BANDWIDTH ALLOCATION FOR VIRTUAL PATHS (BAVP) INVESTIGATION OF PERFORMANCE OF CLASSICAL CONSTRAINED AND GENETIC ALGORITHM BASED OPTIMISATION TECHNIQUES - PowerPoint PPT Presentation

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BANDWIDTH ALLOCATION FOR VIRTUAL PATHS (BAVP) INVESTIGATION OF PERFORMANCE OF CLASSICAL CONSTRAINED AND GENETIC ALGORITHM BASED OPTIMISATION TECHNIQUES

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Title: BANDWIDTH ALLOCATION FOR VIRTUAL PATHS (BAVP) INVESTIGATION OF PERFORMANCE OF CLASSICAL CONSTRAINED AND GENETIC ALGORITHM BASED OPTIMISATION TECHNIQUES


1
BANDWIDTH ALLOCATION FOR VIRTUAL PATHS (BAVP)
INVESTIGATION OF PERFORMANCE OF CLASSICAL
CONSTRAINED AND GENETIC ALGORITHM BASED
OPTIMISATION TECHNIQUES
  • A. Pitsillides, G. Stylianou, C. S. Pattichis, A.
    Sekercioglu, A. Vasilakos

2
Aggregated bandwidth allocation
  • Important for ATM Internet to support QoS
  • Broadband ATM based networks (B-ISDN)
  • VP concept
  • Introduced to minimise complexity of per-call
    resource management and simplify routing
  • is a pre-established path between an OD pair.
  • aggregates a number of Virtual Circuits (VCs)
  • can reserve bandwidth for a time span longer than
    the duration of a specific call.
  • primary objective of VP concept
  • to facilitate fast and simple call setup with
    minimum signalling requirements
  • allocate call bandwidth at network edge, by
    considering only VP bandwidth

3
Aggregated bandwidth allocation (cont.)
  • Internet (new architectures)
  • For Internet based networks, current trends
    emerging to allocate bandwidth (to different
    classes and users), in order to support Quality
    of Service provision
  • Aggregated bandwidth allocation, without need for
    per-session signaling, advocated for diff-serv
    (differentiated services) Internet architectures,
    and could be useful for MPLS
  • This despite complexity introduced when compared
    with current Internet best-effort model

4
Aggregated bandwidth allocation (cont.)
  • Bandwidth Allocation for Virtual Paths (BAVP)
  • assign optimal bandwidth (capacity, service-rate)
    to VPs by taking global network considerations
    into account.
  • located at higher levels of control structure VP
    and network levels.
  • associated with "slow" time scale--minutes to
    tens of minutes
  • We compare throughput, fairness and time
    complexity of GA-BAVP and CCO-BAVP for several
    node topologies

5
Bandwidth Allocation for Virtual Paths (BAVP)
(cont.)
  • given
  • network topology expected OD traffic loads given
    in terms of a general Bandwidth Demand
    Probability Function link capacities
  • find
  • optimal VP bandwidth assignment, which maximises
    total expected network throughput
  • Subject to constraints
  • on link bandwidth and minimum bandwidth
    assignments to VP
  • seek to provide for "fair" allocations of
    bandwidth among all VPs

6
Expected Throughput D(U) when bandwidth
assignment of size U is utilised given the
Bandwidth Demand Probability Function F(U) (here
Normal Probability Function, m150 Mbits/sec,
svariable)
7
Classical Constrained Optimisation method
  • algorithm based on Sequential Quadratic
    Programming (SQP) method as implemented in Matlab
    Optimisation Toolbox
  • a Quadratic Programming (QP) subproblem is solved
    at each iteration.
  • An estimate of the Hessian of the Lagrangian is
    updated at each iteration using the BFGS formula.
  • A line search is performed using a merit function
    similar to that proposed by Hand and Powell.
  • QP subproblem solved using an active set strategy
    similar to that described in Gill, Murray, and
    Wright

8
Genetic programming function optimisation method
(GAs)
  • GAs
  • introduced by John Holland in early seventies,
  • principal search procedures based on principles
    derived from dynamics of natural population
    genetics.
  • successfully applied to numerous large space
    problems where no efficient polynomial-time
    algorithm is known, such as NP-complete.
  • broad applicability of GA techniques,
  • a broad application domain exists in
    telecomunications (e.g www.ee.cornell.edu/bjhaska
    r/ganet-bib.html lists about 90 application
    papers).

