# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# QueueingProcess

QueueingProcess[λ,μ]
represents an M/M/1 queue with arrival rate λ and service rate μ.

QueueingProcess[λ,sdist]
represents an M/G/1 queue with arrival rate λ and service distribution sdist.

QueueingProcess[adist,μ]
represents a G/M/1 queue with arrival distribution adist and service rate μ.

QueueingProcess[adist,sdist]
represents a G/G/1 queue with arrival distribution adist and service distribution sdist.

QueueingProcess[,,c]
represents a queueing process with c service channels.

QueueingProcess[,,c,k]
represents a queueing process with system capacity k.

QueueingProcess[,,c,k,x0]
represents a queueing process with initial state .

## DetailsDetails

• QueueingProcess is a continuous-time and discrete-state process.
• QueueingProcess at time t is the number of customers in the system at time t.
• The times between arrivals are independent and follow the distribution adist, with λ indicating .
• The times taken to serve customers are independent and follow the distribution sdist, with μ indicating .
• QueueingProcess allows c and k to be any positive integers. can be any non-negative integer and the distributions adist and sdist can be any continuous distributions with positive domain.
• QueueingProcess can be used with such functions as QueueProperties, StationaryDistribution, and RandomFunction.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Simulate an M/M/1 queue where the state is the number of jobs in the system:

 Out[1]=
 Out[2]=

Define an M/M/1 queue with arrival rate λ and service rate μ:

Queue properties:

 Out[2]=

## See AlsoSee Also

Introduced in 2012
(9.0)