Consider a M/M/1 system with arrival rate A and service rate 2µ and a M/M/2 system witharrival rate A and service rate u for each server. Assume 2µ > A.(a) Determine Po(M M1), the long-run probability that the system M/M/1 is empty.(b) Determine Po(MM2), the long-run probability that the system M/M/2 is empty.(c) Which one is larger, Po(M M1) or Po(M M2)? If you are a customer, which system wouldyou prefer? You do not need to justify your answer to the latter question.

M/M/1 system refers to the single server, exponential service time and Poisson arrival rate. M/M/2…

Answered: Consider a M/M/1 system with arrival…

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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eBook Problem 15-27 (Algorithmic) Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company's office can be described by a Poisson probability distribution with an arrival rate of four jobs per 8-hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of 1.4 hours and a standard deviation of 1 hour. Answer the following questions, assuming that Gubser uses one welder to complete all jobs: a. What is the mean arrival rate in jobs per hour? If required, round your answer to two decimal places. per hour b. What is the mean service rate in jobs per hour? If required, round your answer to four decimal places. per hour c. What is the average number of jobs waiting for service? If required, round your answer to three decimal places.
A manager intends to order a new machine and must now decide on the number of spare parts to order along with the machine. The parts cost $496 each and have no salvage value. The manager has compiled the frequency distribution for the probable usage of spare parts:7 spare parts with frequency 0.05;8 spare parts with frequency 0.23;9 spare parts with frequency 0.08;10 spare parts with frequency 0.07; and 11 spare parts with frequency 0.57. For what range of shortage costs would stocking 9 spare parts constitute an optimal decision ? a. Between 231.5and 334.8 b. Between 192.9and 279 c. Between 289.3and 418.5 d. Between 96.44and 139.5
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14
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