SAN Models of Optical Network
Joanna Tomasik
Computer Science Department,
Supélec, France
Summary
•
•
•
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DBORN (-s, -a)
SAN
DBORN-a by SAN
Perspectives of the analytical
optical network modelling
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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DBORN : Double Bus Optical Ring Network
modelling aim:
UPSTREAM BUS
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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Everything You Always Wanted to Know
about DBORN
(But Were Afraid to Ask)
• Nodes far from the HUB: are they put at a
disadvantage « too much »?
• The fibre: is it efficiently used? (filling)
• Electronic packets: how long do they have
to wait and how many of them are lost?
• Big electronic packets: do they block their
colleagues? (HOL, segmentation)
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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DBORN-s
synchronous (fixed length packet)
Si
Si+1
n=1
n=0
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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DBORN-s : advantages
The ring is synchronised:
• if a station finds a free space, its length is
known
• a station knows when to start to test the
beginning of a posible free space.
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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DBORN-s : drawbacks
The ring is synchronised :
• optical packets are not always completely
filled,
• necessity of packetisation/depacketisation in
the HUB.
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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DBORN-a
asynchronous (variable-length packet)
Si
Si+1
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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DBORN-a : advantages
The ring is asynchronous:
• there is no packetisation/depacketisation in
the HUB,
• there is no filling algorithm.
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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DBORN-a : drawbacks
The ring is asynchronous :
• a station does not know the length of a found
free space,
• a station has to test constantly an appearance
of free space,
• big electronic packets are prone to be delayed
(and they have tendency to block the others…).
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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DBORN parameters:
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fibre throughput, number of wavelengths
optical packet length (synchronised network)
number of stations attached to the ring
distribution of load emitted by stations
electronic buffers capacity
generation rates of electronic packets
distribution of electronic packet sizes
scheduling discipline in buffers
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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SAN : Stochastic Automata Network
A formalism
of the presentation of a Markovian model
as a set of stochastic processes allowing us to
construct:
• transition matrix (continuous time) or
• stochastic matrix (discrete time)
of the corresponding Markov chain.
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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Transitions in an SAN (1/2)
• local transitions between states
of an SA(i)
(constant or functional rates) :
transition matrix Q(i)
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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Transitions in an SAN (2/2)
• global transitions performed
simultaneously in at least two
SAs, fired by an synchronisation
event (e,t,C) (constant or
functional rate t) : « transition »
matrix S(i)e
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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The i-th station description
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Edinburgh 2004
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Flow of electronic packets (1/2)
• electronic packets : small, mean, big
(classes 1, 2, 3)
• generated by the exponential
sources with rates : g1, g2, g3
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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Flow of electronic packets (2/2)
• electronic packet sizes et their
lengths (in time unit):
50 B, 500 B, 1500 B : tu, 10◊tu, 30◊tu
• transition rates:
t1 = 1/tu, t2 = 1/(10tu), t3 = 1/(30tu)
• delay of a free space test: q
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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Description of a station (edge node)
• the fibre state: s(0),
• numbers of packets of classes 1, 2, 3
in the buffer: s(1), s(2), s(3).
A chain state: (s(0), s(1), s(2), s(3))
The probability that a packet of class k
is first to be transmitted: pk
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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Synchronisation events
• ek : transmission of an electronic
packet of k class on the fibre
(it involves SA(0) and SA(k)
simultaneously)
• Ck : firing condition of ek
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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Fibre automaton for the i-th station, i>1
(0)
SA
li and mi depend on the position i
of the station on the ring
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Edinburgh 2004
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Fibre automaton for the 1st station
(0)
SA
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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Buffer automata of the station i for the class k
(k)
SA , k=1, 2, 3
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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Attainable states, number of chain states
a1 = 1; a2 = 10; a3 = 30;
a1s(1)+ a2s(2)+ a3s(3) £ B
B1=B/a1; B2=B/a2; B3=B/a3;
N1 ( B )
=
B2
B1 + 1
N 2 ( B) =
∑ N ( B − iα
N3 ( B) =
∑ N ( B − iα )
i =0
B3
i =0
1
2
2
)
N = 32N3(B)
3
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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Comparison with simulation
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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DBORN-s…
…was modelled by a Markov chain
in discrete time
(but not with SAN…)
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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There is still some things to do
with the modelling of DBORN…
• Introduction of control mechanisms
in DBORN-a (delays imposed)
• Introduction timing mechanisms in
nodes (Time-Out)
• …
Joanna Tomasik, PASTA Workshop,
Edinburgh 2004
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