The M/M/1 Queue Model

Key Equations

Arrival and service are random, following Poisson and exponential distributions:

$$ f(r) = \mu e^{-\mu r} $$

Utilization ratio: $$ \rho = \frac{\lambda}{\mu} $$

Symbol Meaning
$$ L_q $$ Average packets waiting: $$ L_q = \frac{\rho^2}{1-\rho} $$
$$ W_q $$ Average waiting time: $$ W_q = \frac{\rho}{\mu(1-\rho)} $$
$$ W $$ Total delay: $$ W = \frac{1}{\mu - \lambda} $$