6. Gursoy Car Wash will wash a car in exponential amount of time with mean 10minutes. Arrivals occur as a Poisson process with rate 5 per hour.a) What is percent of the time the car wash is idle?b) On the average how many cars are in the system?c) On the average how many cars are waiting in line?d) On the average how long does a car spends in the system?e) What fraction of times there are more than 3 cars in the system?f) What is the probability that a car spends more than 30 minutes in thesystem?

Find the Calculation methods below: Percentage of the time the car was is idle (p0) = 1-λμHow many…

Answered: Gursoy Car Wash will wash a car in…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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13. Suppose AirOM passengers arrive to the check-in desk every 100 seconds (on average). The desk is staffed by a single ticketing agent, who takes 1.4 minutes (on average) to process a passenger. The arrivals follow a Poisson process and the service time is distributed exponentially. What is a passenger’s average waiting time (in seconds)? Enter a single number as your answer. If your final number is not integer, keep two decimal places in your answer.
(a) Determine the utilization of each of the copy centers. (b) Determine the average waiting time at each of the copy centers. (c) What is the annual cost of the administrative assistants’ average waiting time using the current system? (d) Determine the utilization of the combined copy center with two copiers. (e) Determine the average waiting time at the combined copy center. (f) What would be the annual cost of the administrative assistants’ average waiting time using the combined two copier setup? (g) What would be the utilization of the combined copy center with three copiers? (h) What would be the annual cost of the administrative assistants’ average waiting time using the combined three-copier setup? (i) What would you recommend to Catherine
40) Burger Cart April has a popular burger cart where an average of 12 customers per hour arrive to buy a burger. April can serve an average of 20 customers per hour. What is the average time a person spends waiting in line? Group of answer choices a) 16.0 minutes b) 2.25 minutes c) 3.0 minutes d) 12.0 minutes e) 7.0 minutes f) 4.5 minutes g) 9.0 minutes h) 1.2 minutes
92 Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of 2.5 per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: a. The average number of customers waiting Note: Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places. b. The average time a customer waits. Note: Round your answer to 2 decimal places. c. The average time a customer is in the shop. Note: Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.
A drive-through at a Fast Food serves 424 customers over a 10-hour day. On average, a customer spends 3 minutes waiting in line, 7 minutes placing the order, and 4 minutes completing the order before leaving the drive-through. How many customers on average are "in" the drive-through (i.e., from the time they enter to the time they exit the drive-through) on a typical day? (Specify your answer in two decimal points)
What happens to the length of a waiting line in a highly variable (queuing) setting if a managerattempts to achieve a high percentage of capacity utilization?
One field representative services 5 customers for a computer manufacturer. Customers request assistance at an average (Poisson-distributed) rate of once every 1.5 working days. The field representative can handle an average (Poisson-distributed) of 1.0 call per day. Determine: Use Table 1. a. The expected number of customers waiting. (Round "X" value to 2 decimal places. Round your answer to 3 decimal places.) Expected number of customers waiting b. The average length of time customers must wait from the initial request for service until the service has been completed. (Round your answer to 2 decimal places.) Average length of time days c. The percentage of time the service rep will be idle. (Round your answer to 1 decimal place.) Percentage of Idle time d. By how much would your answer to part a be reduced if a second field rep were added? (Round your answer to 3 decimal places.) Reduced number of customer(s)
Wanda's Car Wash & dry is an automatic, five-minute operation with a single bay. On a typical Saturday morning, cars arrive at a mean rate of eight per hour, with arrivals tending to follow a Poisson distribution. Find a. The average number of cars in line. b. The average time cars spend in line and service.
At a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 15 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? (Round your answer to 2 decimal places.) b. What is the average time that a vehicle must wait to get through the system? (Round your answer to 2 decimal places.) c. What is the utilization of the inspector? (Round your answer to 1 decimal place.) d. What is the probability that when you arrive there will be three or more vehicles ahead of you? (Round your answer to 1 decimal place.)
Passengers arrive at the immigration counter at a rate of one every 4 minutes, and processing their documents takes an average of 10 minutes each. There are 6 employees on duty. If a passenger isn't served immediately, how long on average would the passenger have to wait for service? a. 1.429 minutes b. 3.571 minutes c. 2.857 minutes d. 0.5 minutes
True or False? In a waiting line system, the average system time Wₛ must be longer than the average waiting time Wq
. At a car washing service facility customers arrive at the rate of 8 cars per hour. The service can manage an average of 12 cars per hour. The arrivals follow a Poisson distribution and the service follows a Exponential distribution. Calculate a) Utilization of the system b) Average number of customers in the system c) Average time customers spend in the system

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