A Model for Multiobjective
Routing Optimisation in MPLS
with Two Service Classes
– Resolution Strategies –
Rita Girão-Silva a,c,
José Craveirinha a,c, João Clímaco b,c
Workshop INESC-Coimbra
AIORT’05 – Sep. 16, 2005
a
b
c
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes – Resolution Strategies
Rita Girão-Silva, José Craveirinha, João Clímaco
1
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
Summary
1. Introduction
2. Review of a multiobjective routing framework
for MPLS
– Base model
– Model for two classes of traffic (QoS and Best
Effort)
– Traffic modelling approach
3. Resolution strategies
– Search for non-dominated solutions for each
node-to-node flow
– Possible heuristic / meta-heuristic to choose
adequate compromise solutions
4. Other open issues and difficulties
2
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
Introduction
• In MPLS networks, routing models dealing with
multiple, heterogeneous QoS requirements are
needed.
• There are potential advantages in using
multiobjective formulations for the routing
calculation problem.
• Main features proposed in this model:
– Two classes of traffic (QoS and BE);
– Bi-level stochastic representation of the traffic in the
network.
• Heuristic to solve the problem
3
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
Review of a Framework for Routing
Optimisation in MPLS
[Craveirinha et al, 2005]
It is a network-wide routing model of new type:
1. Hierarchical multiobjective optimisation model
– First level: objective functions formulated at network level
(considering the combined effect of all traffic flows)
– Second level: average performance metrics associated with
different types of services
– Third level: average performance metrics associated with the
µ-flows of packet streams
2. Explicit consideration of fairness objectives at the three
levels of optimisation
4
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Review of a Framework for Routing
Optimisation in MPLS)
3. It includes an explicit and ‘direct’ representation of the most relevant technicaleconomic objectives, namely total expected
revenue and packet total average delay.
4. It considers a bi-level stochastic
representation of the traffic in the network.
– Macro-level: traffic flows that correspond to a
stochastic representation of the connection
demands in the traffic trunks associated with
explicit routes
– Micro-level: stochastic representation of µ-flows
of packet streams inside any given traffic flow
5
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
Base-model
Formulation of a hierarchical multiobjective
routing optimisation problem (P-M3-S)
Network objectives: min Rt{-WT}
min R {BMm}
t
Service objectives: min Rt{Bms}, s S
min Rt {BMs}, s S
µ-flow network objectives: min Rt {D’T}
min Rt{DMm}
6
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Base-model)
• Network objectives
– Total expected network revenue
WT   A cs w s
sS
S: set of service types
Asc: total traffic carried for service s
ws: expected revenue per µ-flow of type s
– Maximal average blocking probability among all
service types (network-level fairness objective)
BMm = max sS {Bms}
• Service objectives
– Maximal blocking probability among all traffic flows
of type s (fairness objective at service level)
BMs = max fsFs {B(fs)}
7
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Base-model)
• Service objectives (cont.)
–Average blocking probability for all traffic flows of type
s (of which the set is Fs)
1
Bms  o  A t (fs )B(fs )
A s fsFs
Aso: total traffic offered for service s
At(fs): traffic offered for traffic flow fs
B(fs): the corresponding end-to-end blocking probability
• µ-flow network objectives
–Average packet delay for all types of services,
weighted by the relative bandwidths
D'T 
1
γ'T
 D'
sS
ms
γ's
8
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Base-model)
• µ-flow network objectives (cont.)
– Maximal average packet delay experienced by all types of
packet streams (fairness objective at µ-flow network level)
DMm=max sS {Dms}
---------------------------------------
• This model should be envisaged as a multiobjective
routing optimisation framework with a significant degree
of flexibility and adaptability.
• The proposed meta-model i.e. the model underlying
concepts and logical relations may be configured for
other specifications of objective functions and /or
constraints as long as the basic structure of the metamodel is preserved.
9
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
Model for QoS and BE service classes
Hierarchical optimisation problem for two service classes
(P-M3-S2)
1st level
QoS network objectives: min Rt {-WT|Q}
min Rt {BMm|Q}
2nd level
QoS service objectives: min R {Bms|Q}, s  SQ
t
minRt {BMs|Q}, s  SQ
BE network objective: min R {-WT|B}
t
3rd level
µ-flow network objectives: min Rt {D’T}
min Rt {DMm}
10
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Model for QoS and Best Effort service classes)
• The functions WT|Q, WT|B, BMm|Q, Bms|Q, BMs|Q
have the meaning described before, but with
the index Q (B) indicating that their calculation
is reported to traffic flows of class QoS (Best
Effort) alone.
• While QoS and BE traffic flows are treated
separately in terms of upper level objective
functions, the interactions among all traffic
flows remain represented in the model (via the
teletraffic model underlying the routing
optimisation model).
– In fact, the link traffic model must integrate the
contributions of all the traffic flows which may use
every link.
11
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
Traffic modelling approach
•
Traffic flows (macro level) are represented
through marked point processes of multirate
Poisson type
– The concept of effective bandwidth (dks) required by
traffic flows fs on link lk, is used.
