# Wolfram Language & System 11.0 (2016)|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.

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

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 x0.

## 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. x0 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:

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

 In[1]:=

Queue properties:

 In[2]:=
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