What percentage of the total available service time is being used?
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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?
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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 is the service rate? (please include units) b.) What is the arrival rate? (please include units)At a one man barber shop, customers arrive according to poison distribution with a mean arrival rate of 5 per hour and hair cutting time was exponentially distributed with an average hair cutting time was exponentially distributed with an average hair cut taking 19 minutes. It is assumed that because of excellent reputation, customers were always willing to wait. Calculate the following a. Average number of customers in the shop and average numbers waiting for a haircut b .Percentage of time arrival can walk in right without having to wait c. The percentage of customers who have to wait before getting into the barber’s chair
- Doña Blanca plans to open a small car wash and must decide how much space to allocate to waiting cars. She estimates that customers will arrive randomly (Poisson process) at an average rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers will take their car elsewhere. The total time attributable to washing a car has exponential distribution with mean 3 minutes. Compare the fraction of potential customers lost due to lack of waiting space if a) 2 and b) 4 spaces (in addition to the wash location) are provided.A tax consulting firm has 5 counters in its office to receive people who have problems concerning their income, wealth and sales taxes. On the average 75 persons arrive in an 8hour day. Each tax adviser spends 25 minutes on an average on an arrival. If the arrivals are Poissonly distributed and service times are according to exponential distribution, find The probability of there being no customer in the system The average number of customers in the system iii. Average number of customers waiting to be served iv. Average time a customer spends in the system v. Average waiting time for a customer5. 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?
- A study-aid desk staffed by a graduate student has been established to answer students’questions and help in working problems in your OSCM course. The desk is staffed eighthours per day. The dean wants to know how the facility is working. Statistics show thatstudents arrive at a rate of four per hour and the distribution is approximately Poisson.Assistance time averages 10 minutes, distributed exponentially. Assume population andline length can be ini nite and queue discipline is FCFS.Before a test, the arrival of students increases to six per hour on the average. What willthe new average line length be?Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the negative exponential distribution. If asingle teller is used, find:a) The average time in the line.b) The average number in the line.c) The average time in the system.d) The average number in the system.e) The probability that the bank is empty.f)CEO Benjamin Neve is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for customers. A single line would be used, and the customer at the front of the line would go to the first available bank teller. He assumes that this will cut the waiting time in half. If a second teller is added, find the new answers to parts (a) to (e).Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the negative exponential distribution. If asingle teller is used, find:a) The average time in the line.b) The average number in the line.c) The average time in the system.d) The average number in the system.e) The probability that the bank is empty.CEO Benjamin Neve is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for customers. A single line would be used, and the customer at the front of the line would go to the first available bank teller. He assumes that this will cut the waiting time in half. If a second teller is added, find the new answers to parts (a) to (e).