distributed resource allocation in wireless data networks: performance and design alexandre...
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Distributed resource allocation in wireless data networks:Performance and design
Alexandre Proutière
Orange-FT / ENS Paris
Outline
Modelling the Internet at flow level Capacity region Rate regions (throughput regions)
Distributed resource allocation in wireless data networks: issues and problem formulation
Rate regions for distributed scheduling Systems without information exchange: the mean field
approach Applications
Outline
Modelling the Internet at flow level Capacity region Rate regions
Distributed resource allocation in wireless data networks: issues and problem formulation
Rate regions for distributed scheduling Systems without information exchange: the mean field
approach Applications
The internet is a flow-level queue
A set of resources shared by a varying number of elastic connections (flows)
QoS: Time to transfer a flow (or flow throughput)
Randomly varying population of flows
Flows randomly generated by users, cease upon transfer completion
Flows of the same class require the same set of resources
Class k flows Mean flow arrival rate per second
Mean size bits Traffic intensity bit/s
The capacity region
Flows are transferred in a finite time, iff the process of the numbers of flows is stable
Capacity region: the set of such that the network is stable at flow-level
(The capacity region quantifies the network provider revenues)
Static population – rate regions
Fix the numbers of flows of different classes
Rate region = set of feasible long term rates of flows of the different classes The long term rate vector is feasible if there exist packet
level mechanisms realizing this rate vector and stabilizing all queues in the network
Packet level mechanisms: resource allocation schemes + congestion control algorithms
Packet level mechanisms
The type of considered networks defines some constraints on packet-level mechanisms Resource allocation in CDMA nets: no time sharing Congestion control algorithms based on losses: at least one
buffer per route must be saturated – the greedy behaviour of TCP
… In wireless networks with distributed scheduling, this greedy behavior reduces the rate region
Rate regions - wireless networks
Slotted ALOHA - two interfering links
1 slot = 1 packet
With or without greedy congestion control
Rate regions - wireless networks
CSMA/CA - two interfering links
Without greedy congestion control
Rate regions - wireless networks
CSMA/CA - two interfering links
With greedy congestion control
The realized resource sharing
The rate vector in each network state belongs to the rate region and is defined by the set of chosen packet level mechanisms:
Example: F. Kelly, schemes designed so as to maximize some network utility
From rate regions to the capacity region
A rough theorem* Consider a system where we are able to characterize the allocation in all states. Define .Then the system is stable at flow-level ifThe converse is true if is convex.
NB: is the largest coordinate convex set containing the contour of
Rate regions Capacity region *true for K = 2, ongoing work in higher dim
The big picture
Flow-level traffic demand
Multi-class queuewith state-dependent capacity
Packet level dynamics: rate regions
Capacity regionFlow-level performanceObjective
Design
Outline
Data network modeling Rate regions Flow-level dynamics
Distributed resource allocation in wireless data networks: issues and problem formulation
Rate regions for distributed scheduling Systems without information exchange: the mean field
approach Applications
Wireless resources
Bandwidth Power Time Space Fading …
time
power
Wireless resources
Bandwidth Power Time Space Fading …
time
power
A single channel shared by active links in time/power
Link rate vs. SINR
Fixed-rate systems SINR
Adaptive variable-rate systems
rate
SINR
Requires the use of rate adaptation techniques
Decision elements
Information at the transmitter
Buffer contentSINR (estimation)The past
Information that can be shared
Intention to transmit Transmission powerBuffer contentSeeds (random access)…..
Distributed systemsThe rate/information tradeoff
sig packetfailure time
packet transmission
Distributed systemsThe rate/information tradeoff
1. For a fixed set of shared information, what is the distributed resource sharing scheme leading to the largest capacity region (flow-level perf.)?
Distributed systemsThe rate/information tradeoff
2. What is the distributed resource sharing scheme leading to the largest capacity region? What info do we need to realize that?
