« View all new features in
Mathematica
9
◄
previous

next
►
New in
Mathematica
9
›
Markov Chains and Queues
Simulate Different Types of Queues
Simulate an M/M/1 queue in which customers arrive at the rate of three per hour and are served at the rate of five per hour.
In[1]:=
X
data = RandomFunction[QueueingProcess[3, 5], {0, 20}]
Out[1]=
Since the arrival rate is less than the service rate, the system reaches a steady state.
In[2]:=
X
ListLinePlot[data, InterpolationOrder > 0, Filling > Axis]
Out[2]=
If the arrival rate is greater than the service rate, then the system does not reach a steady state.
In[3]:=
X
data = RandomFunction[QueueingProcess[5, 3], {0, 150}];
In[4]:=
X
ListLinePlot[data, Filling > Axis]
Out[4]=
Simulate a queueing system that can hold only 12 customers.
In[5]:=
X
data = RandomFunction[QueueingProcess[6, 6.1, 1, 12], {0, 150}];
In[6]:=
X
ListLinePlot[data, Filling > Axis]
Out[6]=
Simulate a queue with 20 customers in the initial state.
In[7]:=
X
data = RandomFunction[ QueueingProcess[2, 3, 1, \[Infinity], 20], {0, 80}];
In[8]:=
X
ListLinePlot[data, InterpolationOrder > 0, Filling > Axis, PlotRange > All]
Out[8]=