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June 12th, 2013, 09:58 AM   #1
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Analysis of a series of non-Markovian queues

Dear all,

I'm from the netherlands and a business student at a university.
In a business case I have to simulate a certain assembling department, and validate the simulation afterwards using queuing theory. I'm interested in finding the mean throughpout time given a certain size of a collection tray (this is the decision variable).
The department consists of machines I, II, III and IV and a collection tray placed prior to machine IV. I added a schematic display of this department. Machines II and III are identical parallel machines.
A product would arrive at machine I, is then disassembled into the parts a and b. Part a gets processed on machine II and part b at machine III. They are then placed in the collection tray after which they are assembled again on machine IV as soon as possible. Machines II and III always start processing at the exact same time. There's no queue prior to machines II and III.
Now, normally this wouldn't be much of hassle, given that the arrival processes are Poisson processes and the service times of each machine is exponentially distributed.

In this case, however, the arrival process at the first machine is the only Poisson process. Each of the machines service times are uniformly distributed (see the attachment).
Machine 1 could be seen as a M/G/1 queue, but I have no idea how to model machines II, III and IV. Can anyone point me into the right direction (some literature for example)?

Thanks in advance, I highly appreciate any kind of help,

Riccardo.
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