Resilient Networks. 3.1 Resilient Network Design - Intro. Mathias Fischer

Transcription

1 Mathias Fischer Resilient Networks. Resilient Network Design - Intro Prepared along: Michal Pioro and Deepankar Medhi - Routing, Flow, and Capacity Design in Communication and Computer Networks, The Morgan Kaufmann Series in Networking, 800 pages, 004

2 Outline Motivation Introduction to Network Design Problems Traffic and Demand Network Design and Routing Multi-layer Networks Network Management Notations and mathematical formulation Link-Path Formulation Link-Demand-Path-Identifier-based Notation Some basic design problems Minimizing costs of network links Capacitated design problems Shortest path routing Summary

3 A Network Analogy NY Frankfurt Moscow Peking San Francisco Kuala Lumpur Sao Paolo Johannesburg Sydney New links are expensive Economies of scale Store and forward concept Hop-by-Hop routing

4 Network Basics Communication network carries traffic Network has different links of different capacity (bandwidth) Economies of scale principle applies Traffic may be routed via different paths to destination According to store-and-forward principle Hop-by-hop We need to have enough bandwidth to carry all data We might want to reduce the average packet traversal delay 4

5 Network Design Questions Can we find better routes? Where should we add more bandwidth? Where and when should we add new nodes (and links) in the network? How does the inherent property of a network technology or protocol can affect our decision making? What level of abstraction is appropriate for a particular network for modeling purpose so that meaningful results can be obtained How to design cost-effective, resilient core/backbone networks taking into consideration properties of the network? - How to do network design? 5

6 Routing in the Internet Autonomous Systems Internet consists out of connected Autonomous Systems (AS) Stub AS: small organization (one connection to the Internet) Multi-homed AS: large organization (several connections, no transit traffic) Transit AS: Provider (several connections, transit traffic) The Internet today consists out of AS Of different size AS Exchange data packets as Peers Provider AS and Customer AS Each AS has a unique ID (number) Each AS needs to know at least one route to any other AS Bildquelle: caida.org 6

7 Communication Networks and Network Providers () Packet sending in the Internet Involves series of different AS networks Each network with own switches or routers Packet routing depends completely on the specific network Network design problems are confined within each network or administrative domain AS AS AS 7

8 Communication Networks and Network Providers () Layered (or Hierarchy of) Networks Private networks of large companies and corporations Telecommunication network providers that operate transport or transmission networks Different ISPs may use the same transport network Multi-layer network environment AS AS AS AS 4 AS 5 Transport Provider Transport Provider 8

9 Autonomous Systems in Germany Bildquelle: Institut für Internet-Sicherheit, Fachhochschule Gelsenkirchen 9

10 Communication Networks and Network Providers () Network providers Design and manage their networks Need to know traffic demands in their networks Considering all network nodes, they need to know traffic volume between any two such nodes Traffic volume matrix or demand volume matrix as input to network design required 0

11 Traffic and Demand () Task of a network Route packets from one end to another, without considering the reliability of delivery Reasons for lost packets Physical transmission errors Traffic congestion and routers running out of buffer space Task of network designer (our task) Keep delay low Design networks to prevent or at least limit congestion at routers

12 Traffic and Demand () What do we need for this? Prediction of traffic demand, e.g., via statistical approaches Estimating traffic volume by capturing statistics about traffic arrival distribution We need this information in between different network points Necessary Measurements Average arrival rate of packets Average size of packets Both influence delay

13 Traffic and Demand () Example: M/M/ queuing system Packet arrival follows Poisson process Packet size is exponentially distributed D λ p μ p C K p average delay in seconds average packet arrival in seconds average link service rate link capacity per second average packet size Average delay increases drastically when average arrival rate is closer to average service rate of the link

14 Traffic and Demand (4) What is the acceptable delay users would like to tolerate? If acceptable delay is 5 ms, then the acceptable average utilization can be no more than 64,5% on the link Good News At least for purpose of network design maximum link utilization can be used as alternative criterion to the delay However, traffic arrival does not follow Poisson process Realistic delay is worse than the calculated one In reality average utilization has to be kept lower, e.g., at 50% to achieve the 5 ms 4

