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llstelle
#1
Feb11-12, 08:19 PM
P: 20
I've been looking up reviews of queueing theory textbooks and seeing their tables of contents on Amazon, but I haven't found a satisfactory one.

In particular, I'm trying to tackle a class of problems where there is a bunch of resources (for example, memory in a computer or empty seats in a train), we assume that the resources are in a "linear sequence" (incoming people on the train have to pass by the first row of seats, then the second row, and so on...) and a way with dealing with queueing the "users" of these resources (for example, computations that require memory or commuters who are boarding the train).

I get to control the way/arrival rate at which these users "enter" the queueing system, and the resources are separated in discrete uniform distribution - if a memory block is already allocated to a computation, the incoming computation cannot use that memory block and travels to the next (takes a constant time) - or even better, I send the first computation ahead in the sequence of memory blocks and then have the subsequent computations occupy "preceding" memory blocks, so they never actually have to "meet".

And what I really want to do is figure out given limited resources, what is the maximum number of computations/users I can accommodate.

I am guessing this is a network of G?/D?/1 queues or something... I don't know; I've never done queueing theory before, so I'll like to know where I can know more about problems like this. I noticed that most queueing theory texts cover Markov processes first (with Poisson arrival rates), i.e. M/M/s, but here I can actually decide the calling population and control their arrival rates to eliminate waiting time altogether, and there isn't much literature on G/D distributions...

OK, basically... can someone point me in the right direction for more literature? Thanks!
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