Accenture,Recruiting day: Accenture, Recruiting day
Robin Groenevelt
26 April 2005
Agenda:
Who am I?
Studies
Work experience
Lessons learned
Agenda
Present
Future Past
PAST – Who am I?: PAST – Who am I? Short biography:
- Dutch nationality
- Born in Denmark
Phase 1: Traveling.
Lived in and went to international schools in
- Denmark (6 years)
- South Korea (2.5 years)
- The Netherlands (2 years)
- Saudi Arabia (4 years)
PAST – Who am I?: PAST – Who am I? Phase 2: Schooling, studies, and work.
Completed high school and university in the Netherlands
Traineeship in a bank in South Africa
Three years of work experience in the Rabobank
PhD in computer science, Sophia-Antipolis
Lecturing / research position at the UNSA
PAST - Studies: PAST - Studies Master of Science in:
Business Mathematics & Computer Science
Mathematics
PAST - Studies: PAST - Studies Master of Science in:
Business Mathematics & Computer Science Idea: Take a (complex) problem from industry and solve it with the help of mathematics, computers, and a high level of thinking
PAST - Studies: PAST - Studies Master of Science in:
Business Mathematics & Computer Science
Examples:
Financial decisions
Optimization (cost/profit, resources)
Scheduling
Extraction of knowledge
System development
Define performance measures
Performance analysis
PAST - Studies: PAST - Studies Master of Science in:
Business Mathematics & Computer Science Subjects:
- statistical data analysis - software engineering
- statistical models - information systems
- simulation techniques - neural networks
- stochastic methods - Finance
- mathematical system theory - Logistics
- Mathematical programming - C++
PAST - Studies: PAST - Studies Master of Science in:
Business Mathematics & Computer Science
Mathematics Why?
Time and finance available
Annoyed me that I did not master theory enough
Wanted to show that I could do more
Constraint: keep evenings and weekends “free” for other activities (even when I started working)
PAST - Work experience: PAST - Work experience Traineeship:
Department of credit risk
ABSA Bank, South Africa
Consultant:
Center for applied mathematics
Rabobank corporation, the Netherlands
PAST - Rabobank experience: PAST - Rabobank experience Finance
Credit risk in compliance with Basel II
Scorecard development
Project manager for management tool at 400 banks
Researched investment index for the average price of properties. Collaborated with insurance companies, persion funds, and investors
Robeco Investment funds
Segmentation research of stock market investors
Rabo International
Profile analysis of warrant clients
PAST - Rabobank experience: PAST - Rabobank experience Call center
Modeling of inbound traffic, optimal scheduling of agents, improved service level
Interpolis insurances
Developed an early warning system for (car) insurance claims
Groenmanagement
Asset/Liability Management analysis for tax related loans and mortgage bonds
PAST - Lessons learned: PAST - Lessons learned Combination of mathematics, economy, and computer science highly in demand
In businesses many different skills have to be acquired
Different types of personalities required at different stages of a project’s / company’s life
High level of conceptual thinking is often more important than what you know
PAST - Lessons learned: PAST - Lessons learned Helicopter view (in particular, the WHY?)
Discuss with people (to “create” work/get ideas)
Often need to act as a bridge between technical people and the customers
Business problems can be challenging and very difficult to solve
Agenda: Past
Future Agenda
Present
Research subject
Thesis contents
Some examples and results
Publications
Lessons learned
Present – Research subject: Present – Research subject PhD in computer science
Project theme:
Models for performance analysis and the
control of networks
Thesis title:
Stochastic models for mobile ad hoc networks
Present – Thesis contents: Present – Thesis contents Thesis is composed of three parts:
1. Message delay in mobile ad hoc networks
2. Polling systems with correlated switchover times
A. The value function of a tandem queue
Idea behind part 1:
Study the effect of mobility on the performance of ad hoc networks.
What is an ad hoc network?: What is an ad hoc network? Sensor network with autonomous radio devices
- Nodes have a radio transmission range
- Routing capabilities
Ad hoc network
- network with no fixed infrastructure
Mobile ad hoc network
- ad hoc network with mobile nodes
Ad hoc networks: Ad hoc networks Examples:
- Emergency situations (rescue, physical disaster)
- Household electronics (connectivity anytime and anywhere)
- Tagged animals
- “Smart” vehicles
- Military applications
Technological examples:
- IEEE 802.11 ad hoc mode
- Bluetooth
Movement patterns: Movement patterns Movement patterns often unknown or have a random component:
Wind
Ocean
Animal movement
Vehicle movement
Human activity
There is a need to analyze the performance of different protocols, under a variety of settings and different mobility patterns
Study of ad hoc networks: Study of ad hoc networks Connectivity
Interference Goal:
Optimal setting of device characteristics due to finite battery power and interferences.