15 Traffic and Demand (5) We need to know whether observed utilization is higher than acceptable threshold for a particular link type In single-link networks Measurement is easy Bandwidth can be easily added In multi-link networks Utilization is further impacted by routing of traffic flows Adding bandwidth becomes complex network design problem Lesson learned / What we need to solve network design problems Average arrival rate in between different nodes in the network Traffic demand volume as input for all network design problems 5

16 Network Design and Routing () In reality we have many source-destination (egress-ingress) traffic demands between various points in the network Traffic-demand matrix required as input to network design Goal: Determine a network with enough capacity and connectivity to route traffic, so that acceptable service guarantees can be provided In single-link networks it is sufficient to determine link utilization threshold for given traffic demand However, this is not the case in multi-link networks anymore 6

17 Network Design and Routing () Role of network design Distinction between (usually continuous) Demand Volume Units (DVU) and (usually discrete) Link Capacity Units (LCU) Three node network with traffic demand of 00Kbps between each node QoS goal: utilization threshold below 60% Three T links (LCU: each.54 Mbps) 00 Kbps/.54Mbps 9,5% Two T links (-, -) (00 +00)Kbps /.54 Mbps 9% Network design also depends on routing capabilities 00 Kbps 00 Kbps 00 Kbps 00 Kbps 00 Kbps 00 Kbps 7

18 Network Design and Routing () Some Definitions Candidate path list: All possible paths between two points Route: Particular path chosen as valid path by network design Flow: The amount of traffic associated with a route 8

19 Multi-layer Networks () Layer 5 Application Layer SMTP/ POP / IMAP/ HTTP / Endsystem Endsystem Layer 5 Application Layer Layer 4 Transport Layer Layer Network Layer UDP / TCP IP Layer 4 Transport Layer Layer Network Layer Traffic networks Aka service level Traffic arrival stochastic in nature Has switching / routing capabilities OpenFlow / MPLS / Layer Data Link Layer Layer Physical Layer Ethernet / GMPLS OC- / OC- / OC-48 / T- / Optical Networks Layer Data Link Layer Layer Physical Layer Transport networks service level traffic as demand input High-data rate services that are required to be set up at permanent or semipermanent basis Traffic deterministic or precise in nature over time 9

20 Multi-layer Networks () The architecture of communication networks A network (or layer) on top another A network may look logically diverse, but may not be diverse in another layer Implications in protection and restoration design (network resilience) due to inter-relation between layers Multi-layer network design as important problem to consider 0

21 Multi-layer Networks () - Traffic and Demand Traffic, Demand, and layered Networks Output bandwidth requirement for each Internet, telephone, and privateline service from service networks, is input demand to layer beneath Capacity requirement of one network becomes traffic demand volume for network below

22 Network Management Cycle () Network management is the entire process from planning a network, to deploying it, and to operate it on a day-to-day basis. Requires network management systems and protocols Different management tasks run at different time granularity

23 Network Management Cycle () Traffic Network Transport Network Micro-secs Mili-secs Packet Discarding, Buffer Management, Packet Routing TCP Feedback control SONET / SDH ring restoration Secs Minutes Hours Days Weeks Months Year(s) Call Routing, Call Setup, Call Admission Control, Call Rerouting, Routing, Information Update Periodic Traffic Estimation Traffic Engineering OSPF weight updates Trunk Rearrangement Traffic Network Capacity Expansion Mesh Transport Network Restoration Transport Network Routing/Loading Transport Network Capacity Planning / Expansion

24 Network Management Cycle () Traffic Networks capacity change routing update various controls Traffic Network (IP) Forecast adjustment Marketing input Traffic data secs-mins Real-Time Traffic Management days-weeks Capacity Management Traffic Engineering months-years Network Planning Network Management 4

25 Network Management Cycle () Transport Networks Capacity expansion/ protection route loading restoration Transport Network Network fill factor, loading New Transport Demand, Marketing Input mins-hours Near Real-Time Management days-weeks Capacity Management Traffic Engineering months-years Network Planning Network Management 5

26 Notation for Network Design Problems Network Design Problems Can be formally specified using mathematical notations Representation of specific design problems in compact way Eventually helps to understand the problem at hand Eventually helps to solve the problem Notations for Network Design Problems Link-Path Formulation Link-Demand-Path-Identifier-based Formulation 6

