7.3 Queuing Notation

Recognizing the diversity of queuing systems, a notational system was introduced in the 50’s which has been widely adopted. The convention is based on the format $A/B/c/N/K$, where the letters represent the following system characteristics:

• $A$ represents the inter-arrival time distribution

• $B$ represents the service-time distribution

• $c$ represents the number of parallel servers

• $N$ represents the system capacity

• $K$ represents the size of the calling population

Common symbols for $A$ and $B$ are include $M$ (exponential or Markov), $D$ (constant or deterministic) and $G$ (arbitrary or general).

For example, $M/M/1/\infty/\infty$ indicates a single-server system that has unlimited queue capacity and infinite population of potential arrivals. The inter-arrival times and service times are exponentially distributed. When $N$ and $K$ are infinity, they may be dropped from the notation. For example $M/M/1/\infty/\infty$ is often shorted to $M/M/1$.

All systems will be assumed to have a FIFO queue discipline.