Photonic Network Communications, 3:4, 391±392, 2001
# 2001 Kluwer Academic Publishers.Manufactured in The Netherlands.
Improved Performance Analysis for Synchronous Single-Hope
National Technical University of Athens, Department of Electrical and Computer Engineering, Athens, Greece
Received February 12, 2001; Revised July 2, 2001
Abstract. This note extends the work in the paper  and presents a precise method without simpli®cations of the receiver collision analysis for
the synchronous transmission protocols in the well known Passive Star WDM topology.
Keywords: wavelength division multiplexing WDM, tunable receiver, receiver collision, collision probability
In the paper  an approximate method is proposed to
evaluate the performance measures reduction due to
the ®nite number of tuneable receivers at the end
stations of a ®nite population network system using a
synchronous WDMA protocol.It is assumed that
stations are statistically identical and the successfully
transmitted data packets on the WDM Passive Star
network are uniformly distributed among M stations.
For sake of simplicity of the analysis, it is assumed
that a station may send packets to itself.
In this note we develop a rigorous method for the
analytic evaluation of P
, the mean value of the
collision probability at the destination of a data
packet due to the ®nite number of tuneable receivers.
In the proposed analysis, we assume that, if a station
Z is a source of one of the r successfully transmitted
data packets on the WDM network, the station does
not transmit to itself.This assumption is more
realistic and permits the strictly estimation of the
receiver collision phenomenon and completes the
work in Pountourakis .
We make the same assumptions made in  and use
the following steady state notations:
G average number of transmitted control packets
per minislot on the control channel.
M number of stations in the system.
v number of data channels in the system.
F number of tunable receivers of a station.
total throughput of the system, de®ned as the
average number of successfully transmitted
data packets during a data packet transmis-
sion time without the effect of receiver
r be the number of transmissions to
destination station ZZ 1; ...; M under the condi-
tion that r packets have been transmitted successfully,
r v.The probability of ®nding k packets to
destination station Z, is given by,
* National Technical University of Athens, Department of Electrical and Computer Engineering, Division of Communication, Electronic and
Information Engineering, 157 73 Zographou, Athens, Greece. E-mail: firstname.lastname@example.org