QoS and Fairness Constrained Convex Optimization of Resource Allocation for Wireless Cellular and Ad

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QoS and Fairness Constrained Convex Optimization
of Resource Allocation for Wireless Cellular and
Ad Hoc Networks
David Julian, Mung Chiang, Daniel ONeil and
Stephen Boyd
EE360 Presentation Donghyun Kim May 17th, 2004
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Motivation

• QoS has become an important research issue as
  users of communication networks become less
  satisfied.
• QoS covers a wide array of network attributes
  bandwidth, delay, and packet delivery guarantee.
• A new framework of convex optimization is
  presented as a computationally efficient tool for
  resource allocation.

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Outline
Cellular Network
P1 Determining feasibility of a set of SIR
requirements P2 Maximizing SIR for a
particular class of users with lower
bounds on the QoS of all other user P3
Satisfying queuing delay requirements for users
in various QoS classes
Ad Hoc Network
P4 Finding the optimum power control to
maximize overall system throughput
consistent with QoS guarantees P5 Determining
feasibility of a set of service level agreement
under network resource constraints P6
Solving for the minimum total transmission delay
of the most time sensitive class of
traffic by optimizing over powers, capacities,
and SLA terms P7 Maximizing the unused
capacity of the network
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Previous Work

• Various iterative methods have been proposed to
  optimally maximize the minimum SIR, to minimize
  total or individual power, or to maximize
  throughput.
• These works are not general enough to allow a
  diverse set of QoS constraints and objective
  functions
• Convex optimization framework can incorporate a
  variety of QoS constraints and objectives not
  just for cellular networks, but also ad hoc
  networks as well

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Geometric Programming

• Definition 1 A monomial is a function fRn ? R,
  where the domain contains all real vectors with
  non-negative components

And

• Definition 2 A posynomial is a sum of monomials

• Geometric Programming

Minimize Subject to
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Convex Optimization

• By change of variables
• yi log xi and bik log cik,

• Convex Optimization

• Convex Optimization can be solved globally with
  the running time of

• Solution also determine feasibility

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Throughput Optimization for Cellular Networks

• A single base station and N links
• Propagation model
• SIR
• SIR is used as a throughput QoS parameter.
• channel capacity scales with log(SIR)
• probability of error scales with

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Throughput Optimization for Cellular Networks,
Contd
Problem formulation

• Formulation 1 (SIR constrained optimization of
  power control) Optimizing
• node powers to maximize SIR for a particular
  user under QoS constraints

• This general formulation can be applied to
  different power control situations

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Throughput Optimization for Cellular Networks,
Contd

• Formulation 2 (SIR constrained optimization for
  minimum power)
• minimize
• subject to Same constraints as in
  Formulation 1

Proportional and Minimax Fairness Extensions

• Formulation 3 (SIR constrained optimization
  with proportional fairness)
• maximize
• subject to Same constraints as in
  Formulation 1
• Maximizing weighted fair power allocation is
  equivalent to minimizing

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Throughput Optimization for Cellular Networks,
Contd

• Formulation 3 (SIR constrained optimization
  with proportional fairness)
• minimize
• subject to Same constraints as in
  Formulation 1
• Maximizing min SIR is equivalent to minimizing
  over an auxiliary scalar variable t such that
  ISRi t for all i.
• In this case t and Pi are optimization
  variables

Simulation

• Number of user 5
• Distance D 1,5,10,15 and 20 units
• power drop off factor 4
• Spreading gain of Ks 10
• Max transmit Power 0.5W, Noise Power 0.5uW

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Throughput Optimization for Cellular Networks,
Contd
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Throughput Optimization for Cellular Networks,
Contd

• Admission control using convex optimization in
  cellular network
• - new user is admitted when feasible solution
  of this geometric program
• exists.
• Pricing
• - Determine the number of standardized users
  that can be added to the
• systems both before and after the new user
  is admitted.
• The difference between these two numbers can
  be taken as price.
• Queuing delay optimization
• - important for bursty digital data
• - M/M/1 queue
• - By constraining the SIR to exceed a minimum
  threshold, so that link
• transmission rate is larger than

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Throughput Optimization for Ad Hoc Networks

• n transmitter/receiver pairs
• Rayleigh fading channel
• Power received from transmitter j, at receiver i

• The distribution of the received power is
  exponential with mean

• SIR for link i

• Multihop routing

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Throughput Optimization for Ad Hoc Networks,
Contd

• Outage probability of a link i

• Outage probability of a path S

• Data rate of link i

• Aggregate data rate for the system

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Throughput Optimization for Ad Hoc Networks,
Contd
Problem formulation

• Formulation 5 (Optimize power for throughput
  maximization)
• maximize Rsystem
• Subject to

• maximizing Rsystem is equivalent to minimizing

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Throughput Optimization for Ad Hoc Networks,
Contd

• Admission control using convex optimization in
  cellular network
• - new user is admitted when feasible solution
  of this geometric program
• exists.
• Pricing
• - The data transport capacity lost by the
  entire network in supporting a
• new user can be taken as price.

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Resource allocation for delay in Ad Hoc Networks

• Resources include power, the number of flows in
  each category of service,
• bandwidth and capacity of each link.
• These resources are allocated according to the
  optimization criteria of
• transmission delay, unused capacity and overall
  system throughput
• Assumption
• Network with J links with capacity of Cj packets
  per second for each link j
• K classes of traffic with different QoS
  requirements, and for each class k,
• the bandwidth requirement is bk Hz.
• Delay guarantee in the service level agreement
  is dk,UB
• Probability of delivering the packet across link
  k is pk,LB
• Number of packets admitted in the kth class of
  traffic is nk

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Resource allocation for delay in Ad Hoc
Networks, Contd
Problem formulation

• Formulation 6 (SLA feasibility under network
  constraints)

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Resource allocation for delay in Ad Hoc
Networks, Contd

• Formulation 7 (Unused capacity maximization)

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Resource allocation for delay in Ad Hoc
Networks, Contd

• Formulation 8 (Weighted Joint Capacity and
  Delay Minimization)

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Resource allocation for delay in Ad Hoc
Networks, Contd
Simulation

• Network topology in the following figure
• class 1 data along path ABCD requiring a rate
  of 50 packets/second
• delay 0.2 seconds
• class 2 data along path DFEA requiring a rate
  of 50 packets/second
• delay 0.2 seconds
• class 3 voice along path ABFD requiring a rate
  of 250 packets/second
• minimize both delay of voice and the cost of
  capacity

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Resource allocation for delay in Ad Hoc
Networks, Contd
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Summary

• Various QoS provisioning problems in cellular
  and ad hoc networks are
• nonlinear optimization problems.
• Geometric programming framework makes possible
  formulations that
• include both throughput and delay as objective
  functions and allow for a
• variety of general network models
• This problem can be transformed into convex
  optimization problem, and
• can be solved efficiently.