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.