Photonic Network Communications, 2:3, 215±225, 2000
# 2000 Kluwer Academic Publishers. Manufactured in The Netherlands.
Network Dimensioning in WDM-Based All-Optical Networks
Chun-Ming Lee, Chi-Chun R. Hui, Frank F.-K. Tong, Peter T.-S. Yum
Department of Information Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
E-mail: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
Received September 17, 1999; Revised February 2, 2000
Abstract. The problem of network dimensioning, which involves optimal network designs using minimal resources for a given well-predicted
traf®c between individual nodes but without a pre-determined network topology, is analyzed in details in this paper. Such optimal designs are
critical as the network resources are directly related to the cost of implementation. The problem complexity increases as the traf®c between
every node pair varies in a periodic manner. Furthermore, the presence of wavelength con¯icts makes the network-dimensioning problem
distinct and more complicated than that for traditional circuit-switching networks. Here, we adopt the approach based on a multi-commodity
¯ow problem. A general cost function covering the resources of all system components is formulated, and two solution approaches are
presented; one based on integer programming and one on heuristics.
Keywords: WDM networks, network dimensioning
Wavelength routing networks [1,2] that are based on
wavelength division multiplexing (WDM) has
become one of the most viable architectures to
achieve a scalable, high-capacity all-optical network.
Although suffering from complex architecture and
management control, the wavelength routing network
has many advantages over the simple broadcast-and-
select network  architecture in wavelength utiliza-
tion, where the same wavelength can be used for
multiple connections in spatially disjoint parts of the
network. The concept of wavelength reuse not only
can expand the network capability in its scalability in
number of nodes and distances, but the small limited
number of wavelengths required relaxes the require-
ments on individual electro-optics components,
making the all-optical network more realizable.
Already, several large-scale WDM networks are
currently being implemented in U.S. [4,5], Europe
, and Japan .
While there is substantial progress and many
studies on different aspects of wavelength routing
networks are made, the network dimensioning
problem, i.e., how to maximize the use of the limited
wavelength resources for different traf®c patterns in
different time segments, is not completely understood.
A core problem in network dimensioning is optical
path assignment. Optical path assignment algorithms
based on integer linear programming for some
wavelength-routing-network con®gurations were pre-
viously reported [7,8]. The network con®guration of
our interest is a variation of the considered wave-
length routing networks [1±6] with an intention to
reduce the size of the wavelength cross-connects and
to improve the network ef®ciency. In addition, results
derived from the network dimensioning analyses yield
essential information on optimal network planning.
This can be translated to minimal network imple-
Two solution approaches, one based on integer
programming and the other based on heuristic, will be
presented. In our analyses, we only assume the
knowledge of the number of required network nodes
and the inter-node traf®c patterns. Although both
approaches can be applied to wavelength routing
networks with and without wavelength conversions,
we restrict our analyses to the latter con®guration
because the former is a simpli®ed case of the latter .
Due to the immense size of the problem, only outlines
of the solution are given for the integer programming
approach based on a multi-commodity ¯ow model.
An algorithm based on minimum variance is
established for the heuristic approach, and its results
are compared with another heuristic based on shortest
path. As will be discussed in a later section, the