Device characteristics:
Radio transmission range
Relay protocol
Memory
Computing capabilities
Performance measures of mobile ad hoc networks:
Throughput / capacity
Message delay
Example: Message delay in one dimension: Example: Message delay in one dimension Question: What is the message delay for two nodes moving independently in one dimension?
Example: Message delay in one dimension: Example: Message delay in one dimension Question: What is the message delay for two nodes moving independently in one dimension? Let us start by taking two nodes: on a discrete state space:
Example: Message delay in one dimension: Example: Message delay in one dimension Nodes hop from state to state (with equal probability)
Example: Message delay in one dimension: Example: Message delay in one dimension Nodes hop from state to state (with equal probability) A node can transfer a message if it is within r states from another node
Visit time distribution = exponential or deterministic
Example: Message delay in one dimension: d a t a d a t a Example: Message delay in one dimension Nodes hop from state to state (with equal probability) A node can transfer a message if it is within r states from another node
Visit time distribution = exponential or deterministic
Assumptions: Assumptions x0 y0 L-1 0 • Take two independent random walkers starting in x0 and y0.
• Transmission range r is fixed and the same for every node.
• Transmission time is zero.
The study is on the message delay due to the mobility
Time to transmit a message small negligible to the time required for nodes to come within communication range of one another.
Message delay for 1-D random walkers: Message delay for 1-D random walkers Proposition: Let the visit times be exponentially distributed.
The expected number of hops for two independent random walkers starting in x0 and y0 to come within r states of one another is given by for x0 – r < y0. Here
Message delay for 1-D random walkers: Message delay for 1-D random walkers Proposition: Let the visit times be deterministically distributed.
The expected number of hops for two independent random walkers starting in x0 and y0 to come within r states of one another is given by for x0 – r < y0. Here
Outline of proof: Outline of proof The position of the two 1-D random walkers can be mapped to a single 2-D random walker.
Outline of proof: Outline of proof
Message delay for 1-D random walkers: Message delay for 1-D random walkers Take L=30 and r=5:
Message delay for 1-D random walkers: Message delay for 1-D random walkers Proposition: Let the random walkers start in steady-state at hop n=0. The expected number of hops is given by
in the case of exponential visit times and
in the case of deterministic visit times. Here
Message delay for 1-D random walkers: Furthermore, there is an insensitivity property towards the
underlying visit time distribution as for both exponential and
deterministic visit times we have
where Message delay for 1-D random walkers
Conclusions drawn from example: This is all very nice, but what can we conclude from this?
Conclusions drawn from example • Simple scenarios already lead to involved expressions!
• Explicit expressions can (rarely) be obtained
• Results can most likely not be extended to the general situation with more than two nodes Because of the complexity it meant that my thesis ended up being more theoretical of nature than application orientated.
What happens in two dimensions?: What happens in two dimensions? We consider three movement patterns:
1) Random waypoint 2) Random direction
3) Random walkers
Assumptions: Assumptions Nodes move according to the same mobility model.
Nodes move independently of all the other nodes.
Nodes start from steady-state.
Every node has a fixed transmission range r.
Transmission time is zero.
One source node and N other nodes in the network.
No interference
Relay protocols: Relay protocols We consider two relay protocols:
Unrestricted multicopy protocol:
nodes copy the message whenever possible.
Two-hop multicopy protocol:
the message gets copied only by the source node or to reach the destination in the second hop.
Quantities of interest: Define
T2 (resp. TU), the message delay under the two-hop (resp. unrestricted) multicopy protocol.
N2{1,…,N} (resp. NU {1,…,N}), the number of occurrences of the message in the network (excluding the message at the destination) at the moment the destination receives the message.
L = the length of the square area the node move on Quantities of interest
Inter-meeting time between two nodes: Proposition: Let r<<L. The inter-meeting time for the random direction and the random waypoint mobility models is approximately exponentially distributed with parameter
Here E[V*] is the average relative speed between two nodes and is the pdf in the point (x,y). Inter-meeting time between two nodes
Inter-meeting time between two nodes: Inter-meeting time between two nodes Proposition: Let r<<L. The inter-meeting time for the random direction and the random waypoint mobility models is approximately exponentially distributed with parameter
resp.
