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3. Jobs arrive to a server as a Poisson process with a mean time between arrivals of 7.6 minutes. The service time is distributed exponentially with a mean time of 5.2 minutes. a) Find the long-run probability that the server is vacant. (.- - ) b) Find the long-run expected number in the system. c) Find the long-run average waiting time in the queue.

3. Jobs arrive to a server as a Poisson process with a mean time between arrivals of 7.6 minutes. The service time is distributed exponentially with a mean time of 5.2 minutes. a) Find the long-run probability that the server is vacant. (.- - ) b) Find the long-run expected number in the system. c) Find the long-run average waiting time in the queue.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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3. Jobs arrive to a server as a Poisson process with a mean time between arrivals of 7.6 minutes. The service time is distributed exponentially with a mean time of 5.2 minutes. a) Find the long-run probability that the server is vacant. (.- - 3) b) Find the long-run expected number in the system. c) Find the long-run average waiting time in the queue.
Transcribed Image Text:3. Jobs arrive to a server as a Poisson process with a mean time between arrivals of 7.6 minutes. The service time is distributed exponentially with a mean time of 5.2 minutes. a) Find the long-run probability that the server is vacant. (.- - 3) b) Find the long-run expected number in the system. c) Find the long-run average waiting time in the queue.
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