From Tassiualas-Ephremides … … to Modiano, Shah, Zussman
A scheme achieving max rate when exchanging the queue lengths within connex components of the graph of schedule
Thru unknown …
State-of-the-art
What is the maximum capacity region of distributed systems without any signaling? When users play with time and power only (they decide
when and at which power to transmit)
Today …
Outline
Data network modeling Rate regions Flow-level dynamics
Distributed resource allocation in wireless data networks: issues and problem formulation
Rate regions for distributed scheduling Systems without information exchange: the mean field
approach Applications
Mean field for random multi-access algorithms
A fixed number of saturated sources Fixed rate system All links are interfering with each other Each node runs a random multi-access algorithm
(e.g. exponential back-off algorithm)
System state evolution
All nodes share the same "slot point process"empty slot
collision
successful trans.
The slot point process
System state evolution:
System state evolution (cont'd)
Example 1: Exponential back-off algorithm (DCF)
Issue: Analyzing the Markov chain is not possible…
Example 2: Impatient Back-off Algorithm*
* R. Gupta, J. Walrand 2005
The mean field asymptotics
Idea: let the number of sources be large, and see … Renormalization: Trajectories (instead of marginals): Use Sznitman's propagation of chaos to prove asymptotic
decoupling:
The processes of back-offs of the various sources are almost independent*.
* A heuristic used by G. Bianchi 2000, it works for N=3!
Propagation of chaos
Theorem 2
Evolution of marginals
Theorem 3
A stable dynamical system!
Stationary regime
Theorem 4Same results hold in stationary regimes. The system is decoupled, and the stationary behavior of the system can be explicitly characterized
Example: Exponential back-off algorithm
Extensions
Non-saturated sources Power control (instead of time control) Systems with partial interaction … All systems where no information is exchanged?
Coupled vs. decoupled systems
Ideal scheduling schemes lead to coupled systems
decoupled coupled
*A proof via mean field
Outline
Data network modeling Rate regions Flow-level dynamics
Distributed resource allocation in wireless data networks: issues and problem formulation
Rate region for distributed scheduling Systems without information exchange: the mean field
approach Applications
Performance of existing systems
The mean field principle provides explicit asymptotic performance results (e.g. rate regions)
Example: Rate region of fixed ALOHA systems
Stability unknown and sensitive.The DP provides good approximation of the stability condition.
*An open problem for 30 years
The limit
A set of links interacting with each other One slot = one packet
The feasible set of rate vectors achievable without information exchange is:
If fairness is imposed the global throughput does not exceed
Design of optimal systems
Proportional fairness in single hop networks
Decoupling principle
*See Kar et al., Gupta-Stolyar
What about power control?
Fixed rate systems, tuning power… … impacts the network connectivity in ad-hoc networks Clear incentives to tune power
Variable rate systems Does implementing a distributed power control scheme
make sense?
The decoupling principle says that thescheme results in stationary powers depending of the number of flows on each link ( e.g. the scheme cannot emulate time-sharing)
Rate regions (single hop nets)
Power limitation:
SNR:
Max Power policy
We compare the capacity region of smart power control policies with that obtained with the "stupid" max power policy (I transmit with full power when I have a packet)
Playing with power reduces the capacity region
Well … worse scenario for me …
30m 52m 30m
802.11a channelsP = 100mW
No more than 7% better thanthe max power policy!
Summary
We derived a general model to evaluate the performance of data networks
Accounting for user dynamics is crucial! We applied the model to networks with distributed
resource allocation The rate region of such networks is unknown in
general When no information is shared, the decoupling
principle allows to compute the rate region, to compare different approaches
Summary / Perspectives
The DP allows to easily identify the best performance one can obtain without sharing information.
What capacity gain when exchange traffic information?
What information do we need to share to obtain some desirable coupling? Need new math models to study coupled systems
?
Thanks!
http://perso.rd.francetelecom.fr/proutiere