in the long term we are all phds

Decision Problem Chapter Progress

2010-06-16T01:31:00.001-07:00

10:30 - 16-06-10 31
10:30 - 17-06-10 33
12:21 - 20-06-10 33
10:29 - 21-06-10 34

Nested beliefs, sharing private information

2010-06-08T09:46:00.001-07:00

Read aumann.

2010-06-04T15:30:00.001-07:00

http://motion.comp.nus.edu.sg/software/appl/appl.html

solve POMDP again with this fixed point algorithm.

decision theory from the economy point of view

2010-06-01T08:11:00.000-07:00

http://afinetheorem.wordpress.com/category/decision-theory/

read!

articles to find in the library

2010-03-09T11:50:00.000-08:00

1 - Explicit formulas for the variance of conditioned sojourn times in M/D/1-PS

Operations Research Letters
Volume 35, Issue 4, July 2007, Pages 463-466

2 - Processor sharing: A survey of the mathematical theory

Automation and Remote Control
Volume 68 , Issue 9 (September 2007)

proof idea markovian property of aggregated states

2010-02-25T05:34:00.000-08:00

show that the transition between states correspond to transitions in the original bcmp. if aggregated were non-markovian, so would be the bcmp. this is a contradiction. so aggregate states are markovian. qed.

Plan for 2010

2010-01-06T05:50:00.000-08:00

January

Multi-class extension
Formulation & Solution of the optimization problem
Formulation of Strategical Analysis
Formulation Manipulation Analysis
Find the right decision tool

February

Braess Paradox
Solution Strategic Analysis
Solution Manipulation Analysis
Mapping PS to technologies
Include Sebastian's Work

March

Include theoretical sections.
Wrap-Up Simulation
Wrap-Up State of the art
1. Draft Ready

April

Include comments

May

Publish and wait.

Queueing Networks Tag Search

2009-12-04T02:10:00.000-08:00

1 - Queueing Networks @ IEEE. Done.
2 - Queueing Networks + Communication(s) @ IEEE. Done.
3 - Queueing Networks + Telecommunication(s) @ IEEE.
4 - Queueing Networks + Wireless @ IEEE. Done.
5 - Queueing Networks + Cellular @ IEEE.
6 - Queueing Networks + Data @ IEEE.
7 - Queueing Networks + Inegrated Systems @ IEEE.
8 - Papers that reference BCMP

Ergodicity of Markov chains

2009-12-03T07:37:00.000-08:00

1- A Markov chain is called an ergodic chain if it is possible to go from every state to every state (not necessarily in one move).

2- A Markov chain is called a regular chain if some power of the transition matrix has only positive elements.

3- Any transition matrix that has no zeros determines a regular Markov chain.

4- However, it is possible for a regular Markov chain to have a transition matrix that has zeros.

For an ergodic Markov chain P, there is a unique probability vector w such that wP = w and w is strictly positive

source:
http://www.math.dartmouth.edu/archive/m20x06/public_html/Lecture15.pdf

state of the art - 4G

2009-11-23T02:50:00.001-08:00

th3r3 is a ind3x3d se3arch option in i333 3xplor3r.

(4g mobile communicationde)

To do

2009-11-19T09:26:00.000-08:00

Request these books:

1- Chang, Cheng-Shang: Performance guarantees in communication networks / Cheng-Shang Chang
2- Chen, Hong: Fundamentals of queueing networks : performance, asymptotics, and optimization
3- Disney, Ralph L.: Traffic Processes in queueing networks : a Markov renewal approach / Ralph L. Disney and Peter C. Kiessler. - Baltimore [
4- Gelenbe, Erol: Introduction aux réseaux de files d'attente Introduction to queueing networks /
5- Hogarth, John: Optimization and analysis of queueing networks

Status

2009-11-18T10:00:00.000-08:00

Basic model is complete. Reading
1- Towsley: State Dependent Routing for closed form networks.
2- Krezinski: State Dependent Routing for open form networks.
3- Akyildiz: Blocking solutions for product form networks.

tik tak tik tak tik tak

2009-10-06T09:20:00.000-07:00

officially started writing the official thesis. 5 months to go.

Plan

2009-09-22T04:44:00.000-07:00

Handover Calls Not Poisson

2009-09-16T07:27:00.000-07:00

There is strong evidence that handoff traffic is not Poisson. Boltch p.787.

What implication does this have to the model of Tonguz and Yanmaz. Queueing networks can take this into account.

To Do's

2009-09-16T07:25:00.000-07:00

1- Understand PS.
2- Implement PS.
3- Modify PS.

PS PS PS.
4- Akyildiz papers on exact solution for blocking systems.
5- State dependent routing papers.

Queueing Model

2009-09-08T06:03:00.000-07:00

Tough schedule ahead:

08-13 finish up the Queueing reading.
14-21 formulate the model.
22-27 write and simulate.
28-30 wrap-up.

Mechanism Design for SLA

2009-07-16T08:26:00.000-07:00

Mechanism design: The design of an interaction, in which being truthful is the dominant strategy.

