A Bicriterion Approach for Routing Problems in
Multimedia Networks
Joa˜o C. N. Clı´maco
Faculdade de Economia da Universidade de Coimbra, Avenida Dias da Silva, 165, 3004-512 Coimbra, Portugal
Instituto de Engenharia de Sistemas e Computadores—Coimbra, Rua Antero de Quental, 199,
3000-033 Coimbra, Portugal
Jose´ M. F. Craveirinha
Departamento de Engenharia Electrote´cnica e de Computadores, Polo II da Universidade de Coimbra,
Pinhal de Marrocos, 3030-290 Coimbra, Portugal
Instituto de Engenharia de Sistemas e Computadores—Coimbra, Rua Antero de Quental, 199,
3000-033 Coimbra, Portugal
Marta M. B. Pascoal
Centro de Informa´tica e Sistemas and Departamento de Matema´tica, Polo I da Universidade de Coimbra,
Apartado 3008, 3001-454 Coimbra, Portugal
Routing problems in communication networks supporting
multiple services, namely, multimedia applications, involve
the selection of paths satisfying multiple constraints (of a
technical nature) and seeking simultaneously to “optimize”
the associated metrics. Although traditional models in this
area are single-objective, in many situations, it is important
to consider different, eventually conflicting, objectives. In
this paper, we consider a bicriterion model dedicated to
calculating nondominated paths for specific traffic flows
(associated with video services) in multiservice high-speed
networks. The mathematical formulation of the problem
and the bicriterion algorithmic approach developed for its
resolution are presented together with computational tests
regarding an application to video-traffic routing in a high-
speed network. The algorithmic approach is an adaptation
of recent work by Ernesto Martins and his collaborators,
namely, the MPS algorithm. © 2003 Wiley Periodicals, Inc.
Keywords: path ranking; bicriterion shortest path; multimedia
network; routing problems
1. INTRODUCTION
Routing problems in communication networks support-
ing multiple services, namely, multimedia applications, in-
volve the selection of paths satisfying multiple constraints
of a technical nature, designated as QoS (Quality of Service)
requirements and seeking simultaneously to “optimize” the
chosen objective functions. The objective functions are con-
cerned with the necessity of minimizing the consumption of
(transmission) resources along a path and to obtain a min-
imum negative impact on all other traffic flows that may use
the network. The specific models of these cost functions and
of the QoS constraints depend on the type of multimedia
service associated with the “calls” which are being routed
from origin to destination. In this context, the term traffic
flow is the representation (usually of a stochastic nature) of
the calls associated with a given application/service, which
are being offered and transported by the network. Typical
objective functions are the number of arcs (usually desig-
nated in telecommunications as hops or links) and the cost
of accepting a call in each arc, as measured by an appro-
priate traffic model related to the bandwidth available in
each link. As for the constraints on the paths, in the case of
multimedia applications, these are typically the minimum
bandwidth required by the call and the maximum allowed
delay and jitter.
Although traditional models in this area are single-ob-
jective, in many situations, it is important to consider dif-
ferent, eventually conflicting objectives. Routing algorithms
that have been employed in current networks, or proposed
for this type of problem, are heuristics based on the Dijkstra
or Bellman–Ford shortest path algorithms. Significant ex-
amples of this type of approach are found in Kompella et al.
[7], Lee et al. [8], and Pornavalai et al. [16].
Received October 2001; accepted January 2003
Correspondence to: M. M. B. Pascoal; marta@mat.uc.pt
Contract grant sponsor: Fundac¸a´o para a Cieˆncia e Tecnologia (FCT);
contract grant number: POCTI/GES/37707/2001
Contract grant sponsor: Portuguese Ministry of Science and Technology (MCT)
© 2003 Wiley Periodicals, Inc.
NETWORKS, Vol. 41(4), 206–220 2003