27 Link-Path Formulation () Three node network example Demand volume h ij in between nodes i and j Example demand Each demand volume between two nodes can be routed over two paths Path - Path - Path - Path -- Path -- Path -- 7

28 Link-Path Formulation () Demand between nodes and can be routed via direct link - and via alternate route -- Demand path flows x^ are non-negative, i.e., x^ > 0 for all paths Link capacities c ^, c ^ ^, c Assumption, capacity of first two links is 0 and the third is 5 8

29 Link-Path Formulation () System of linear equations and inequalities (constraints) x are unknowns for all three considered demands System has multiple solutions and defines set of feasible solutions But which solution is of interest? 9

30 Link-Path Formulation (4) Different goals/objectives possible Minimizing total routing costs Minimizing congestion of most congested link... In mathematical way, goals are expressed as objective functions that needs to be either minimized or maximized Example: Minimizing total routing costs cost of routing one unit of flow on every link along a path is simply Resulting objective function F: 0

31 Link-Path Formulation (5) Routing minimization problem Objective Function Demand Volume Constraints Capacity Constraints

32 Link-Path Formulation (6) Routing Minimization Routing minimization problem Multi-Commodity Flow Problem Multiple demands (or commodities) Need to be routed in a network simultaneously Compete for resources Optimization Context: Linear Programming Problem All constraints are linear The objective function is linear

33 Link-Path Formulation (7) Routing Minimization Optimal solution for demand Required: feasible solution for decision variables ( x) that minimize F Common sense solution Route everything on direct (cheapest) path, other x-variables are zero Total optimal cost F*=0

34 Link-Path Formulation (8) Routing Minimization However Optimal solution may not be unique Not in all cases a solution is that simple to obtain Constraints Need to be satisfied by optimal solution Especially link capacity constraints need not be violated 4

35 Link-Path Formulation (9) Routing Minimization Let s change the objective function From To For demand Solution not that easy anymore Cheapest path routing violates capacity constraints of link - We are happy to announce a solution with total cost F*=5 5

36 Link-Path Formulation (0) Routing Minimization Lessons learned from Routing Minimization Problem Changing objective function affects optimal solution to a problem and the way of finding it Carefully selection of right objective function (or goal) for particular network required, Otherwise obtained solution might not be meaningful 6

37 Link-Path Formulation () Pros and Cons All demands and paths easy to follow from node-reference point of view Works well for three-node example but not in general case Drawbacks Paths may contain many intermediate nodes Flow variables have indices of different length Some node pairs might not have any demand Not all nodes directly connected Link-Path Formulation insufficient for Multi-Commodity-Flow Problems 7

38 Link-Path Formulation () Pros and Cons More Problems When network gets larger the indices grow as well: X i-m-...-n-j No easy way to represent multiple-paths For specific demand pair when each path may go through different number of intermediate nodes Not all paths might be acceptable For example, due to the distance between the nodes This requires additional exceptions for paths not used Notation cannot handle more than one link between two nodes, e.g., multi-graph case Multiple demands between nodes cannot be handled Not possible to write summations over paths 8

39 Link-Demand-Path-Identifier-based Notation () Compact, allows to list only necessary objects Non-zero demand pairs with indices from to their total number Total number of demands D, index d (D=, d=,,) Links are assigned labels from to total number of links Total number of links E, index e (E=, e=,,) 9

40 Link-Demand-Path-Identifier-based Notation () Mapping for demand volumes h and link capacities c Path identifiers (path-flow variables) x dp Demand-pair identifier d used as first subscript Path label p for demand pair as second subscript Candidate paths for demand pair numbered from to total number Total number of candidate paths for demand d will be denoted P d Paths are labeled with index p 40

41 Link-Demand-Path-Identifier-based Notation () Example Demand between nodes and identified by label d = (first subscript) has two candidate paths (P = ) Paths - and -- are labeled with p=, (second subscript) Paths are identified as (,) and (,) Path-flow variables 4

