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SAN Models of Optical Network Joanna Tomasik Computer Science Department, Supélec, France Summary • • • • DBORN (-s, -a) SAN DBORN-a by SAN Perspectives of the analytical optical network modelling Joanna Tomasik, PASTA Workshop, Edinburgh 2004 2 DBORN : Double Bus Optical Ring Network modelling aim: UPSTREAM BUS Joanna Tomasik, PASTA Workshop, Edinburgh 2004 3 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 4 DBORN-s synchronous (fixed length packet) Si Si+1 n=1 n=0 Joanna Tomasik, PASTA Workshop, Edinburgh 2004 5 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 6 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 7 DBORN-a asynchronous (variable-length packet) Si Si+1 Joanna Tomasik, PASTA Workshop, Edinburgh 2004 8 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 9 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 10 DBORN parameters: • • • • • • • • 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 11 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 12 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 13 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 14 The i-th station description Joanna Tomasik, PASTA Workshop, Edinburgh 2004 15 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 16 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 17 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 18 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 19 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 Joanna Tomasik, PASTA Workshop, Edinburgh 2004 20 Fibre automaton for the 1st station (0) SA Joanna Tomasik, PASTA Workshop, Edinburgh 2004 21 Buffer automata of the station i for the class k (k) SA , k=1, 2, 3 Joanna Tomasik, PASTA Workshop, Edinburgh 2004 22 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 23 Comparison with simulation Joanna Tomasik, PASTA Workshop, Edinburgh 2004 24 DBORN-s… …was modelled by a Markov chain in discrete time (but not with SAN…) Joanna Tomasik, PASTA Workshop, Edinburgh 2004 25 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 26