## 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.