Survivability Function A Measure of Disaster-Based Routing Performance

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1 Survivability Function A Measure of Disaster-Based Routing Perforance Journal Club Presentation on W. Molisz. Survivability function-a easure of disaster-based routing perforance. IEEE Journal on Selected Areas in Counications 22(9): Noveber July 6 th 2007 Abdul Jabbar Mohaad Research Group Inforation and Telecounication Technology Center University of Kansas 07 July 2007 Abdul Jabbar 1/27

2 Outline Introduction Related Work Network Survivability Model Network Model Survivability Function Survivability Attributes Survivability Assessent Models Calculation Coplexity Finding Survivability Function Heuristic Procedures Deand Matrix Backbone Network Exaple Conclusion 07 July 2007 Abdul Jabbar 2/27

3 Introduction Internet Traffic Explosive growth in traffic carried by telco networks Potential ipact of network failure significant traffic carried by a single fiber WDM adds to this capacity (up to Tbits per sec) network survivability is crucial higher ipact in ters of traffic loss scope & users affected Network survivability assessent survivability function & survivability attributes easure of disaster-based perforance illustrated exaple on polish backbone network 07 July 2007 Abdul Jabbar 3/27

4 Introduction Objectives Disaster type one or ore node and/or arc failures Survivability function the probability function of the percentage of total data flow delivered after failure Survivability attributes easures of disaster based routing perforance p-percentile values worst case survivability Factors considered varying traffic environents affect of routing protocols traffic priorities network load 07 July 2007 Abdul Jabbar 4/27

5 Related Work Related works in network survivability Fiber network survivability (Tsong-Ho Wu) optical network survivability ANSI T1A1 subcoittee concept of disaster-based survivability perforance following the occurrence of a failure Survivability function (Liew & Lu) probabilistic easure of network survivability nuber of users/nodes still connected fraction of working links Shortcoings no foral definitions no foral odels to express survivability as a whole 07 July 2007 Abdul Jabbar 5/27

6 Network Survivability Model Network odel network odeled as a directed graph Г(N A) where N is a set of nodes N =N ; A is set of directed arcs A = M topology described with node-to-node incidence atrix each arc has a finite capacity C ; = 1 2 M. flows between all pair of nodes given by deand atrix R where r pq ; p = 1 2 N; q = 1 2 N; p q is a coodity failures a ij 1 if arc e ( i j) A = 0 otherwise + randoness and statistical independence is assued + network nodes and arcs fail with known distribution 07 July 2007 Abdul Jabbar 6/27

7 Network Survivability Model Survivability function failure scenario (denoted by ζ ) is set of coponent failures subset N D out of N nodes or subset M D out of M arcs note: different scenarios ( ζ ) ay result in siilar surviv. values survivability function: probability function of total data flow delivered after failure S( x) = P( ζ ) ζ : X ( ζ ) = x X ( ζ ) P ( ζ ) rando variable percentage of flow delivered after failure ζ probability of scenario ζ characterized by the percentage x of total data flow still delivered S ( x ) always less than 1 07 July 2007 Abdul Jabbar 7/27

8 Network Survivability Model Survivability attributes based on S (x) expected percentage of total data flow delivered after a failure p percentile survivability E ( x) = x S( x) x P px = P( X = p) worst case survivability x = in S ( x) > 0 x 07 July 2007 Abdul Jabbar 8/27

9 Survivability Assessent Models Coplexity of calculations assue arc failures only in the given M arcs nuber of scenarios to be investigated to calculate S (x) is 2 M intractable even for sall networks Siplified calculations assue probability distribution of arc failures to be unifor each arc M fails with a probability of M -1 Probability P ( ζ ) of scenario ζ with M D failed arcs P(ζ ) = 1 M M l= 1 M k = 1 D M D M 1 M P ( ζ ) decreases rapidly with increasing M D 07 July 2007 Abdul Jabbar 9/27

10 Survivability Assessent Models Siplified calculations the nuber of such scenarios with M D failed arcs LM D M = M D = M D M!!( M M )! increase in the cuulative probability ass (c.p.) due to all scenarios with M D failed arcs vm = LM D D actual value of c.p. achieved due to all scenarios investigated fro no arc failures to M D failed arcs v + v + K+ 0 1 calculate S (x) until c.p. of all exained scenarios reaches a given threshold (e.g. 99%) 07 July 2007 Abdul Jabbar 10/27 D ( ζ ) P( ζ ) v M D

11 Survivability Assessent Models Siplified calculations [Molisz-2004] 07 July 2007 Abdul Jabbar 11/27

12 Survivability Assessent Models Finding survivability functions depends on the routing protocol user priorities and network load consider only the routing protocol DV and flooding in case of DV + find optial coodity for each failure scenario ζ + ulti-flow coodity route optiization can be set as linear prograing proble + can be solved using a linear prograing package (e.g. PPRN) + constraint atrix too large with few non-zero eleents heuristic procedure based on Seidler s result + optial ulti-coodity flows x* are a superposition of the nonbifurcated flows on all shortest paths where the length of the path is the cost of sending unit data on all the coponent links 07 July 2007 Abdul Jabbar 12/27