42 Link-Demand-Path-Identifier-based Notation (4) Mapping of path identifiers and paths from: node-identifier-based notation to link-demand-path-identifier-based notation Node-identifier-based Link-demand-path-identifier-b. Path identifier Path Path identifier Path -- {,} -- {,} - {} 4

43 Link-Demand-Path-Identifier-based Notation (5) Routing Minimization Problem in Link-Demand-Path-Identifier-based Notation 4

44 Link-Demand-Path-Identifier-based Notation (6) Comparison Link-path formulation Link-demand-path-identifier-based 44

45 Link-Demand-Path-Identifier-based Notation (7) Notation Summary 45

46 DP: Minimizing Costs of Network Links () Minimizing costs of networks links Minimizing total link capacity cost required to carry given demand Assuming not a fixed, but variable capacity y e of links Demand Dimensioning Problem (DP): Determine required demand flows and link capacities to carry given demand volumes Network 4 46

47 DP: Minimizing Costs of Network Links () 4-node example network Four nodes with routable demands Node 4 is only transit node ξ e as costs for sending one unit via link e Demands: d=, only one path P ={,4} allowed d=, paths P ={5}, P ={,4} d=, paths P ={}, P ={,} Demand Demand constraints Network 4 47

48 DP: Minimizing Costs of Network Links () Demand constrains in general form Vector of flows assigned to demand d: Hence, we can write In summation notation Flow allocation vector x 48

49 DP: Minimizing Costs of Network Links (4) Capacity constraints Assures that for each link e its capacity c e (or y e, if capacity is a variable) is not exceeded by the flows using the link Sum on left side are link loads y e (total flow through that link) 49

50 DP: Minimizing Costs of Network Links (5) To write down link loads in compact manner we need to know relationships between links and paths Formally defined via link-path incidence coefficients e\ P dp P ={,4} P ={5} P ={,4} P ={} P ={,} In more compact manner via coefficient δ edp : 4 50

51 DP: Minimizing Costs of Network Links (6) Link load y e on link e in compact manner Summation over all paths appearing in routing lists of all demands, over all combinations (d,p) 5

52 DP: Minimizing Costs of Network Links (7) Minimizing capacity costs, objective function ξ e as costs for sending one unit via link e 5

53 DP: Minimizing Costs of Network Links (8) DP: Minimizing capacity costs Demand Network 4 5

54 DP: Minimizing Costs of Network Links (0) Optimal solution for DP Feasible solution (x,y) with y (x)=y =5, y (x)=y =0, y (x)=y =0,y 4 (x)=y 4 =0, y 5 (x)=y 5 =5, and thus y = (y, y, y, y 4, y 5 ) = (5,0,0,0,5) has total cost F=5 However, solution not optimal, because of usage of P with costs ζ = ξ + ξ 4 = + = 4 Other possible path P has costs ζ = ξ 5 = Demand Cost of path P dp is given by: Network 4 54

55 DP: Minimizing Costs of Network Links () Optimal solution to DP In example we need to move all the flow for demand d= from path P to path P, which gives savings of (ζ - ζ ) = per flow unit, in our case the total savings are x (ζ - ζ ) = 5 d=: x * = 5 d=: x * = 0, x * = 0 d=: x * = a, x * = 0-a, for any 0 a 0 y * = 0 a, y * = 5 + a, y * = a, y * 4 = 5, y * 5 = 0 Demand Network F * =

56 DP: Minimizing Costs of Network Links () Shortest Path allocation rule: For each demand allocate entire demand volume to its shortest path (w.r.t. to link unit costs and candidate paths) If there is more than one shortest path for a demand then demand volume can be split among shortest paths arbitrarily Works well for dimensioning problems, but no general solution approach for other multi-commodity flow problems, e.g., Restriction to non-bifurcated flows Modular design problems: in real networks capacities can be installed only in modular units (e.g., T, E, OC-) 56

57 DP: Minimizing Costs of Network Links () The observed DP is an uncapacitated design problem Another type of problem are capacitated design problems Link capacities c e given instead of variable y e Find a feasible flow allocation that satisfies demand and capacity constraints with c e appearing on the right-hand sides In such scenario there might not be an objective function, except flow routing cost minimization is required Capacitated problem in compact form 57

