## Queueing Notation

The statistical model that has notation in three parts.

The first part denotes the process of arrivals at the start of a queue. Usually the process of arrival of customers is radom or 'Markovian' and denoted 'M'.

The second part denotes the process by which elements of the queue exit the queue. If elements of the queue exit in a predetermined manner, this is labelled 'D' and if elements exit the queue according to a uniform distribution this is labelled 'U'. Other models of exit are possible.

The third part denodes the number of exit route. These are all identical and act to release members of the queue. Each exit takes some time to process.

The overall process models a queue in a bank or similar. There is a single queue, which people may join according to various models and leave to be served at any one of a numnber of tellers.

Suppose elements arrive at the queue in a random manner. This is labelled 'M' for 'Markovian'. If after leaving the queue elements are served in a fixed time T, then this is labelled 'D'. If elements leave the queue to be served by any one of five tellers the the queue is modelled by the model M/D/5.

Suppose elements arrive at the queue in a random manner. This is labelled 'M' for 'Markovian'. If after leaving the model of the time taken to serve a customer is a Uniform distribution between 10 and 20 minutes then this is labelled 'U'. If elements leave the queue to be served by any one of two tellers the the queue is modelled by the model M/U/2.

If the leaving and exiting queue processes are both random and there is only one teller then the queue model is M/M/1. This is called the simple queue.