Recommend a queueing theory/network resource?

[llstelle]

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!

 

[llstelle]

My description above is really bad. I meant, I am interested in a queueing network text (first priority).

But the exact problem I am working on is a open network of queues in series, with some fixed number of nodes, and the arrival rates of various classes of "customers" are decision variables. And I might be maximizing a utility curve that is a nondecreasing function of the sum of arrival rates.

 

[chiro]

Hey llstelle and welcome to the forums.

One book that I have personal experience with and can recommend is a book Written by Sheldon Ross. This will help you get a good foundation for queueing problems/network theory.

https://www.amazon.com/gp/product/0123756863/?tag=pfamazon01-20

Since you mention utility theory it seems like to get more specific information for your problem (which I am unfamiliar with) would come from sources like Operations Research texts and journals or economic journals.

If you already have a utility function (which seems to be what you are saying), then I think you can just use the queueing/network theory fundamentals and apply the utility function using first principles for probability and statistics. Standard optimization techniques in combination with this should do the trick.

Usually the way we model queues and similar processes is to use a markov model of some sort. Sheldons book I think would be of great use to you.

There are probably many other free resources that would offer you what you need but unfortunately I am unaware of them.

 

[Teresa_Hubsch]

You might want to check out Queuing Theory with MATLAB and SimEvents (http://www.mathworks.com/discovery/queuing-theory.html). SimEvents is a discrete event simulation software tool used with MATLAB and Simulink for hybrid simulation. I know you were asking for books and not software, but I think it might be helpful to do simulation for modeling.

 

[blue_raver22]

I would recommend exploring the field of stochastic modeling and queuing theory for your research on resource allocation and queueing systems. This field involves the study of mathematical models to analyze and optimize the performance of systems with limited resources and stochastic arrivals. Some specific areas to explore within this field include Markov chains, birth-death processes, and queuing networks.

In terms of specific resources, I would suggest looking into the textbook "Stochastic Modeling: Analysis and Simulation" by Barry L. Nelson, which covers a wide range of topics in stochastic modeling, including queuing theory. Another helpful resource is the book "Queueing Systems: Theory and Applications" by Leonard Kleinrock, which provides a comprehensive overview of queuing theory and its applications.

Additionally, you may want to consider reaching out to experts in the field or attending conferences and workshops focused on stochastic modeling and queuing theory. These opportunities can provide valuable insights and connections to further literature and resources.

Overall, the field of stochastic modeling and queuing theory has a vast amount of literature and resources available, and with some research and exploration, I am confident you will find the information and tools you need to tackle your specific problems effectively.