In the M/G/1 queue, let service times σ = [Erl(r, µ)], i.e., Erlang (r, μ)-distributed. Give th Kendall (Pollaczek-Khinchine) formula for this special case. Hint. Use Kendall's formu P(≈) = (1 − p)ß(A — λ) (-2) and recall the main characteristics of a gamma r.v. - => wer. ß(0) = (±±)* ⇒ P(2) = (1 − p) (µ±±x²)” 1-z - -Az where p = Xb and b = r/µ.
In the M/G/1 queue, let service times σ = [Erl(r, µ)], i.e., Erlang (r, μ)-distributed. Give th Kendall (Pollaczek-Khinchine) formula for this special case. Hint. Use Kendall's formu P(≈) = (1 − p)ß(A — λ) (-2) and recall the main characteristics of a gamma r.v. - => wer. ß(0) = (±±)* ⇒ P(2) = (1 − p) (µ±±x²)” 1-z - -Az where p = Xb and b = r/µ.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![In the M/G/1 queue, let service times σ = [Erl(r, µ)], i.e., Erlang (r, µ)-distributed. Give the
Kendall (Pollaczek-Khinchine) formula for this special case. Hint. Use Kendall's formula
P(≈) = (1 − p)ß(\ — A≈) (A) and recall the main characteristics of a gamma r.v.
μ
Answer. ß(0) = (±)" ⇒ P(≈) = (1 − p) (µ±Ãª¯x²)”
=>
1-z
where p = Xb and b = r/µ.
μ.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb82eee3-c597-43b7-b98f-cffc18fbca72%2Fc4ac368c-b07b-4ccc-b686-5ff67e7c50fa%2F1dxa9jr_processed.png&w=3840&q=75)
Transcribed Image Text:In the M/G/1 queue, let service times σ = [Erl(r, µ)], i.e., Erlang (r, µ)-distributed. Give the
Kendall (Pollaczek-Khinchine) formula for this special case. Hint. Use Kendall's formula
P(≈) = (1 − p)ß(\ — A≈) (A) and recall the main characteristics of a gamma r.v.
μ
Answer. ß(0) = (±)" ⇒ P(≈) = (1 − p) (µ±Ãª¯x²)”
=>
1-z
where p = Xb and b = r/µ.
μ.
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