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Queuing functions syntax

Dear Friends:
I am aware that Mathematica 9 has a new functionality for queues. However, I am not 100% sure how to use it.

Suppose I have a queue, say with 3000 clients, at the moment I start the service. Say lambda (arrival rate) is 0.1, and mu (departure rate) is 0.8 per time unit.
The queue discipline is first arrived first served. and it has one service channel. Imagine the simplest possible model (M/M/1).
I want to calculate the conventional things: 

a. Waiting time for clients

b. Stationary properties

c. Time needed to serve N  number of clients

My main doubt refers where to put in the queuing functions the key datum that I start with a backlog of 3000 clients. Anybody can help me?
Francisco
To get you started, the function for simulating M/M/1 queues in Mathematica is QueueingProcess. There are a number of examples in that documentation which might be helpful.

You defined the process as you described with the following code:
myProcess=QueueingProcess[0.1, 0.8, 1, Infinity, 3000]

There are many things you do with myProcess. The first is to ask about its properties:
QueueProperties[myProcess]
This will give you some steady state properties such as:
"MeanSystemSize"  - mean number of jobs in the system
"MeanSystemTime"  - mean time spent in the system
"MeanQueueSize"  - mean number of jobs in the queue
"MeanQueueTime"  - mean time spent in the queue

You can simulate it:
data = RandomFunction[myProcess, {0, 100}]
ListLinePlot[data, InterpolationOrder -> 0, Filling -> Axis]
POSTED BY: Sean Clarke
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