# 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.

# Details

• 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.

# Examples

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## Basic Examples(2)

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

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 In[2]:=
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Define an M/M/1 queue with arrival rate λ and service rate μ:

 In[1]:=

Queue properties:

 In[2]:=
 Out[2]=