Question

Show that, for the GI/M/1 queueing system, $$ \sigma_N^2=\frac{\rho\left(2-\pi_0-\rho\right)}{\pi_0^2} . $$

   Show that, for the GI/M/1 queueing system,
$$
\sigma_N^2=\frac{\rho\left(2-\pi_0-\rho\right)}{\pi_0^2} .
$$

Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Arnold O. Allen 2nd Edition

Chapter 5, Problem 64

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Step 1

The GI/M/1 queue is a model where arrivals follow a general independent (GI) distribution, the service times are exponentially distributed (M for Markovian), and there is 1 server. The key parameters are the arrival rate \(\lambda\), the service rate \(\mu\), and Show more…

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Show that, for the GI/M/1 queueing system, $$ \sigma_N^2=\frac{\rho\left(2-\pi_0-\rho\right)}{\pi_0^2} . $$

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