13 07 July 2007 Abdul Jabbar 13/27 Journal Club: Molisz-2004 Survivability Assessent Models Finding survivability functions ( ) ( ) = = = = = = = = > = = + = = K k M k k k K k k k k k k n j N j A j n e k n i N i A n i e k x cost x M K k x nonnegativity constraints M c x finite arc capacities t n r s n r x x flow conservation constraint x ; 12 ; ) ( : ; 12 ; ) ( : The linear cost function is defined as 12 ; 12 0; 12 ; otherwise 0 if if subject to: iniizing cost function Find optiu ulticoodity flows ϕ ϕ K K K K K

14 Survivability Assessent - Heuristic procedure (DV) 0. preparatory step: define disaster type (node/arc) c.p. threshold calculate prob. of no failures and let S (x = 0) = 0 1. generate the next ost probable failure scenario ζ 2. set to zero all eleents of A corresponding to failures in ζ 1. check for net. partitioning if so add P(ζ) to value of S (x = 0) else go to step1 07 July 2007 Abdul Jabbar 14/27

15 Survivability Assessent - Heuristic procedure (DV) 0. preparatory step: define disaster type (node/arc) c.p. threshold calculate prob. of no failures and let S (x = 0) = 0 1. generate the next ost probable failure scenario ζ 2. set to zero all eleents of A corresponding to failures in ζ 1. check for net. partitioning if so add P(ζ) to value of S (x = 0) else go to step1 3. for each coodity find the shortest path and its capacity 1. if deand < capacity set flow = deand; calculate residual capacity on the path and go to set if deand >capacity set flow = capacity; find the next shortest path and allocate the reaining portion of the deand to it 3. calculate which percentage of total flow x s has been found and save pair ( S x P(ζ) ) to the database 4. if c.p. < threshold go to step 1 other wise go to step 5 5. group order results and calculate the survivability function for whole range (0 100%) of x with specified granularity (say 1%) 07 July 2007 Abdul Jabbar 15/27

16 Survivability Assessent - Heuristic procedure (FL) 1. For flooding algorith sae as DV except for step allocates ulti coodity flows on shortest paths 3.2 the possibility of sending additional flows is exained. + at a selected node the procedure finds any other non-zero capacity paths + if found either the unsatisfied deand or the capacity of the new path is assigned for this coodity flow ( as suppleentary fraction). + stop if no path with non-zero capacity available. 07 July 2007 Abdul Jabbar 16/27

17 Survivability Assessent Deand atrix how are the deands in the previous algoriths deterined? find axiu feasible and fair flows in fully operational network denote this flow atrix as the optial flows atrix F* for a given load the atrix of required flows (deand atrix) is R=load x F* in case of priority traffic deand atrices for each priority are specified R 1 R 1 R P 07 July 2007 Abdul Jabbar 17/27

18 Backbone Network Exaple Polish backbone network N = 12 M = 34 ; C = 2.5 Gb/s survivability function in case of routing protocols + based on iniu nuber of hops and on flooding [Source: Molisz-2004] [Source: Molisz-2004] 07 July 2007 Abdul Jabbar 18/27

19 Backbone Network Exaple - Analysis Fig 1: Survivability function S(x) for node (or arc) failures load=60% routing based on iniu nuber of hops E[x] = 80.41% E[x] = 95.69% [Source: Molisz-2004] 07 July 2007 Abdul Jabbar 19/27

20 Backbone Network Exaple - Analysis Fig 1: Survivability function S(x) for node (or arc) failures load=90% routing based on iniu nuber of hops E[x] = 78.03% E[x] = 89.60% [Source: Molisz-2004] 07 July 2007 Abdul Jabbar 20/27

21 Backbone Network Exaple - Analysis Fig 1: Survivability function S(x) for node failures only load=60% routing based on iniu nuber of hops; traffic has five priorities E[x] = 80.47% [Source: Molisz-2004] 07 July 2007 Abdul Jabbar 21/27

22 Backbone Network Exaple - Analysis Fig 1: Survivability function S(x) for node failures only load=90% routing based on iniu nuber of hops traffic has five priorities E[x] = 70.47% E[x] = 78.42% E[x] = 80.47% [Source: Molisz-2004] 07 July 2007 Abdul Jabbar 22/27

23 Backbone Network Exaple - Analysis Fig 1: Survivability function S(x) for node failures only load=200% routing based on iniu nuber of hops traffic has five priorities [Source: Molisz-2004] 07 July 2007 Abdul Jabbar 23/27

24 Backbone Network Exaple - Analysis Fig 1: Survivability function S(x) for node failures only; three loads routing based on iniu nuber of hops [Source: Molisz-2004] 07 July 2007 Abdul Jabbar 24/27

25 Backbone Network Exaple - Analysis Fig 1: Survivability function S(x) for node failures only load=60% routing based on flooding; traffic has five priorities [Source: Molisz-2004] 07 July 2007 Abdul Jabbar 25/27

26 Conclusions lowest survivability occurs due to node failures routing protocol has significant ipact in. nu of hops gives relatively good results flooding diinishes survivability draatically congestion further reduces survivability greater degradation is observed at higher loads ore visible when dealing with priority traffic Quantitative evaluation of flow degradation due to failure scenarios is achieved 07 July 2007 Abdul Jabbar 26/27

27 THANK YOU! 07 July 2007 Abdul Jabbar 27/27

Oblivious Routing for Fat-Tree Based System Area Networks with Uncertain Traffic Demands

Oblivious Routing for Fat-Tree Based Syste Area Networks with Uncertain Traffic Deands Xin Yuan Wickus Nienaber Zhenhai Duan Departent of Coputer Science Florida State University Tallahassee, FL 3306 {xyuan,nienaber,duan}@cs.fsu.edu