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Delivering Packets During the Routing Convergence Latency Interval through Highly Connected Detours Elias P. Duarte Jr. Rogério Santini Federal University of Paraná Jaime Cohen StateUniversity of Paraná at Ponta Grossa BRAZIL Outline • Routing Convergence Latency • A Case Study: BGPv4 • Alternative Routing through Detours • The Proposed Connectivity Criteria • Algorithms for Computing #C(v) and MCC(v) • Algorithms for Selecting Detours • Experimental Results Routing Convergence Latency • After the network topology changes, routers have to update their local tables in order to reflect the new topology • Before ALL routers have consistently updated their tables, it is not possible to guarantee that existing routes will work • The time interval required for all routers to reach consistency over the new topology is called the routing convergence latency interval Routing Convergence Latency: Consequences • Network applications may not be able to communicate during this interval – Applications are increasingly critical for both organizations and individuals • How long does it take? • The convergence latency of the Internet’s exterior gateway protocol BGP has been extensively studied Internet Routing with BGPv4 • Border Gateway Protocol version 4 • BGP is an exterior routing protocol, used by Autonomous Systems (AS’s) to exchange network reachability information • BGP is an application protocol that uses TCP • BGP implements the distance vector routing algorithm, also allowing policy-based routing • Initially routers exchange their entire BGP table • Incremental updates are sent when the table changes BGP’s Convergence Latency • In the protocol specification (RFC 1771) the following parameter is defined: – HoldTime: employed to determine whether a given BGP connection is alive; suggested value = 90 seconds – If during this interval the BGP speaker does not receive UPDATE or KEEPALIVE messages, the BGP connection is closed, and all routes through the neighbor are considered – MinRouteAdvertisingInterval: employed to determine the minimum time interval between two advertisements of a given route; suggested value = 30 seconds – Thus BGP’s Convergence Latency Interval is • HoldTime + diameter * MinRouteAdvertisingInterval BGP’s Convergence Latency • Previously published results show that – BGP experimental average latency is 3 minutes – Intervals of 15 minutes have also been reported – In theory, the protocol may never even converge... • During the convergence latency interval: – The number of packets lost increases 30 times – The response time increases 4 times – Several connections are closed, even if both ends are up and running Alternative Routing Through Detours • If the regular IP (Internet Protocol) route is not working, an alternative route may work • Re-Routing has been proposed for MPLS (MultiProtocol Label Switching) • We propose the selection of alternative backup routes the pass through highly connected detours Highly Connected Detours • A detour is a network node that that acts as a bridge between source and destination • The alternative route is employed when the regular route is not working, and the location of faults or even of the actual topology is unknown • If the detour belongs to a highly edge-connected component the probability that there is a working route throught the detour to the destination is higher (the number of distinct paths is higher) • The network is represented as graph G = (V, E) Highly Connected Detours - Node A belongs to higher connected component in comparison to node B Proposed Connectivity Criteria • The connectivity number, #C(v), v є G, is defined as the edge-connectivity of a non-trivial subgraph of G containing v such that the number of edges of any cut separating nodes of this subgraph is the largest in any subgraph to which v belongs • Let MCC(v) be the largest subgraph of V containing v such that any pair of vertices of this subgraph cannot be separated by a cut of size less than #C(v) #C(v) and MCC(v): Examples 2 2 2 4 4 3 3 3 3 3 3 4 3 4 4 Vertex Numbering & Components with Maximum Edge-Connectivity • Let #C(v) be the edge connectivity of a non- trivial subgraph containing v and such that the cardinality of any cut separating nodes of this subgraph is maximized • Let MCC(v) be the largest subset containing v and such that any pair of vertices of this subgraph cannot be separated by a cut of size less than #C(v) An Exact Algorithm for Computing #C(v) and MCC(v) • Consider all cuts separating a given vertex v from any other vertex of G • The connectivity number #C(v) is equal to the largest number of edges in any of those minimum cuts • The all-pairs minimum cut separating each vertex of a graph from all other is given by a Gomory-Hu Tree or Cut-Tree • Algorithms for constructing a Cut Tree include both the original and a more recent