Photonic Network Communications, 2:3, 267±295, 2000
# 2000 Kluwer Academic Publishers. Manufactured in The Netherlands.
A Comparison of Allocation Policies in Wavelength Routing Networks*
Yuhong Zhu, George N. Rouskas, Harry G. Perros
Department of Computer Science, North Carolina State University, Raleigh, NC 27695-7534
Received March 15, 2000; Revised April 28, 2000
Abstract. We consider wavelength routing networks with and without wavelength converters, and several wavelength allocation policies.
Through numerical and simulation results we obtain upper and lower bounds on the blocking probabilities for two wavelength allocation
policies that are most likely to be used in practice, namely, most-used and ®rst-®t allocation. These bounds are the blocking probabilities
obtained by the random wavelength allocation policy with either no converters or with converters at all nodes of the network. Furthermore, we
demonstrate that using the most-used or ®rst-®t policies gives an improvement on call blocking probabilities that is equivalent to employing
converters at a number of nodes in a network with the random allocation policy. These results have been obtained for a wide range of loads for
both single-path and general mesh topology networks. The main conclusion of our work is that the gains obtained by employing specialized and
expensive hardware (namely, wavelength converters) can be realized cost-effectively by making more intelligent choices in software (namely,
the wavelength allocation policy).
Keywords: wavelength division multiplexing, wavelength routing networks, call blocking probability, wavelength allocation
Recent advances in wavelength division multiplexing
(WDM) and optical switching make it possible to
contemplate the deployment of wavelength routing
networks that will provide backbone connectivity
over wide-area distances and at very high data
capacities [8,4]. A wavelength routing network
consists of wavelength routers and the ®ber links
that interconnect them [6,11,7]. Wavelength routers
are optical switches capable of routing a light signal at
a given wavelength from any input port to any output
port, making it possible to establish end-to-end
lightpaths, i.e., direct optical connections without
any intermediate electronics. The functionality of
optical switches may be enhanced by employing
wavelength converters, devices that are capable of
shifting an incoming wavelength to a different
outgoing wavelength . Wavelength conversion is
a desirable feature since it improves the performance
of the network in terms of call blocking probability.
However, this gain in performance must be weighted
against the cost of wavelength converters.
While the operation of wavelength routing net-
works is expected to be similar to that of conventional
circuit-switched networks, several new issues arise
which add signi®cant complexity to the problems of
design and performance evaluation of the former.
Speci®cally, the existence of multiple distinct wave-
lengths makes it necessary to employ a wavelength
allocation policy to assign an available wavelength to
an incoming call. Similarly, the wavelength conver-
sion feature gives rise to new problems associated
with evaluating the bene®ts of conversion and
optimally placing the converters at the various
network nodes. Also, dynamic (or adaptive) routing
is tightly coupled with wavelength allocation, since it
involves a search over the available wavelengths in
addition to a search over the possible paths for
establishing a call.
The problem of computing call blocking probabil-
ities under static (®xed or alternate) routing with
random wavelength allocation and with or without
wavelength converters has been studied
[1,13,2,10,16,18]. The model presented in Barry and
Humblet  is based on the assumption that the
wavelength use on each link is characterized by a
®xed probability, independently of other wavelengths
and links, and thus, it does not capture the dynamic
nature of traf®c. In Kovacevic and Acampora  it
*This work was supported by the NSF under grant ANI-9805016.