The Copy Shop is open 5 days per week for copying materials that are brought to the shop. It has three identical copying machines that are run by employees of the shop. Only two operators are kept on duty to run the machines, so the third machine is a spare that is used only when one of the other machines breaks down. When a machine is being used, the time until it breaks down has an exponential distribution with a mean of 2 weeks. If one machine breaks down while the other two are operational, a service representative is called in to repair it, in which case the total time from the breakdown until the repair is completed has an exponential distribution with a mean of 0.2 week. However, if a second machine breaks down before the first one has been repaired, the third machine is shut off while the two operators work together to repair this second machine quickly, in which case its repair time has an exponential distribution with a mean of only 1/15 week. If the service representative finishes repairing the first machine before the two operators complete the repair of the second, the operators go back to running the two operational machines while the representative finishes the second repair, in which case the remaining repair time has an exponential distribution with a mean of 0.2 week. (a) Letting the state of the system be the number of machines not working, construct the rate diagram for this queueing system. (b) Use the balance equations to find the steady-state distribution of the number of machines not working. (c) What is the expected number of operators available for copying?
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.Read more
Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.Read more
Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.Read more
Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.Read more
By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.Read more