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Probability theory

Queueing theory

M-G-1 queue

Embedded departure chain of an M-G-1 queue

{c}

For a stable $M/G/1$ queue with traffic intensity $\rho=\lambda\mathbb ES<1$, the mean waiting time before service is
$$
W_q=\frac{\lambda\mathbb ES^2}{2(1-\rho)}.
$$
Equivalently, the mean number in the system is
$$
L=\rho+\frac{\lambda^2\mathbb ES^2}{2(1-\rho)}.
$$

Pollaczek-Khinchine mean formula

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 27J / Solution

Pollaczek-Khinchine mean formula

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Pollaczek-Khinchine mean formula

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