Photonic Network Communications, 3:4, 383±390, 2001
# 2001 Kluwer Academic Publishers. Manufactured in The Netherlands.
Approximate Modeling of Optical Buffers for Variable Length Packets
D.E.I.S., University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
Received January 17, 2001; Revised June 10, 2001
Abstract. This paper addresses the problem of dimensioning buffers realized by means of ®ber delay lines in optical routers able to switch
packets that have variable length and are sent asynchronously on the optical links.
The optical buffer is analyzed focusing on the different behavior of a delay buffer and an electronic memory. The role of the time unit of the
®ber delay lines is discussed, showing that it is a crucial parameter to determine the queuing performance.
The paper presents two approximate analytical models that can be used both for analysis and engineering of the optical buffer and in
particular to dimension the buffer time unit in an way that is optimal with respect to packet loss probability. The ®rst model is based on an
in®nite queuing approximation. It is not very accurate and is valid for a limited set of values of the traf®c load, but is extremely simple. The
second model is based on a ®nite queuing approximation. It is more complex but more accurate and is valid for any value of traf®c load.
The accuracy of the models is compared with simulation and their range of applicability purposes is discussed.
Keywords: optical packet switching, ®ber delay line buffers, optical internet, queuing systems
The explosion of the Internet, with the exponential
increase of traf®c in the national and international
backbones, requires powerful, very ¯exible and
scalable networks. The optical technology is able to
meet these requests providing a very high bandwidth
and a good ¯exiblility as well as scalability with the
introduction of dense wavelength division multi-
plexing (DWDM) systems.
Optical packet switching is posed to be the next
step towards the ful®llment of the aforementioned
needs, making available the optical resource on a per
packet basis, and several network and switching fabric
architectures for optical packet switching have been
investigated recently (see, for instance, Yao et al. 
for a survey).
In this paper, the focus is placed on optical buffers,
that are an integral part of any optical packet switch.
Up to now, the most common way to realize an optical
buffer has been by means of ®ber delay lines (FDLs).
Since the purpose of the FDLs is to delay a packet,
their length is measured in terms of delay units, called
D in this paper. In a network with synchronous ®xed
length packets it is natural to choose D equal to the
length of the packets. In this case, the optical buffer is
equivalent to a normal queue and the teletraf®c
performance is related to the buffer occupancy,
namely the number of packets in the buffer.
Dimensioning of FDL buffers as well as congestion
resolution techniques tailored to this scenario has
been widely studied in the last few years [2±5].
On the other hand, in the case of asynchronous
variable length packets the behavior of the delay
buffer is different from that of a normal queue, as
pointed out in Tance
vski et al.  and Callegeti . At
the same time, the problem is extremely up to date
since the proposals for optical packet switching to
support Internet traf®c goes into the direction of the
so-called ``optical burst switching'', where packets
have variable length [8,9].
This paper presents and compares two approximate
analytical models that can be used to engineer an
optical buffer in this case. The models were originally
presented separately in Callegati [7, 10]. Here they are
reviewed in a uniform perspective and compared in
terms of performance and accuracy. The models are
not tailored to a speci®c switching matrix, and only
assume output queuing and a ®rst-come-®rst-served
scheduling policy. The focus is on a single output
buffer, seen as a stand-alone queuing system. In a real
implementation, it is very unlikely that an optical
packet switch will be equipped with a set of FDLs per
output port. Usually a switching matrix is equipped-