places. a-2. How long would a customer expect to spend in the camera department (total time)? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. b. What is the utilization of the clerk? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. c. What is the probability that there are more than two people in the camera department (excluding the clerk)? Note: Round your intermediate calculations to 3 decimal places and final answer to 1…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 five trucks per hour. Use the Single Server Queue Excel 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?
- Patients arrive to a small hospital emergency room according to a Poisson process withan average rate of 1.5 per hour. Because service times for these patients vary considerably, the service times are accurately described by an exponential distribution. Supposethat the average service time is 26 minutes. If there is only a single doctor working atany point in time, find the following measures of service for this emergency room:c. The expected number of patients waiting for service.Queuing theory refers to the fundamental concepts of a phenomenon that we constantly experience, the concept of queues. These queues are in production processes, such as in banks, service providers, etc.Based on the concepts of Production Modeling and Simulation, do the following: a) Assuming that cars arrive at a toll, on average, every 0.5 minutes, and the toll has only one payment window, and both the time between arrivals and the time between calls follow an exponential distribution. The toll attendant takes an average of 0.3 minutes to collect. Calculate the system performance measures, ie the car arrival rate and the toll service rate.A clinic has only one dentist. During working days, the traffic is uniformly busy with patients arriving at the rate of 8 patients per hour. The doctor’s service time is 3 minutes. (Please keep three digits after the decimal and do not omit 0 before the decimal, good example: 0.132) What is the probability that the clinic is empty (except for the dentist)? What is the average number of patients in the waiting room? What is the average time (in minutes) a patient spends in the office (wait plus service)? What is the probability that the clinic has exactly two patients?
- 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?A summer camp that offers one-week programs faces the challenges of long queues asparents try to check in their children each Saturday morning. If they were to add morestaff to assist with the check-in process, then which of the following will occur?i. The average time parents wait decreases.ii. The maximum time the parents wait decreases.iii. The average number of parents waiting to check in their child decreases. a. Just Ib. Just IIc. Just IIId. I and IIe. I and IIIf. II and IIIg. I, II, and IIICustomers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.d. Calculate the probability a customer will spend more than an hour at the bakery(time in queue plus service time).