work by Gusfield An Example Cut Tree Obtaining #C(v) and MCC(v) from the Cut Tree • For graph G, a Cut Tree T of G, and vertex v, the value of #C(v) is equal to the largest weight of an edge of T which is incident to v in T • For graph G, a Cut Tree T of G, and vertex v, those nodes that can be reached from v in T using edges with weights equal to or larger than #C(v) belong to MCC(v) Complexity • Let n be the number of vertices in V, and m the number of edges in E • A version of the algorithm by Ford and Fulkerson can be employed to compute the cut between two vertices and has complexity O(n*m) • The algorithm by Gusfield executes the algorithm by Ford and Fulkerson n-1 vezes, with complexity O(n2*m). • From the Cut Tree, the complexity to obtain #C(v) and MCC(v) is linear A Heuristic for Computing #C(v) • Besides the exact algorithm a fast heuristic is presented to compute #C(v) • The heuristic builds a Depth First Tree, and seeks, at each step, a small number of cover edges to form a 2-edge connected components • Vertices that belong to those components have their connectivity numbers increased by 2, for the others the increase in #C(v) just 1 • The algorithm runs in the worst case in O((m/n)*(m+n)) steps Selecting The Detours • new-length(v,a,b): is the length of the alternative route from node a (source) to vertex b (destination) employing v as detour • The algorithm initially finds detours within the neighborhood of both source and destination • At each step the size of the neighborhood is increased • The size of MCC(v) is also employed • The algorithm returns a list of candidate detours ordered from best to worst The Algorithm for Detour Selection Find_Detours(Graph G=(V,E), vertex a, vertex b) (1) L <- Empty List; (2) For each vertex v de V do: (3) Compute #C(v), and the size of MCC(v); (4) Find new-length(v,a,b); (5) P <- regular IP route used for a to communicate with b (6) d <- |P| * 2; (7) While |L| <= |V|-2 do (8) Sort vertices v that belong to V-L and to d-neighborhood(a,b) by <#C(v),|MCC(v)|,-new-length(v,a,b)>; (9) Insert the ordered vertices in the end of L; (10) d = d + |P|; // increase the neighborhood (11) Return L; Detour Selection: An Example Detour Selection: Complexity • Using the Cut Tree – O(n2*m) + O(m*log(n)) • Using the Heuristic – O(n+m) + O(m*log(n)), is the graph is sparse Experimental Results • Simulation was executed on over 2,000 random graphs • The Waxman method for generating Internet-like topologies was employed • The number of nodes varied from 10 to 100, the average vertex degree varied from 3 to 8 Evaluation of the Heuristic #C(v) • We computed the average exact #C(v) and the heurist #C(v) normalized using the average vertex degree • For all graphs considered, 90% of the heuristic values obtained is less than 23% of the average vertex degree Evaluation of the Heuristics Comparison of #C(V) average vertex average error n degree per node 50 [4,5) 0.207 60 [7,8) 0.192 70 [4,5) 0.210 100 [7,8) 0.194 Dependability Evaluation: Fault Coverage • Consider a pair of network entities that CANNOT communicate because of a routing fault • The fault coverage measures how often the usage of a routing proxy selected by the presented approach allows the system to continue working in the presence of faults Computing the Fault Coverage • Initially the shortest paths of all vertice pairs was computed; then, for each pair – The ordered list of detour candidates was obtained – For each edge (x,y) that is not a cut edge and belongs to a path: • (x,y) is marked as faulty and a counter is incremented • If the alternative route created by using the 3 best detours does not contain edge (x,y) another counter is incremented • The fault coverage is given by the rate of these two counters Fault Coverage: 3 Best Detours that Do Not Belong to The Regular Route • Results varied from 87% to 99 Fault Coverage: 3 Best Detours Heuristic • Results were similar Conclusions & Future Work • The main contribution of this work is to present practical connectivity criteria to evaluate network nodes as detours • Both an exact algorithm and a fast heurist were presented to compute the proposed criteria • Highly Connected detours belong to network component with more distinct paths... • ...thus the probability that they will work if regular routes are not working (during the converge latency) is higher • Future (current) work includes finding highly connected routes, instead of nodes • And the implementation of a prototype specific for MPLS re- routing

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faulty nodes, the network, routing algorithm, Fault Tolerant, virtual channels, destination node, fault tolerance, adaptive routing, safety level, destination nodes

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posted: | 2/21/2010 |

language: | English |

pages: | 30 |

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