Stochastic Processes : M/M/s Queue, Stationary Distribution and Long-Run Proportion
Not what you're looking for?
Consider the M/M/s queue, with arrival rate...
5. Consider the M/M/s queue, with arrival rate Λ >0 and service rate μ >0.
(a) Find the condition involving Λ, μ and s that is necessary for there to exist a stationary distribution. Why does this condition makes sense?
(b) Find the long-run proportion of time that there are k customers in the system, for k = 0,1,...
See the attached file.
Purchase this Solution
Solution Summary
M/M/s queue, stationary distribution and long-run proportion are investigated and discussed. The solution is detailed and well presented.
Solution Preview
Please see the attached file for the complete solution.
(a) For system to be stationary, has to be less than 1, that is, .
This is because is the arrival rate of customers, which is the expected number of arrivals per hour, and ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.