Transcript Scheduling and AP selection in wireless data networks

Distributed resource allocation
in wireless data networks:
Performance and design
Alexandre Proutière
Orange-FT / ENS Paris
Outline
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Modelling the Internet at flow level
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Capacity region
Rate regions (throughput regions)
Distributed resource allocation in wireless data
networks: issues and problem formulation
Rate regions for distributed scheduling
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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
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A set of resources shared by a varying number of elastic
connections (flows)
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QoS: Time to transfer a flow (or flow throughput)
Randomly varying population of
flows
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Flows randomly generated by users, cease upon
transfer completion
Flows of the same class require the same set of
resources
Class k flows
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Mean flow arrival rate
Mean size
bits
Traffic intensity
per second
bit/s
The capacity region
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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
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Fix the numbers of flows of different classes
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Rate region = set of feasible long term rates of flows of
the different classes
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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
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The type of considered networks defines some
constraints on packet-level mechanisms
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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
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Slotted ALOHA - two interfering links
1 slot = 1 packet
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With or without greedy congestion
control
Rate regions - wireless networks
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CSMA/CA - two interfering links
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Without greedy congestion control
Rate regions - wireless networks
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CSMA/CA - two interfering links
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With greedy congestion control
The realized resource sharing
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The rate vector in each network state belongs to the rate
region and is defined by the set of chosen packet level
mechanisms:
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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 if
The 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
Design
Flow-level traffic
demand
Objective
Packet level
dynamics: rate regions
Multi-class queue
with state-dependent
capacity
Capacity region
Flow-level performance
Outline

Data network modeling
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


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
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Bandwidth
Power
Time
Space
Fading
…
power
time
Wireless resources
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Bandwidth
Power
Time
Space
Fading
…
power
time
A single channel shared by active links in time/power
Link rate vs. SINR
SINR
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Fixed-rate systems
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Adaptive variable-rate systems
rate
Requires the use of rate
adaptation techniques
SINR
Decision elements
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Information at the transmitter
Buffer content
SINR (estimation)
The past
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Information that can be shared
Intention to transmit
Transmission power
Buffer content
Seeds (random access)
…..
Distributed systems
The rate/information tradeoff
sig failure packet
packet transmission
time
Distributed systems
The 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 systems
The 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?
State-of-the-art
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From Tassiualas-Ephremides …
… to Modiano, Shah, Zussman
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A scheme achieving max rate when exchanging the
queue lengths within connex components of the graph of
schedule
Thru unknown …
Today …
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What is the maximum capacity region of distributed
systems without any signaling?
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When users play with time and power only (they decide
when and at which power to transmit)
Outline
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Data network modeling
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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 multiaccess algorithms
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A fixed number of saturated sources
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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
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All nodes share the same "slot point process"
empty slot
collision
successful trans.
The slot point process
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System state evolution:
System state evolution (cont'd)
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Example 1: Exponential back-off algorithm (DCF)
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Example 2: Impatient Back-off Algorithm*
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Issue: Analyzing the Markov chain
possible…
is not
* R. Gupta, J. Walrand 2005
The mean field asymptotics
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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 4
Same 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
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Non-saturated sources
Power control (instead of time control)
Systems with partial interaction
…
All systems where no information is exchanged?
Coupled vs. decoupled systems
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Ideal scheduling schemes lead to coupled systems
decoupled
coupled
*A proof via mean field
Outline

Data network modeling



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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
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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
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limit
A set of links interacting with each other
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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
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Proportional fairness in single hop networks
Decoupling principle
*See Kar et al., Gupta-Stolyar
What about power control?
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Fixed rate systems, tuning power…
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… impacts the network connectivity in ad-hoc networks
Clear incentives to tune power
Variable rate systems
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Does implementing a distributed power control scheme
make sense?
The decoupling principle says that the
scheme 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
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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 channels
P = 100mW
No more than 7% better than
the max power policy!
Summary
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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
?
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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