Having in mind to explore the multicriterion nature of
this type of problem, this paper considers a bicriterion
model dedicated to calculating the whole set of nondomi-
nated paths for traffic flows associated with multimedia-
type services in multiservice networks. For this purpose, an
exact algorithmic approach is developed based on the bicri-
terion shortest path algorithm by Clı´maco and Martins [5]
and on the MPS algorithm [11, 12]. Note that both algo-
rithms belong to a research stream headed by Ernesto Mar-
tins at the University of Coimbra during the last two de-
cades. The speed of the proposed approach in calculating
the set of nondominated solutions seems to make it rather
appropriate for application to the selection of nondominated
solutions in networks of practicable size, up to certain
limits, as discussed in the analysis of computational results
and in the Conclusions.
The major contributions of this paper are the following.
It is an application of a bicriterion shortest path model to a
multimedia network routing problem (concerning the rele-
vance of multicriterion shortest path models in practical
applications, see [15]). As far as we know, this is the first
time that an exact algorithm is used for obtaining the solu-
tions of a bicriterion model of this specific type; for this
purpose, it was necessary to adapt a ranking algorithm for
generating the set of nondominated paths. It would be
expected that the use of a labeling algorithm could be a
better approach; however, the explicit consideration of ad-
ditional constraints in the bicriterion shortest path problem
showed that the ranking algorithm leads to a better perfor-
mance. This new approach was tested on randomly gener-
ated networks and on U.S. intercity-based networks, thereby
simulating realistic types of applications. Although the
number of nondominated solutions obtained is not very
high, the advantages of using a bicriterion approach in many
problems of this type will be made clear.
The notation, the basic definitions, and the mathematical
formulation of the routing problem are presented in Section
2 of the paper. The algorithmic approach dedicated to the
calculation of the set of nondominated solutions is described
in Section 3. An application of this model to a specific
routing problem of video traffic in a high-speed network
together with extensive computational results are presented
in Section 4. Conclusions concerning the inherent advan-
tages of this approach and its applicability are outlined in
the final section.
2. MATHEMATICAL FORMULATION
In this section, we will recall some basic concepts and
present the multimedia traffic routing problem and its for-
mulation in terms of a bicriterion shortest path problem.
In a teletraffic routing problem, we consider a represen-
tation of a communication network, the nodes of which may
represent routers, servers, or switches and the arcs of which
represent links in the network with a certain transmission
capacity expressed in terms of bandwidth.
Let (
, ) represent an undirected network, where


{v1, . . . , vn} denotes the set of nodes and 
{a1, . . . ,
am} denotes the set of arcs (or links). Every arc ak

corresponds to an unordered pair (i, j), where i, j

.
Two distinct nodes are considered in this network: s (the
initial node) and t (the terminal node).
With no loss of generality, it is assumed that there is, at
most, one arc between a given pair of nodes. Therefore, a
path from i

to j

in (
, ) is defined as a
sequence of nodes in the network, p
i  v1, v2, . . . , j
 v

, where (vk, vk1)
, for any k
{1, . . . ,  
1}. A path is said to be a null path if it is formed only by
one node. A cycle (or loop) is a path with no repeated nodes,
except the first one which coincides with the last. A path p,
the nodes of which are all different, that is, a path without
cycles, is said to be a loopless path.
The set of paths (loopless paths) from i to j in (
, ) will
be denoted by ij (
ij) and st (
st) will be denoted by 
(
). A subpath of a path p is a subsequence of nodes of p.
Let u be a node of p; then, subp(s, u) represents its subpath
from s to u. Given two paths p
iu and q
uj, the
concatenation of p and q, denoted by p { q
ij, is the
path formed by p and followed by q. Sometimes, p { (i, j)
will be written instead of p { i, j.
Let us now introduce the multimedia traffic routing prob-
lem as a network problem. Assume that three values are
associated with each arc (or link) (i, j) in (
, ) namely, cij
 0, representing the cost of (i, j), bij  0, representing
the available bandwidth of (i, j), and, finally, dij  0,
representing the associated delay. Moreover, let c, b, and d
be functions which assign to each path p, respectively, c( p)

¥(i, j)
p cij, b( p)
min(i, j)
p{bij} and d( p)
¥(i, j)
p
dij. Let us still consider another function h which assigns to
each path p its number of arcs. Note that the cost cij of
accepting a call on arc (i, j) is, in general, a function of
some associated link working condition and the objective of
minimizing c is to obtain the most favorable traffic distri-
bution in the overall network (maximum traffic carried). In
most models, cij is a function of the blocking probability or
the available bandwidth of the arc.
Given the values jitter
IN, bandwidth
IR, and delay

IR, the goal of the problem presented in this work is to
determine loopless paths p

with, simultaneously, a
minimum cost and a minimum number of arcs and also
satisfying the following constraints:
● b( p)
bandwidth;
● d( p)  delay;
● p has at most jitter arcs (jitter constraints are expressed in
terms of the maximum number of arcs).
In other words, considering f :  3
2 such that f( p)

(c( p), h( p)), we want to
“min”

fp : p


1
s. a. bp
bandwidth 2
dp delay 3
hp jitter. 4
NETWORKS—2003 207