3. (for all students) Jobs arrive to a single server queue according to a Poisson process with a rate of 2.5 jobs per hour. You have collected past data and determined that service times have a mean of 19.8 minutes and variance of 123.8 minutes squared.
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- A priority waiting system assigns arriving customers to one of four classes. Arrival rates (Poisson) of the classes are shown in the following table. Five servers process the customers, and eachcan handle three customers per hour.a. What is the system utilization?b. What is the average wait for service by customers in the various classes? How many are waiting in each class, on average?c. If the arrival rate of the second priority class could be reduced to three units per hour by shifting some arrivals into the third priority class, how would your answers to part b change?d. What observations can you make based on your answers to part c?5. Eat well is a small drive through fast food restaurant, staffed by an efficient employee John, is located in a super mall area. Customers arrive at the counter at an average of one every 15 minutes, and the customer arrival follows a Poisson distribution. John takes at most 10 minutes to process each food order. 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) What percentage of time is John Idle?. A manager must determine requirements for waiting space for customers. A priority system isused to process customers, who are assigned to one of two classes when they enter the processingcenter. The highest-priority class has an arrival rate of four per hour; the other class has an arrivalrate of two per hour. Both can be described as Poisson-distributed. There are two servers, andeach can process customers in an average of 15 minutes.a. What is the system utilization?b. Determine the number of customers of each class that are waiting for service.c. Determine the average waiting time for each class.d. If the manager could alter the assignment rules so that arrival rates of the two classes wereboth 3/hour, what would be the revised average waiting time for each priority class?
- An automated car wash will wash a car in 10 minutes.Arrivals occur an average of 15 minutes apart (exponentiallydistributed).a On the average, how many cars are waiting in linefor a wash?b If the car wash could be speeded up, what wash timewould reduce the average waiting time to 5 minutes?Determining the Number of ServersIn the service department of the Glenn-Mark Auto Agency, mechanics requiring parts for auto repair or service present their request forms at the parts department counter. The parts clerk fills a request while the mechanic waits. Mechanics arrive in a random (Poisson) fashion at the rate of 40 per hour, and a clerk can fill requests at the rate of 20 per hour (exponential).If the cost for a parts clerk is $30 per hour and the cost for a mechanic is $60 per hour, determine the optimum number of clerks to staff the counter. (Because of the high arrival rate, an infinite source may be assumed.)A fast-food restaurant has one drive-through window.On average, 40 customers arrive per hour at thewindow. It takes an average of one minute to serve acustomer. Assume that interarrival and service timesare exponentially distributed.a. On average, how many customers are waiting in line?b. On average, how long does a customer spend at therestaurant (from time of arrival to time service iscompleted)?c. What fraction of the time are more than three carsin line? (Here, the line includes the car, if any,being serviced.)
- (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?Eat Well is a tiny drive-through quick food restaurant in a shopping malltown, manned by an efficient employee named John. Customers arrive at the counter at a rate of one per 15 minutes on average, with a Poisson delivery for customer entry. Each food order takes John no more than ten minutes to process. a) How many customers are handled on average at any given time? b) The anticipated amount of clients that would be represented. c) Determine the average consumer wait time in the scheme. d) How much of the day is John Idle idle?In an M/M/1 queueing system, the arrival rate is 3 customers per hour and the service rate is 5 customers per hour. a. What is the utilization? (round your answer to 3 decimal places) b. What is the expected number of customers in the system (L)? (round your answer to 3 decimal places) c. What is the expected waiting time in the system (W)? (express the waiting time in hours, round your answer to 3 decimal places) d. What is the expected number of customers in the queue (Lq)? (round your answer to 3 decimal places) e. What is the expected waiting time in the queue (Wq)? (express the waiting time in hours, round your answer to 3 decimal places)
- 4.) The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. a.) What percentage of the total available service time is being used? b.) Due to Covid restrictions, only two customers are allowed in the office at the same time. What percent of the time will there be customers waiting outside?Paula Caplin is manager of a major electronics repair facilityowned by Fisher Electronics. Recently, top management ex-pressed concern over the growth in the number of repair jobs in process at the facility. The average arrival rate is 120 jobsper day. The average job spends four days at the facility.a. What is the current work-in-process level at the facility?b. Suppose that top management has put a limit of one-halfthe current level of work-in-process. What goal mustPaula establish, and how might she accomplish it?5. The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. d.) Because the state has received less than expected tax receipts, the DMV is thinking of cutting one position. Is this a good idea? Why?