The comparative analysis of big networks with various network topologies

Transcription

1 The Seventh International Conference on Network Analysis NET June 2017, Nizhniy Novgorod, Russia 1 The comparative analysis of big networks with various network topologies Ilya Kurochkin 12, Alexandra Prun 1, Pavel Ivanov 2 1 Institute for information transmission problems of Russian academy of sciences 2 National university of science and technology MISiS

2 Base networks topologies 2

3 3 Cisco telecommunication network design scheme * from ciscopress.com

4 4 Distance between nodes Max distance(diameter) = less than 4-5 edges in route

5 Threshold of order of vertex 5

6 6 Network topologies for big corporative networks (datacenter, supercomputer et al.) Fat tree N-dimensional torus N-dimensional grid Hypercube Dragonfly Jellyfish All-connected topology

7 All-connected network topology 7

8 Grid 8

9 Torus 9

10 10 Hypercube

11 11 FatTree All-known and useful network topology Better for big networks than classical tree Restriction of vertex order is possible The fault tolerance network topology but is sensitive to multiple failures

12 FatTree 12

13 JellyFish 13

14 14 JellyFish Stochastic network topology Simple to add or delete nodes Restriction of vertex order is possible Fault tolerance and scalable network topology

15 DragonFly 15

16 16 DragonFly Hierarchical network topology Restriction of vertex order is possible Fault tolerance and scalable network topology

17 17 Attempts to comparative analysis different network topologies Singla, A., Hong, C. Y., Popa, L., & Godfrey, P. B. (2012, April). Jellyfish: Networking Data Centers, Randomly. In NSDI (Vol. 12) Williams, B., & Camp, T. (2002, June). Comparison of broadcasting techniques for mobile ad hoc networks. In Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing ACM. Li, M., Li, Z., & Vasilakos, A. V. (2013). A survey on topology control in wireless sensor networks: Taxonomy, comparative study, and open issues. Proceedings of the IEEE, 101(12) Raveau, S., Guo, Z., Muñoz, J. C., & Wilson, N. H. (2014). A behavioural comparison of route choice on metro networks: Time, transfers, crowding, topology and socio-demographics. Transportation Research Part A: Policy and Practice, 66

18 18 Parameters for comparative analysis Group 1. Parameters of initial graph Group 2. Results of network simulation Network size Network diameter Network resource Percent of nonnull edges Min/mean/max capacity of edges Et al. Total flow refusals Values of min cuts between pairs (Source- Target) Parameters of end graph Et al.

19 19 Network model Telecommunication network consisting of commutation nodes(vertices) and communication edges with limited capacities Network has set of pairs(source-target) and Set of sequence requests for flow route which have to be sent from one vertex(source node) to another (target node) Model has discrete time (timeticks) Main goal maximized total flow before refusal (first or total)

20 20 Network + set of requests Let G(A, B) be a network graph consisting of N vertices A 1, A 2,,A N, and K edges B 1,,B K, with b k >0, k=1,2,,k, capacities. And set of pairs Source-Target (S i ; T i ), i=1,2, P, S i,t i A, P N(N-1)/2 Set of request for commodity flow set Order j (PairNumber, StartTime, LifeTime, FlowSize), j=1,2,,r Requests arrive sequentially in time Total flow j FlowSize j for the satisfied requests only Used centralized dynamical routing

21 21 Prepare data for simulation Generate network graph with certain network topology Select set of pairs (Source-Target) Genearate set of requests Order j with properties StartTime (random values with combination of exponential and uniform distributions) LifeTime (random values with normal distribution) FlowSize (random values with uniform distribution)

22 22 Check of adequacy of parameters Max of mincuts Theoretical assessment of network loading Flow Mean of mincuts Min of mincuts Time ticks

23 One more method for comparative analysis 23

24 24 Algorithms for minimal cuts Algorithms for determine values of minimal cuts o Ford-Falkerson algorithm o Edmonds-Karp modification o Dinits algorithm o Karzanov algorithm Algorithms for determine set of edges of minimal cuts set o Karger algorithm o Stoer-Wagner algorithm Algorithms for determine each minimal cut o Timofeev-Karzanov algorithm

25 Initial parameters for simulation 25 vetrices Order of vertex FatTree pair (S,T) timeticks in simulation requests vetrices Order of vertex JellyFish pair (S,T) timeticks in simulation requests vetrices Order of vertex DragonFly pair (S,T) timeticks in simulation requests

26 26 Parameters of graph (in the moment) Min edge capacity Max edge capacity FatTree JellyFish DragonFly FatTree JellyFish DragonFly Percent of attain pairs(source-target) FatTree JellyFish DragonFly nonnull edge FatTree JellyFish DragonFly

27 27 Preliminary results of simulation processed requests refusal requests FatTree nonnull edges (start) nonnull edges (stop) processed requests refusal requests JellyFish nonnull edges (start) nonnull edges (stop) processed requests refusal requests DragonFly nonnull edges (start) nonnull edges (stop)

28 28 Example of preliminary results 18 Capacity reduction in % FatTree JellyFish DragonFly

29 29 Use in distributed computing The BOINC platform (Berkeley Open Infrastructure for Network Computing) is an open noncommercial software for the organization of the voluntary distributed computing on personal computers. For tasks of high computing complexity the versions for usage in multiprocessor systems and the version for the distributed computing on BOINC platform is implemented.

30 30 Conclusions Modified technique for comparative analysis of networks with various network topology is given Define groups of estimate parameters for comparative analysis Generators of network topology are realized Usefulness of the parameters characterizing the minimum sections is confirmed In future: Define more parameters Big experiment for DragonFly, JellyFish and FatTree networks topologies

31 31 Thank you for attention Centre for distributed computing Institute for information transmission problem Russian academy of sciences (IITP RAS) web: distributed-computing.ru