Upload
trankhuong
View
230
Download
0
Embed Size (px)
Citation preview
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
Amar Azad, INRIA France04/10/2017 6
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
Amar Azad, INRIA France04/10/2017 7
Outline
• Introduction
• System Model
• Joint Dynamic Optimal Control– Activation Control
– Transmission Control
• Simulation Validation
• Conclusion and perspective
• Other Research Topics
Amar Azad, INRIA France04/10/2017 8
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)
Amar Azad, INRIA France04/10/2017 9
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.
Amar Azad, INRIA France04/10/2017 10
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
Amar Azad, INRIA France04/10/2017 1111
Activation and Beaconing
D
Nodes may die just doing beaconing
Fresh nodes may be activated latter.
S: Source node
D: Destn. node
Amar Azad, INRIA France04/10/2017 12
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).
Amar Azad, INRIA France04/10/2017 13
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
Amar Azad, INRIA France04/10/2017 14
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
Amar Azad, INRIA France04/10/2017 15
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
Amar Azad, INRIA France04/10/2017 16
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
Amar Azad, INRIA France04/10/2017 17
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.
Amar Azad, INRIA France04/10/2017 18
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.
Amar Azad, INRIA France04/10/2017 19
Optimal Transmission Control
Using Pontryagin Maximum Principle
Proved that Hamiltonian is linear in U and has single switch
Amar Azad, INRIA France04/10/2017 20
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.
Amar Azad, INRIA France04/10/2017 21
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.
Amar Azad, INRIA France04/10/2017 22
Infected Nodes with Uniform Activation
• Uncontrolled DynamicsSlower activation slows the infection
• Optimally Controlled Dynamics (x=0.1)
Slow activation delays the threshold.
Amar Azad, INRIA France04/10/2017 23
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
Amar Azad, INRIA France04/10/2017 24
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.
Amar Azad, INRIA France04/10/2017 25
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
Amar Azad, INRIA France04/10/2017 27
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
Amar Azad, INRIA France04/10/2017 28
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
Amar Azad, INRIA France04/10/2017 29
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
Amar Azad, INRIA France04/10/2017 30
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.
Amar Azad, INRIA France04/10/2017 31
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
Amar Azad, INRIA France04/10/2017 32
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