Void-creating algorithms for fixed packet length in OPS/OBS

Transcription

1 Void-creating algorithms for fixed packet length in OPS/OBS Kurt Van Hautegem, Wouter Rogiest & Herwig Bruneel {kurt.vanhautegem, wouter.rogiest, Ghent University, Belgium (UGent) Department of Telecommunications and Information Processing (TELIN) Stochastic Modelling and Analysis of Communication Systems (SMACS)

2 Overview presentation Contention resolution & scheduling basics Void-creating scheduling algorithm Performance results Conclusions 2/24

3 Overview presentation Contention resolution & scheduling basics Void-creating scheduling algorithm Performance results Conclusions 2/24

4 The optical backbone demand for bandwidth Future: packet-based switching shared links improved usage of fiber capacity contention possible potentially, packet loss no fixed delay potentially, substantial delay main motivation of this work: improving contention resolution 3/24

5 Contention & resolution node 2, now! node 1 node 2 node 2, now! Arrival process single wavelength fixed packet lengths B exponentially distributed interarrival times (Poisson) 4/24

6 Contention & resolution node 2, now! node 1 node 2 node 2, now! Arrival process Fiber Delay Lines ( FDLs) single wavelength fixed packet lengths B exponentially distributed interarrival times (Poisson) set of fibers, # = N+1 lengths j D, j=0 N N= buffer size D= granularity = packet lenght = B 4/24

7 Provisional schedule =N D time shows already scheduled packets upon arrival of a packet horizontal axis: future time vertical lines: delays of FDLs (N=5, D=1) updated at every arrival choppy but uniform movement of all packets to the left 5/24

8 Provisional schedule choose: delay line j (j=0 N) constraints: no overlap void 1 void 2 gap =N D horizon time current algorithms: : first FDL after horizon no fillable voids are created (=voids larger than packet length B=D) 6/24

9 Overview presentation Contention resolution & scheduling basics Void-creating scheduling algorithm Performance results Conclusions 7/24

10 Overview presentation Contention resolution & scheduling basics Void-creating scheduling algorithm Performance results Conclusions 7/24

11 Void-creating scheduling algorithms gap =N D horizon time choose between normal scheduling point first FDL after horizon creates unfillable void alternative scheduling point second FDL after horizon creates fillable void 8/24

12 Why instead of? =N D gap time gap gap gap gap + D gap 1 gap 2 9/24

13 Why instead of? =N D time delay = 4 delay= 5 delay= 5 delay= 3 9/24

14 Why instead of? gap =N D horizon time IF fillable void is filled: average gap / packet: average delay / packet: stacking becomes more dense 10/24 loss probability

15 Why instead of? gap =N D horizon time IF fillable void is filled: average gap / packet: average delay / packet: stacking becomes more dense loss probability not all fillable voids will be filled: position with respect to FDL has to be favorable depends on arrival instances future packets (stochastic arrival process) gap : chance of filling horizon : chance of filling 11/24

16 Overview presentation Contention resolution & scheduling basics Void-creating scheduling algorithm Performance results Conclusions 12/24

17 Overview presentation Contention resolution & scheduling basics Void-creating scheduling algorithm Performance results Conclusions 12/24

18 Assumptions inter-arrival time packets = exponentially distributed, E[T] fixed packet size = B = 100 D = granularity = 100 N+1 = # Fiber Delay Lines = 10 load = ρ = B E[T] = 80 % AND 60 % 3 sets of simulations: without void creation single creation point actual void-creating algorithm 13/24

19 set 1: without void creation horizon always : first position after horizon no fillable voids are created ρ = 80 % : loss probability = 14,46 % ρ = 60 % : loss probability = 2,08 % 14/24

20 set 2: single creation point gap horizon YES fill it! favorable position of fillable void w.r.t. an FDL? YES NO fillable void present? YES NO (n-1) D < horizon < n D YES gap > y n D NO NO 15/24

21 set 2: single creation point gap horizon YES fill it! favorable position of fillable void w.r.t. an FDL? YES NO fillable void present? YES NO (n-1) D < horizon < n D YES gap > y n D NO n : horizon index : 1, 2,, 8 NO 15/24 y n : gap threshold : 0, 0.01,, 1

22 set 2: single creation point gap horizon Optimal gap threshold 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0, load=0.8, single creation point load=0.6, single creation point Horizon index 16/24

23 set 2: single creation point gap horizon Relative loss probability 100% 95% load=0.8, single creation point 90% 85% 80% load=0.6, single creation point Horizon index 17/24

24 set 3: actual void-creating algorithm gap horizon void creation allowed for all horizon indexes optimal gap threshold determined for each horizon index YES favorable position of fillable void w.r.t. an FDL? fillable void present? NO gap > y n D YES NO YES NO 18/24 fill it!

25 set 3: actual void-creating algorithm gap horizon void creation allowed for all horizon indexes optimal gap threshold determined for each horizon index YES fillable void present? NO y n : 0, 0.01,, 1 favorable position of fillable void w.r.t. an FDL? gap > y n D parameter space too large (~100 8 ) YES NO YES NO 18/24 fill it!

26 set 3: actual void-creating algorithm 8 optimal gap thresholds single creation point keep 7 fixed, optimize 1 (do this 8 times) 8 new gap thresholds (iteration 1) keep 7 fixed, optimize 1 (do this 8 times) 19/24 8 new gap thresholds (iteration 2)

27 set 3: actual void-creating algorithm 8 optimal gap thresholds single creation point keep 7 fixed, optimize 1 (do this 8 times) 8 new gap thresholds (iteration 1) little difference keep 7 fixed, optimize 1 (do this 8 times) 8 new gap thresholds (iteration 2) ~ convergence accept iteration 2 as approximation true optimal gap thresholds 19/24

28 set 3: actual void-creating algorithm Optimal gap threshold 1,0 0,9 0,8 0,7 0,6 0,5 0,4 load=0.8, single creation point load=0.6, single creation point load=0.8, actual algorithm 0,3 0,2 load=0.6, actual algorithm 0,1 0, Horizon index 20/24

29 set 3: actual void-creating algorithm Optimal gap threshold 1,0 0,9 0,8 0,7 0,6 0,5 0,4 load=0.8, single creation point load=0.6, single creation point load=0.8, actual algorithm 0,3 0,2 load=0.6, actual algorithm 0,1 0, Horizon index 20/24

30 set 3: actual void-creating algorithm Relative loss probability 100% 90% 80% 70% 60% 50% load=0.8, single creation point load=0.6, single creation point load=0.8, actual algorithm load=0.6, actual algorithm 40% Horizon index 21/24

31 set 3: actual void-creating algorithm Relative loss probability 100% 90% 80% 70% 60% 50% load=0.8, single creation point load=0.6, single creation point load=0.8, actual algorithm load=0.6, actual algorithm 40% Horizon index 21/24

32 Overview presentation Contention resolution & scheduling basics Void-creating scheduling algorithm Performance results Conclusions 22/24

33 Overview presentation Contention resolution & scheduling basics Void-creating scheduling algorithm Performance results Conclusions 22/24

34 Conclusions gap =N D horizon time current algorithms: void creating algorithms: or : creates fillable void (1 allowed) if filled: more dense stacking loss probability optimize void creation via gap threshold and horizon index LP reduction: load = 80 %: 32 % load = 60 %: 51 % 23/24 future work: more complex settings, mathematical approximation

35 Questions? 24/24!