Title: BANDWIDTH ALLOCATION FOR VIRTUAL PATHS (BAVP) INVESTIGATION OF PERFORMANCE OF CLASSICAL CONSTRAINED AND GENETIC ALGORITHM BASED OPTIMISATION TECHNIQUES
1BANDWIDTH 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
2Aggregated 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
3Aggregated 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
4Aggregated 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
5Bandwidth 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
6Expected 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)
7Classical 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
8Genetic 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).
9GA 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
10CASE 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
11results
- 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.
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13Seven-node network topology (42 ODs, 84 VPs),
showing only VP1 links because of the network
complexity
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15Fairness 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.
16Convergence 7-node network topology for the
scarce link capacity case (480 Mbit/sec).
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18Concluding 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
19GAs 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.
20GENOCOP 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.
21Three-node network topology
22(Sum of means)160