# Queueing model - Public Transportation PhD thesis

1. Feb 23, 2011

### Mark J.

Queueing model -- Public Transportation PhD thesis

Just started to work on my PhD.
Thesis is on public transport modeling basing on passenger waiting time on bus station for bus routes inside the city.Actually I found plenty of materials on queueing theory but specifically on this problem seems that I cannot find anything to read.Somebody can help?

Regards

2. Feb 23, 2011

### chiro

Re: Queueing Theory

Hey Mark J and welcome to the forums.

You will need to be a little more specific with what you want and what you are having trouble with.

What kind of background in math do you have? What problem specifically are you having? Do you have information on the assumptions you are making for your model? Do you understand the mathematical preliminaries of queuing theory?

3. Feb 23, 2011

### Mark J.

Re: Queueing Theory

Thx Chiro,
I have a master on system engineering so I presume I have a good math background.Specifically I am having a problem of not finding any material from people who have researched similar problem on public transport.So I am a little disappointed on having enough data for the assumptions I have to make on my model.The professor in charge for surveying my work is always busy and I cannot count very much on help so I presume I have to create all the model by myself.I need some help pls.

4. Feb 23, 2011

### chiro

Re: Queueing Theory

I think the first thing to do is to outline the states of your system. If you have a discrete system you will want to build a markov chain out of the conditional probabilities. Then you can evolve the chain for any time-step to see how it evolves over time.

You can then use the chain to state conditional distributions and using those you can find statistics like mean, variance etc.

I am not really sure about the states in your system (or even what the system is!) so I can't really give a specific answer.

One book that you should probably get is called "Introduction to Probability Models" 9th Edition by Sheldon M. Ross. It describes markov chains and processes, and has an entire chapter dedicated to queuing theory. If you are good at picking up math, you will probably find what you're looking for faster than I can help you. Since you're doing a PhD, I'm betting that the library should have a copy (even if it isn't the latest edition).

5. Mar 13, 2011

### Mark J.

People arriving at the bus station

Hi.
I want to create a math model of people arriving at bus stations on a single route.The idea is to study the whole process in order to make some suggestions about minimizing waiting time at the bus station.I am not very well understanding the problem so please can you suggest some literature about this specific problem?
I have seen some books on queueing theory bu I need some more specific topics on these problem in order to get acquainted with the problem ASAP.

6. Mar 14, 2011

### HallsofIvy

7. May 15, 2011

### Mark J.

Modeling

Where can I find a tutorial/literature explaining step by step modeling of Poisson processes?
I find rather confusing all this math literature explaining modeling without some real life cases.

8. May 15, 2011

### mathman

Re: Modeling

A simple example is radioactive decay.

9. Jun 11, 2011

### Mark J.

Modeling of stochastic processes

Hi
Maybe my question is a little bit general but I really need some source of reading for queuing process modeling.
I am working on a thesis about modeling of bus arrival process but actually I am not quite acquainted with modeling process(the steps that I should follow for making it real)
I really need some step by step tutorial on modeling stochastic processes no matter which process it is.The problem is that I am really not very oriented about way I should follow on making this modeling.

Best regards and sorry if my question sounds strange maybe :)

10. Jun 11, 2011

### chiro

Re: Modeling of stochastic processes

Hello MarkJ and welcome to the forums.

A good book that I've used is Introductory To Probability Models by Sheldon M. Ross. I'm not sure what edition it's up to, but I've got the tenth edition which was published in 2010.

From the sounds of it, you need to first set up a rate diagram and then use some probability results to calculate what you need to calculate (like a probability distribution, expected waiting time and so on). The book goes into these kinds of things in some detail.

If you need more examples of "worked out problems" I can recommend Shaums Outline of Probability, Random Variables, & Random Processes. Chapter 9 of that book is dedicated to Queuing Theory and has a lot of worked out problems.

In terms of orientation, the queuing models typically use the in/out model of a queue. You use poisson processes to model probability of so many "events" happening (think number of customers entering a queue, number of passengers waiting for bus and so on).

You then construct a rate diagram, and use that to calculate what you need to calculate.

For your situation, I would study the generic queuing models and then simplify from there. It will help you since most real world problems do not simplify, and I'm guessing yours is no exception. If it does simplify, then just use the constraints to get simplified answers.

11. Jun 13, 2011

### ych22

Re: Modeling of stochastic processes

The key question is, what type of mathematical model are you looking to build?

If your bus arrival process is simple and clean, maybe you can look at building a Markov model and solve it analytically. (Sheldon Ross, etc.)

Chances are, though, that the actual process is too complicated to be modelled analytically. A common solution is to build a discrete-event simulation model based on the assumptions of the bus arrival process. You can do so with simulation packages such as Arena, Simul8 or AutoMod; or even write programs out of C++. Then you are better off with a book on discrete event simulation, which will give you the basics on markov models anyway.

12. Jun 14, 2011

### Stephen Tashi

Re: Modeling of stochastic processes

Mark J,

To me, "modeling" and "simulation" have different connotations. So when you say you are interested in "modeling" a real world problem, I think in terms of creating symbolic equations. In contrast, if you are interested in "simulating" a real world problem, I think in terms of writing a computer program that represents the situation you wish to analyze.

Even if you are not interested in "simulating" the problem, I suggest that you at least try to imagine how you would write a simulation of it because that would give you a hint at how to "model" it.

13. Aug 12, 2011

### Mark J.

Data collection

Hi All
Working on my "Transport Planning Model" research I am on the phase of data collecting.
I am working on a single bus route with about 22 bus stops.
It is very difficult to collect data about bus arrivals and people arrivals at the bus stop(to check later which distribution they fit) for a long period.
I even don't know how much data is needed for this research.
Regards

14. Aug 12, 2011

### Stephen Tashi

Re: Data collection

Suppose you have a probability model for a process and it requires specifying certain parameters. You can simulate the process and also simulate your data collection. From the simulated data collection you can see how well you are able to reconstruct the parameters that you used. You can also simulate the process using two different probability models and see how well you can use simulated data collection to discriminate between the two models. If you data collection method can make errors you may also be able to simulate that.

For very simple cases you can use the theory of "confidence intervals" to tell you how much data to collect (although the term "confidence interval" is an over-selling of what such intervals really are).

If you are going to fit a multivariate polynomial equation to your data, collecting data for that purpose is covered by a theory called "the design of experiments" ( which is another example of misleading terminology since it doesn't study the full generality of the things that normal people call experiments).

15. Aug 12, 2011

### Mark J.

Re: Data collection

Thank you for the fast answer.
Anyway I am not very clear on the steps I should undertake.
Can you please kindly recommend me any reading describing similar simulation process step by step.
On the net I really didn't find anything suitable .
Regards

16. Aug 17, 2011

### Mark J.

Combining 2 processes...

Hi...
Talking about passengers arrival at the bus stop and buses arrival at the bus stop how can I combine these processes together to think about people waiting time for the bus?
Any topic to be studied or literature advised?

Regards

17. Aug 17, 2011

### SteveL27

Re: Combining 2 processes...

Queueing theory. A word with five consecutive vowels, if you're looking to win a bar bet.

http://en.wikipedia.org/wiki/Queueing_theory

18. Aug 18, 2011

### Mark J.

Queueing model

Hi
Which in your opinion is the queueing model that better fits to public bus transport if we suppose that passenger numbers arriving to station is infinite?I tried to find something like