The output of the Queueing Model should be in the form of (required bandwidth, probability) and (available bandwidth, probability), which translates to the SLA. Now the question is, what are the values that needs to be truthful?

Next steps, read Manzoor's paper. MAnzoor makes a short state of the art.

PASTA Theorem

2009-06-12T08:46:00.000-07:00

Poisson Arrivals See Time Average (PASTA)

* Valid for M/*/*
* The the probability that an arriving user sees the system in state i, is equivalent to the average time spent in that state

Review of Telatar "Combining Queueing Theory with Information Theory for Multiaccess"

2009-06-08T08:38:00.000-07:00

Paper.

To Do:

* Summarize.
* Check the citing papers. They are of multiple.

Summary of De Veciana and Zemilanov's Work

2009-06-08T06:01:00.000-07:00

Papers
1- Main conference paper.
2- Book Chapter describing the derivations.

Scenario:

* A WAN operator who aims to give universal coverage.
* A WLAN operator who aims to give local high performance coverage.
* Users deciding independently.

Modeling:

* Stochastic geometry is used to model both the position of WAN an WLAN AP's, and users.
* The users make greedy decisions maximizing a given utility function.
* Utility functions are either proximity based or capacity based.
* Proximity based changes with the distance.
* Capacity takes into account the delay of an file download assuming Processor Sharing discipline is used at the base station. The delay is modeled as the delay of a M/G/1-Processor Sharing queue. The more number of users, larger the delay.

Results

* The utility function that include both proximity and capacity reaches a global equilibrium.
* The performance metrics are the average delay over the entire user population, and average worst case delay averaged on different WAN service zones. The congestion sensitive mechanisms give %300-%600 increase over the proximity only metrics.
* Furthermore, the congestion sensitive utility functions reduce the spatial load fluctuations, and are able to reduce the back-haul bandwidth required for the WLAN's this is the largest expenditure for these type of access networks.

Notes

* The congestion sensitive utility function, based on the M/G/1/PS is taken from Sem Borst's paper. Borst in turn takes this from Telatars 1995 paper.

03-04-09 Meeting Minutes

2009-04-03T09:39:00.000-07:00

The key to closed form expressions is the property that the state transitions occur between neighbor states only. This is why choosing the state variables correctly matters.

Till Wednesdey Nadim will do state of the art in network sharing, and I will review the books.

03-04-09

2009-04-02T16:52:00.000-07:00

Finished reviewing ans summarizing Soft Load balancing. It is a tight coupled solution, that is not applicable for multiple operators. What is relevant are the load monitoring 3gpp standards and two references. Check em by tomorrow.

23-02-09

2009-02-24T01:58:00.000-08:00

To do:
solve direct load balancing formula for C=1, B=1.
Finish the slides.

new years resolution 1.5 months late

2009-02-17T04:57:00.000-08:00

write here every day. even if you did not find time for phd.

status:

summarize Tonguz and Yanmaz paper until thursday.
have a look at bgp.

-10.5 months!

A new performance criterion? Service deviation?

2009-01-06T07:25:00.000-08:00

I came across a performance metric the early designers of the cellular systems employed. In their 1978 paper where they define the hybrid channel sharing algorithm, the authors Kahwa and Georganas, make use of the concept of Service Deviation defined in an early paper in 1973.

Defined as the standard deviation of call blocking probabilities of different cells, they took it as a performance metric, and wanted to make it as small as possible.

What is the relevance of this for an operator in data calls? Or across heterogeneous networks? Would it force network operators to cooperate? I will have to think about this.

Possible Mathematical Models

2009-01-06T07:11:00.000-08:00

I found three interesting papers.

Tonguz and Yanmaz -2008- A mathematical Theory of Dynamic Load Balancing in Cellular Networks.
Alanyali and Hajek - 1996 - On Load Balancing in Erlang Networks.
Bühler and Wunder - 2007 - Optimal Dynamic Admission Control in Heterogeneous Networks.

The first one derives closed form expression for the blocking probability of various load sharing algorithms for cellular networks. The authors themselves mention that this can be a basis for load sharing among heterogeneous networks. Closed form solutions are necessary for dynamically adjusting the system parameters. This seems the most relevant, and I've started reading it.

-360 days. 12 Months.

Waiting time - Channel Holding time?

2008-12-19T09:56:00.000-08:00

- In the queue model, can we say the waiting time models the channel holding time? or perhaps the sojourn time?

Meeting with Prof. Yener and Dr. Sivrikaya

2008-12-19T09:54:00.000-08:00

-check BGP. It involves similar policy based sharing of resources.
-Think about the queue model. Start with easiest first.
-3 party game: User-Operator-Operator.

Plan for 15-21 December

2008-12-15T02:18:00.000-08:00

- Finish up Chapter 5 and 6 in rules of encounter.
- Summarize dynamic flow assignment alpcan et al.
- State of the art on geographical stochastic modelling
- Find good intro to queing theory as applied to communication systems.

365. 12.