– This is a stochastic measure of the utilization of
network transmission resources capable of
representing the variability of the rates of different
traffic sources, as well as effects of statistical
multiplexing in the network.
• This and other parameters are included as
‘attributes’ contained in the traffic engineering
descriptors γ s , η (fs ) of traffic flow fs=(vi,vj, γ s ,η (fs ))
from node vi to vj.
12
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Traffic modelling approach - macro level)
The traffic model of a link for calculating the blocking
probabilities Bks experienced by flows fs on link lk is a
multidimensional Erlang system M1+M2+...+Mn/M/Ck/0.
Bks=Ls( dk , ρk,Ck)
Ls is a function implicit in the analytical model.
Its values can be calculated by adequate efficient and
robust algorithms (as the Kaufman/ Roberts algorithm
or the UAA (Uniform Asymptotic Approximation) for
large Ck).
dk =(dk1,...,dk|S|): vector of equivalent effective
bandwidths
ρk=(ρk1,..., ρk|S|): vector of reduced traffic loads
offered by flows of type s to lk
13
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Traffic modelling approach - micro level)
• Traffic modelling at packet µ-flow level (micro level)
uses marked point processes characterised by their
intensities I’t(fs) [packet/s] and hk(fs) (mean service time
in lk of a packet from µ-flows in fs).
– The mean [Erl] of each of these processes defines the
potential traffic offered ρtk(fs) to lk by fs, at time period t.
– The loss and control access mechanisms are represented by a
multidimensional access function for each link.
– This access function enables the calculation of reduced
offered loads ρtk*(fs) and of the fictitious equivalent total
offered traffic
ρkt *    ρkt * (fs )
sS fs Fs
14
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Traffic modelling approach - micro level)
• The average expected delay Dk(fs)
experienced in lk by packets in µ-flows from fs
may be estimated from a M/GI/1/∞ queue
model.
– A first approximation to the service time
distribution is a hyper-exponential distribution, of
which the weights represent the probability of an
arbitrary packet offered to lk being originated from
each fs.
15
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
Resolution strategies
• The MODR-S model, originally proposed by [L.
Martins et al., 2003] may be considered as a
particular case of the base model P-M3-S
previously reviewed.
– The MODR-S was founded on the formulation of a bilevel hierarchical multiple objective routing
optimisation problem for multiservice networks.
– It is based on an underlying bi-objective shortest path
algorithm including preference thresholds, for
calculating alternative paths for each flow (MMRA-S).
16
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Resolution strategies – MODR-S)
– It uses a heuristic for synchronous path selection
aiming to obtain a set of routes which is a satisfactory
compromise solution for the network routing
optimisation problem.
– This approach is based on the MMRA-S algorithm,
that seeks to solve the auxiliary bi-objective shortest
path problem in the MODR-S framework.
• Two metrics: the blocking probabilities, the implied costs.
• Soft constraints in the form of required and / or accepted
values for each metric, defining preference regions in the
objective function space.
17
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Resolution strategies – Heuristic aproach)
I. Heuristic approach – Extension of the ‘rational’ of
MODR-S to address the problem P-M3-S2
• The calculation of candidate solutions for each
traffic flow will be based on the resolution of an
auxiliary multiobjective shortest path problem for
each node-to-node flow.
• The objectives include the blocking probabilities,
the implied costs and possibly the delay.
– The definition and calculation of the implied costs has
to be reformulated taking into account the
consideration of two different classes of service.
18
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Resolution strategies)
• A suitable resolution approach for this auxiliary
problem has to be developed.
– Optimisation of a weighted sum of the objective functions
– Reference point-like method
----------------------------------------------------------------------------
• The heuristic approach for solving the problem
under analysis (P-M3-S2) has to be devised to
generate and select adequate compromise
solutions (routing plans Rt ).
– As the routing problem is formulated as a hierarchical
optimisation problem, the heuristic must include the
representation of a system of preferences, which is
necessary for an automatic ordering and selection of
candidate solutions.
19
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
(Resolution strategies – Possible
heuristics for the selection of solutions)
II. Development of a heuristic based on a
lexicographic optimisation method
– A transformation of the initial formulation of the P-M3S2 according to an aggregated achievement function
has to be made.
– This implies that a hierarchy of preferences within
each priority level has to be defined.
III. Development of an evolutionary algorithm,
where a population of solutions may be
evaluated and possibly evolve into increasingly
“better” solutions
20
A Model for Multiobjective Routing Optimisation in MPLS with Two Service Classes –
Resolution Strategies
R. Girão-Silva, J. Craveirinha, J. Clímaco
Other open issues and difficulties
raised by this modelling framework
• Great complexity of the problem (NP-complete)
• Interdependencies among the objective
functions
• Representation of the system of preferences in
an automatic decision environment
• Treatment of inaccuracy and uncertainty
associated with many parameters
• Simulation environment for further testing of the
resolution approaches
• Comparison with results obtained with other
methods
21