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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?