Utilization, in queueing theory, is the proportion of the system's resources which is used by the traffic which arrives at it. It should be strictly less than one for the system to function well. It is usually represented by the symbol $\backslash rho$. If $\backslash rho\; \backslash geq\; 1$ then the queue will continue to grow as time goes on. In the simplest case of an M/M/1 queue (Poisson arrivals and a single Poisson server) then it is given by the mean arrival rate over the mean service rate, that is,

$\backslash rho=\backslash frac\{\backslash lambda\}\{\backslash mu\}$

where $\backslash lambda$ is the mean arrival rate and $\backslash mu$ is the mean service rate.

Stochastic processes