combined optimal activation and transmission control … · combined optimal activation and...

Combined Optimal Activation and TransmissionControl in Delay Tolerant Network

Amar Prakash Azad

INRIA Sophia AntipolisFRANCE

Supelec, Paris

Joint work with:

Eitan Altman,

Tamer Basar

Franceso De-Pallegrini

Amar Azad, INRIA France04/10/2017 2

Inter-Planet Network

• Task : Deliver message from Earth to Jupiter. How?

Carry Store And Forward

Interplanetary Internet (IPN)

http ://ipnsig.org/home.htm

Originally talked for

..Communicating with it…

“Multi-player” Neighborhood Gaming

“Media Swap”

“Proximate Context-aware Gaming”

Mobile Social Network “Profile Matching”

In-building Automation Control

“Vouch” – building 3rd-party Trust Nets

“Flash Pay” – eCash between eWallets5


Scenario

• A person is driving on a highway, carrying his own Laptop/ PDA wants to send an email. There is no nearby connectivity (Base station/Access point).

• The user passes by other cars/buses/trains that are having similar devices. These users can serve as relays for the email and pass it on to other and so on.

• Eventually, the message reaches someone having Internet connectivity through which delivered to destination.

DakNet: Bus ferries from remote village to city carrying emails back and forth.http://www.firstmilesolutions.com/

Yet Another Application


Outline

• Introduction

• System Model

• Joint Dynamic Optimal Control– Activation Control

– Transmission Control

• Simulation Validation

• Conclusion and perspective

• Other Research Topics


Challenges

• Major Challenges

– Data delivery : Routing from source to destination

– Energy efficiency : Conserve energy from undesired transmissions, beaconing, etc..

• Exploit the inherent properties of DTN

– Node Mobility

– Transmission control

– Signaling control (Beaconing Control)


Operational OverviewForwarding Protocols

•Epidemic Forwarding – Data Flooding •Quicker data dissemination at the cost of more system resources, e.g., Energy, Buffer memory, etc..

•Two Hop Routing- Relay to destination•Resource efficient but suffersthe performance due to slower dissemination.

Our study comes under the category of controlled two hop routing.

•Basic Tradeoff : Quicker Delivery vs. Resource Efficiency.


Beaconing - Periodic source node discovery signalling

– Enhances source node discovery

– Consumes energy

• Node may drain-out even without participating

– especially those nodes which are not infected early .

Dynamic Node Activation

– Activate the node only when required.

A Joint Optimal Dynamic Control:

Activation control + Transmission control

– Both Controls are proved as Threshold optimal. • Benefit: Threshold policies are easier to implement.

Main Results

• Beacon Signalling

•Dynamic Node Activation

Main Contribution and Main Results

Main Contribution

Beacon range

Tx range


Activation and Beaconing

D

Nodes may die just doing beaconing

Fresh nodes may be activated latter.

S: Source node

D: Destn. node


System Model

• 1 packet, 1 source, 1 destination

• # of mobiles nodes : N + 1

• # of infected nodes : X(t)

• # of fresh nodes : Y(t)

• Mobility : Random way point

• Node intermeeting rate : ξ

• Death rate due to beaconing : μ

• Activation rate is upper bounded by K(t).


States and Control

States• Inactive: does not take part in any communication.

• Active: fresh node, beacon until receive a message. -Y(t)

• Infected: active but does not send beacons. – X(t)

Control

• Activation rate control -V(.): by activating less/more mobiles per unit of time, one can use resources when needed.

• Transmission control - U(.): the beaconing transmission power is controlled in order to mitigate the battery discharge rate of active relay nodes.

Control•Activation •Transmission

• Inactive

•Active

•Infected

States of Mobile


System Dynamics• Evolution rule (Mean field approximation)

– X(t) grows at a rate given by the following pair of coupled differential equations :

• Delivery Delay Distribution Td


Problem Formulation

• Our goal is to obtain joint optimal policies for the activation[0<V(t)<K(t)] and the transmission control [u<U(t)<1], satisfying the additional energy constraint [X(T)] , that maximizes the Delivery probability [ ] ,

• Total energy consumed in beaconing during [0, T] is


Optimal Control• Earlier approaches were based on

– Pontryagin maximum principle in (Altman, Basar, & De Pellegrini, 2008)

– Sample path comparisons(Altman, Neglia, Pellegrini, & Miorandi, 2009)

These approaches are works with only one type of population, are not applicable here.

• Issues – It has two dimensions.

– Controls are coupled.

• Main Trick – Follow Two step optimization: Hold U(.) and optimize w.r.t. V(.). Pluginn

optimal V*(.) and find optimal U*(.). • Can’t apply directly because the controls are coupled.

