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Waiting Line Model Situation

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In a waiting line model situation, arrivals occur around the clock at a rate of six per day, and the service occurs at one very three hours. Assume the Poisson and exponential distributions.

a. What is Mean Arrival Rate?
b. What is Mean Service Rate?
c. Find probability of no units in the system.
d. Find average number of units in the system.
e. Find average time in the waiting line.
f. Find average time in the system.
g. Find the probability that there is one person waiting.
h. Find the probability that an arrival will have to wait.

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This solution is comprised of a detailed explanation of a Waiting Line Model Situation and the various aspects related to it. Supplemented with more than 200 words of text, this step-by-step explanation provides students with a clear perspective of the concepts of Mean Arrival Rate, Mean Service Rate, Average number of units in the system, Probability of having no units in the system, Average time in the waiting line, Average time in the system, Probability that there is one person waiting and Probability that an arrival will have to wait, etc.

Solution provided by:
Anwesha Ghosh, MSc
Education
  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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