What do the letters and number in $M/M/1$ stand for?

The key formulas are: Average Queue Length $L = \frac{\lambda}{\mu - \lambda}$, Average Waiting Time $W = \frac{1}{\mu - \lambda}$, and Utilization $\rho = \frac{\lambda}{\mu}$.

Conditions: The model is $M/M/1$.; $\lambda$ is the arrival rate.; $\mu$ is the service rate.; $\lambda < \mu$ for stability.

Queuing theory is the mathematical study of waiting lines, used to analyze and optimize the performance of service systems.

Conditions: The context is operations research.; The system involves arrivals, waiting, and service.

For an $M/M/1$ queue to be stable, the utilization factor $\rho$ must be strictly less than 1. This means the arrival rate $\lambda$ must be less than the service rate $\mu$.

Conditions: The model is $M/M/1$.; $\rho = \lambda / \mu$.