– Key Step: A linear relation (m(t) is linear) is obtained


Optimal Activation Control

• (Turnpike property): For all T large enough (in fact for all T that satisfy

), the optimal threshold is the same.

Threshold policies may need just a common timer to implement.

Independence from time stretching.


Some Calculus

• Once V* is known, the system dynamics can be simplified

• Note that we can express X(t) as a single differential equation, reduced to one dimension.

• Now we know how to solve this using Pontryagin Maximum Principle.

f(t) is +ve fn.


Optimal Transmission Control

Using Pontryagin Maximum Principle

Proved that Hamiltonian is linear in U and has single switch


Activation Example

• Activation Scheme (activation threshold time = )– Uniform Activation :

• Closed form for thresholds are obtained.

• An equivalent model for energy harvesting scenario. (See the plots latter.)

– Linear Activation :

– Exponential Activation :

Recall that K(t) is the upper bound on Activation rate.

• Relation between two thresholds, Activation and Transmission

control plays role in performance.


Simulations

• Simulation setting

– Simulation Method : Trace based with Matlab Script. Steady state capturing.

– Mobility : Random Waypoint (RWP) model,

v = 4.2m/s.

– Region parameters : Square region with 5kms side.

– N = 200.

– Communication range : R=15m.


Infected Nodes with Uniform Activation

• Uncontrolled DynamicsSlower activation slows the infection

• Optimally Controlled Dynamics (x=0.1)

Slow activation delays the threshold.


Optimal Thresholds• Uniform Activation

for x=0.05 and x=0.1 • Different Activation Policies

• Exponential activation is faster -> transmission threshold comes early.

• Smaller the energy constraint (x), early the transmission threshold


Concluding Remarks

• Optimal thresholds and control trajectory are derived based on analytical study. Both controls are Threshold optimal.

• Devised a new method that is based on identifying the exact weight of the activation control at each time instant.

• Validated our theoretical results through simulations for various activation schemes.

• Perspective– One can formulate the problem with soft constraints,

instead of hard constraints, using a weighted sum of throughput and energy cost.


Some Other Works• Queuing Theoretic Analysis for Power Save Mode of

IEEE 802.16e (WiMAX)

• MDP Based modeling for Power Saving Mechanism of Wireless Networks

• Network Routing Games - Egoism to Altruism

• Sparse Mobile Delay Tolerant Networks (Game theoretic and Multi population)

• Scheduling Algorithms Analysis in Heavy Traffic Regime


Thanks for your

Attention!


Queuing Theoretic Model• Model

– M/G/1 with inhomogeneous repeated vacations• Performance evaluation of a sleep policy

– Constraint Optimization problem formulation • Energy Saving vs. System Response time tradeoff

• Objective– Get insight on how to choose parameters that are

left to the mobile (lowest and largest window size)

– Examine and optimize default parameters of IEEE 802.16e standards


Queueing Model

• V1, V2 … are independent but need not be identical

• Optimization: Larger V saves more energy but

increases Z System response time

• Questions ?: Answers

– Is standard policy optimal ?: No, standard policy is not optimal.

– Why multiplicative increase (2) ?: No, rather it depends a lot on arrival intensity.

– Why not use random sleep windows ?: No, deterministic policy performs better.

no arrivals

Z = 4 arrivals

Idle period I Busy period B

V1 Vacation V3V2 B4 B3 B2 B1

Tw


MDP Based Model• Decision is taken at each wake up instant to sleep or not to

sleep based on cost

• Optimizes delay and energy saving a simultaneously.

• System priority is balanced by tuning ε.

• An arbitrary off time can be handled.

• Optimal sleep policy

• Sub Optimal policy– Policy iteration


Dynamic Programming

• Allows to obtain optimal policy

– Periodic fixed size is optimal for exponential off time

– No policy is optimal for an arbitrary hyper exponential off time.

• Policy iteration yields Suboptimal – strictly better than periodic ones. Larger step converges to optimal.


Routing Games

• General Network Routing Scenario

– Data has to be routed from s --> r

– User “s” decides the route

– Cost minimization is the criteria

• Link Cost depends on amount of data routed

– Link cost increases with Flow

• Game theoretic framework

– Nash equilibrium


Routing Games• Selfish Users (Existing literature)

– Unique Nash equilibrium for several cases

• Cooperation ? What happens

• Proposed a method to study

cooperation in

Non-cooperative framework

• Entire range of Cooperation

– From Egoistic to Altruistic

• Punch line

– Nash Uniqueness breaks down

– Cooperation Paradox

A Sample result with M/M/1 Cost in Load Balancing Network

combined optimal activation and transmission control … · combined optimal activation and...

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