Here E[V*] is the average relative speed between two nodes and ω ≈ 1.3683 is the Waypoint constant. If the speeds of the nodes are constant and equal to v,
then
The model: two-hop multicopy: The model: unrestricted multicopy The model: two-hop multicopy Model the number of occurrences of the message as an absorbing Markov chain: State i{1,…,N} represents the number of occurrences of the message in the network.
State A represents the destination node receiving (a copy of) the message.
Message delay in two dimensions: Proposition: The Laplace transform of the message delay under the two-hop multicopy protocol is: Message delay in two dimensions and
Message delay: Proposition: The Laplace transform of the message delay under the unrestricted multicopy protocol is: Message delay and
Expected message delay: Corollary: The expected message delay under the
two-hop multicopy protocol is Expected message delay and under the unrestricted multicopy protocol it is Where γ ≈ 0.57721 is Euler’s constant.
Examples: Nodes move on a square of size 4x4 km2 (L=4 km)
Different transmission radii (r=50,100,250 m)
Random waypoint and random direction:
no pause time
[vmin,vmax]=[4,10] km/hour
Random direction: travel time ~ exp(4)
Random walker: streets 80 meters apart
speed = one street/minute
Examples
Example: two-hop multicopy: Example: two-hop multicopy
Example: two-hop multicopy: Example: two-hop multicopy Distribution of the number of copies (R=50,100,250m):
Relative performance: Relative performance and The relative performance of the two relay protocols: Note that these are independent of λ!
Some remarks: Remarks:
These expressions hold for any mobility model which has exponential meeting times.
Mean message delay scales with mean first-meeting times.
Two mobility models which give the same λ also have the same message delay for both relay protocols!
Some remarks
Conclusions: two dimensions: Conclusions: two dimensions Requires a different approach than in one-dimension due
to the additional complexity: use models instead of
deriving explicit expressions
Generic model presented with 2 parameters which:
can compute the message delay;
captures more than one mobility model;
studies the message delay due to relay strategies apart from the underlying mobility models.
Present - Publications: Present - Publications Conferences
ACM SIGMETRICS, Banff, Canada. June 2005
Message delay in mobile ad hoc networks
IEEE INFOCOM, Miami. March 2005 Analysis of alternating priority queueing models with (cross) correlated switch-over times
Modeling and Optimization in Mobile, Ad hoc, and Wireless Networks (WiOpt), Cambrdige, UK. 2004
Relaying in mobile ad hoc networks
Present - Publications: Present - Publications Journals
Wireless Networks (WINET), 2005
Relaying in mobile ad hoc networks: the Brownian motion mobility model
QUAESTA (Queueing Systems), special ussue. 2005 Analysis of alternating priority queueing models with (cross) correlated switch-over times
Mathematical methods in operations research, 2002
On the bias vector of a two-class preemptive priority resume queue
Present - Publications: Present - Publications In submission
Performance, 2005
Relaying in mobile ad hoc networks
In preparation
IEEE INFOCOM (2 papers)
Journal (1 paper)
Present - Lessons learned during PhD: Present - Lessons learned during PhD Theoretical research is usually incremental and often less applied
Difficult to work on your own in a new field (it is possible, but it costs a LOT more time)
Discussion gives rise to new ideas, therefore best not to work (too much) alone
Present - Lessons learned during PhD: Present - Lessons learned during PhD Very rewarding work (once you finally get results)
You learn to get the details right
Presenting to the scientific community is different from what I was used to!
Future = ???: Future = ??? Teaching/research position at the UNSA / INRIA
Courses taught at the university
Sas programming
Datamining
Finance
Discrete mathematics
Game theory
Contract until the end of August, but I can leave before if I wish
Conference in June (ACM Sigmetrics, Canada)
Future - Wishes : Future - Wishes Career wishes:
Challenging work
Work more with people
More applied (the what/how/WHY)
The exact contents of future work is of less importance to me
Depends on future employer
I will learn and adapt
My added value: My added value Person who can adapt easily
International background
Diverse interests
Eager to learn
Vast amount of energy
Enjoy human interaction
Various fields of study / experience
Economy
Mathematics
Computer science
Telecommunication
Added Value: Added Value Capable of both depth and diversity
Multiple studies
PhD
Experience
Banking / insurance
Consultancy / project management
Research
University
Q & A: Q & A
Thank you for listening!
Questions?