9
GA used for BAVP
  • Genetic Algorithm for Numerical Optimisation for
    Constraint Problems (GENOCOP) based on the
    floating point representation
  • concerned with optimizing a non-linear function
    subject to a set of linear constraints.
  • By appropriate choice of genetic operators and
    once an initial feasible solution is found (or
    given) no need to check constraints at each
    iteration
  • GENOCOP for BAVP
  • code bandwidth allocated to each VP Ui to
    represent each chromosome use fitness function
    to maximise throughput subject to given
    constraints

10
CASE STUDIES
  • we consider in detail two topologies for
    evaluating the optimisation methods a 3-node and
    a 7-node network.
  • also solve 4-, 5- and 6-node problems, and
    provide some general observations regarding
    throughput, time complexity and fairness for all
    cases considered.
  • Also in case of the GA algorithm we provide some
    observations regarding selection of the tuning
    parameters

11
results
  • maximising throughput
  • GA-BAVP and CCO-BAVP in close agreement (within
    few )
  • fairness
  • GA-BAVP outperforms CCO-BAVP, especially for
    complex topologies, e.g. 7-node network, with
    scarce link capacity.
  • Convergence
  • Similar performance GA-BAVP outperforms CCO-BAVP
    in initial stages, and vice-versa for longer time
    scales.
  • as problem complexity increases solution time for
    GA-BAVP does not increase as fast as CCO-BAVP
    algorithm.
  • tuning parameters selection recommended are ok
  • hybrid scheme
  • better overall convergence but same solution as
    CCO-BAVP.

12
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13
Seven-node network topology (42 ODs, 84 VPs),
showing only VP1 links because of the network
complexity
14
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15
Fairness Deviation of assigned capacity for
7-node network topology problem from capacity
required for 95 satisfaction of the utility
function Di(Ui) for each VPi.
16
Convergence 7-node network topology for the
scarce link capacity case (480 Mbit/sec).
17
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18
Concluding remarks
  • investigated problem of aggregated bandwidth
    allocation for VPs using two different
    algorithms CCO-BAVP and GA-BAVP with network
    topologies ranging from 3- to 7- node (2 to 42 OD
    pairs, 4 to 84 VPs).
  • compared performance with regard to throughput
    maximisation, time complexity, and fairness.
  • Based on results, use of GA-BAVP can be justified
    on basis of
  • fairer bandwidths allocated to the competing
    Virtual Paths
  • the observed trends regarding time solution for
    complex topologies
  • achieved throughput
  • Expect these results to be applicable to the
    Internet (e.g. in the differentiated services
    model and MPLS for allocating aggregated
    bandwidth)
  • work in that area in progress

19
GAs philosophy
  • problems represented as one- or multi-dimensional
    structure,
  • represents a search point in the search space.
  • problem should be encoded in such way as to
  • find pattern to represent each solution, called
    chromosome, as a chain of characters taken in a
    finite alphabet.
  • GAs operate on chromosomes grouped into a set
    called population.
  • Successive populations are called generations.
  • Each chromosome is evaluated by the fitness
    function, which reflects its merit and its
    chances to survive in the next generation.

20
GENOCOP implemention
  • N real valued chromosomes, Ui, i 1,, N, (P
    N) initialized.
  • All chromosomes, Ui, i 1,, N, evaluated with
    respect to the fitness function
  • Some chromosomes of population (the winners)
    reproduce, while others (the losers) die.
  • Genetic operators applied on winners and a new
    generation produced to replace members that died.
  • genetic operators based on floating point
    representation of GENOCOP system
  • During reproduction, randomly selected genetic
    operators are applied on random winner
    chromosomes, one or two each time depending on
    operator, until all members that died are
    replaced.
  • Go to step 2 for a predetermined number of
    generations.

21
Three-node network topology
22
(Sum of means)160
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