Since all queues are characterised by arrival, service and queue and its discipline, the queue system is usually described in shorten form by using these characteristics. The general notation is:

[A/B/s]:{d/e/f}

Where,

$\text{ A = Probability distribution of the arrivals} $

B = Probability distribution of the departures

s = Number of servers (channels)

d = Queue ranking rule (Ordering of the queue) or service discipline

e = The capacity of the queue(s)

f = The size of the calling population

There are some special notation that has been developed for various probability distributions describing the arrivals and departures. Some examples are:

$\text{ M = Arrival or departure distribution that is a Poisson (Markovian) process} $

E = Erlang distribution

G = General distribution

GI = General independent distribution

D = Deterministic distribution

Some examples for service disciplines are:

$\text{ FCFS = first come, first served} $

LCFS = last come, first served

SIRO = service in random order

GD = general service discipline

1. Probabilistic queuing models:

   a. (M/M/1):(FCFS/∞/∞) represents Poisson (Markovian) arrival and departure, single server, first come first served service discipline, and infinite queue length and population.

   b. (M/M/1):(SIRO/∞/∞) is the same as the previous, except that the service is in random order.

   c. (M/M/1):(FCFS/N/∞) represents a model in which the capacity of the queue is finite, i.e. N.

   d. (M/M/c):(FCFS/∞/∞) is the same as the first model, except that here there are ‘c’ servers working simultaneously.

   e. (M/M/1):(GD/m/n) represents a machine repair queue, with a single repairman, where ‘n’ is the machines present out of which ‘m’ machines are broken down and are in queue to be repaired. GD represents general service discipline.

   f. (M/M/c):(GD/m/n) is similar to the above model, except that here ‘c’ repairmen are available.

2. Deterministic model:

   a. (D/D/1):(FCFS/∞/∞) is a model in which interarrival time as well as service time are fixed and are known with certainty.

3. Mixed queuing model:

   a. (M/D/1):(FCFS/∞/∞) represents a model in which arrival rate is Poisson distributed while service rate is deterministic or constant.