58 Capacitated Design Problems () 4-Node Network Example Capacity vector c = c, c, c, c 4, c 5 = (5,0,0,5,0) Additional path for d=: P = {,,4} All solutions are necessarily bifurcated Possible solution: Demand Note that d= also uses path P, its longest path When non-bifurcated solutions are required, additional constraints necessary to force single-path solution Network P P 4 P P P P 58

59 Shortest Path Routing () Shortest path routing, e.g., OSPF routing in IP networks Shortest paths are essential for network design, pre-requisite for resilient network design For each d all volume h d realized on shortest path w.r.t. to given link weight system w = w, w,, w E and link weight cost w e for link e Path selection based on additive calculation of link weights Flow allocation vector x(w), thus flow allocation dictated by link weights w Shortest-path routing and term shortest-path allocation are not the same! 59

60 Shortest Path Routing () Modified 4-Node Network Example Capacity vector c = c, c, c, c 4, c 5 = (5,0,0,5,0) Additional paths for d=: P = {,5} P = {,,4} Demand Network P 4 P P P P P P 60

61 Shortest Path Routing () 4-Node Network Example Link weight system w = (,,,,4) Solution Rest of flow variables are 0 Shortest paths are unique for each demand pair flow allocation vector x(w) is also unique Demand Network w 4 = w = 4 w = w 5 = 4 w = 6

62 Shortest Path Routing (4) 4-Node Network Example However, flow allocation not feasible for capacity vector c=(5,0,0,5,0) Link loads resulting from allocation vector x(w) would be y(w) = (y,y,y,y4,y5) = (5,0,5,5,0) Solution violates capacity constraints! Changing link capacity so that c = y(w): shortest path allocation w.r.t. to w becomes (trivially) feasible again 6

63 Shortest Path Routing (5) Single shortest-path allocation problem For given link capacities c and demand volumes h, find a link weight system w such that the resulting shortest paths are unique and the resulting flow allocation vector x(w) is feasible, i.e., such that x(w) satisfies Three reasons for complexity of the problem A non-bifurcated (single-path) feasible flow allocation may not exist, while bifurcated feasible flow allocations may exist Even if single-path solution exists, in most cases it can be hard to determine Even if we find single-path flow solution, the weight system to induce it may not exist 6

64 Shortest Path Routing (6) Infeasible unique shortest path case Two demands d= between nodes and 7 d= between nodes and 6 h = h =, c e ( e E) Two paths per demand d=: P :--5-7, P : d=: P : , P : Allocating flows d=: x =, d=: x = No link weight system that induces single shortest path solution! 64

65 Shortest Path Routing (7) 4-Node Example Considering weight system w=(,,,,), which is shortest path routing w.r.t. hop count d=: there are two shortest paths P =,4, P = {,5} Which path has to be used for traffic? In OSPF: Equal Cost MultiPath (ECMP) rule Split all outgoing demands at a node among its outgoing links that are on shortest paths to destination Demand Network w 4 = w = 4 w = w = P P w 5 = 65

66 Shortest Path Routing (8) Infeasible unique shortest path case Two demands: d=, d=, h = h =, c e ( e E) Paths: P :--5-7, P : , P : , P : Solution: assign link weight to all links except to links - and 4-5 that obtain weight Result is feasible solution under ECMP rule w= w= w= 5 w= w= 7 w= w=

67 Additional Network Design Problems Fair Networks Demand is elastic and can consume any bandwidth assigned to its path, e.g., within certain predefined bounds (lower and upper bound for demand) Capacity constraints should not be violated Network needs to carry more than lower bound for each demand volume to maintain fairness, e.g., Max-Min-Fairness or Proportional Fairness criterion Topological Design Cost function takes into account not only capacity-dependent costs of links ξ e, but also link installation costs κ e Additional binary variable u e that indicates if link is installed or not Problem similar to uncapacitated design problem with modular links 67

68 Summary Network design as generic problem in multitude of areas Traffic and demand as input to network design Networks have multiple layers Network management based on multitude of different systems and protocols Right notation makes a lot of problems way easier Even when it seems to be more complicated on first sight Even when you do not believe me yet ;) Network design problems covered Capacitated vs. uncapacitated problems Minimizing costs of networks links Shortest path routing 68