There are m users who share a computer system. Each user alternates between "thinking" intervals whose durations are independent exponentially distributed with parameter Y, and an "active" mode that starts by submitting a service re- quest. The server can only serve one request at a time, and will serve a request completely before serving other requests. The service times of different requests are independent exponentially distributed random variables with parameter μ, and also independent of the thinking times of the users. Construct a Markov chain model and derive the steady-state distribution of the number of pending requests, including the one presently served, if any.
There are m users who share a computer system. Each user alternates between "thinking" intervals whose durations are independent exponentially distributed with parameter Y, and an "active" mode that starts by submitting a service re- quest. The server can only serve one request at a time, and will serve a request completely before serving other requests. The service times of different requests are independent exponentially distributed random variables with parameter μ, and also independent of the thinking times of the users. Construct a Markov chain model and derive the steady-state distribution of the number of pending requests, including the one presently served, if any.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Transcribed Image Text:There are m users who share a computer system. Each user alternates between "thinking" intervals whose durations are
independent exponentially distributed with parameter Y, and an "active" mode that starts by submitting a service re-
quest. The server can only serve one request at a time, and will serve a request completely before serving other requests.
The service times of different requests are independent exponentially distributed random variables with parameter μ,
and also independent of the thinking times of the users. Construct a Markov chain model and derive the steady-state
distribution of the number of pending requests, including the one presently served, if any.
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