D,E,F 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?

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Answered: Car Wash will wash a car in exponential…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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You observe an average of 10 customers in the System. On average, you also observe customers are in the system for 50 minutes before they leave. What is the arrival rate into the system in customers per hour?
Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is exponentially distributed, with a mean of two hours per call. Requests for copierrepairs come in at a mean rate of three per eight-hour day (assume Poisson).A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?D) What is the average number of customers awaiting repairs?
27. Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is two per minute and the average service rate of a single server is five per minute, what portion of the time is there less than 3 people in line? Answer to three decimal points please and thank you
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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?
A vending machine dispenses hot chocolate or coffee. Service time is 35 seconds per cup and is constant. Customers arrive at a mean rate of 66 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customers ?? b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes ??
Explain in what kind of situations is queuing analysis is most important under waiting line models ?
28. Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is two per minute and the average service rate of a single server is five per minute, what is the average number of customers in line? Answer to three decimal points. thanks!
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
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.
Give and explain briefly that in what kinds of situations is queuing analysis is most appropriate.
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 76 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number customers

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