BUILT-IN MATHEMATICA SYMBOL

# QueueingProcess

represents an M/M/1 queue with arrival rate and service rate .

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

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

represents a G/G/1 queue with arrival distribution adist and service distribution sdist.

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

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

QueueingProcess[..., ..., c, k, x0]
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 indicating .
• The times taken to serve customers are independent and follow the distribution sdist, with 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:

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

Queue properties:

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