Kendall's notation

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In queueing theory, Kendall's notation (or sometimes Kendall notation) is the standard system used to describe and classify the queueing model that a queueing system corresponds to. First suggested by D. G. Kendall in 1953 as a 3 factor A/B/C notation system for chacterising queues, it has since been extended to include up to 6 different factors.

The notation now appears in most standard reference work about queueing theory. e.g. ^[1]

[edit] Notation

1/2/3/(4/5/6) where the numbers are replaced with:

A code describing the arrival process. The codes used are:
- M stands for "Markovian", implying exponential distribution for service times or inter-arrival times. Such a distribution is characteristic of a Poisson (or random) arrival or service process.
- M^[X] stands for "Markovian" with bulk input where X is a random variable describing the number of customers in the arriving group.
- D stands for "degenerate" distribution, or "deterministic" service times.
- Ek stands for an Erlang distribution with k as the shape parameter.
- G stands for a "General distribution". (Note that although G usually refers to independent arrivals, some authors prefer to use GI to be explicit)
- PH stands for Phase-Type Distribution. (Note that few of the above distributions are considered as Phase-type distributions)
A similar code representing the service process. The same symbols are used.
The Number of service channels (or servers).
The capacity of the system, or the maximum number of customers allowed in the system including those in service. When the number is at this maximum, further arrivals are turned away. If this number is omitted, the capacity is assumed to be unlimited, or infinite.
The size of calling source. The size of the population from which the customers come. A small population will significantly affect the effective arrival rate, because, as more jobs queue up, there are fewer left available to arrive into the system. If this number is omitted, the population is assumed to be unlimited, or infinite.
The Service Discipline or Priority order that jobs in the queue, or waiting line, are served:
- First Come First Served (FCFS) or First In First Out (FIFO),
- Last Come First Served (LCFS) or Last in First Out (LIFO),
- Service In Random Order (SIRO),
- some other service regime, including
- Priority service, including preemptive and non-preemptive (PNPN), or
- Processor Sharing.

Note: An alternative notation practice is to record the queue discipline before the population and system capacity, with or without enclosing parenthesis. This does not normally cause confusion because the notation is different.