ECE 158A: Lecture 5. Fall 2015

Transcription

1 8: Lecture Fall 0

2 Routing ()!

3 Location-ased ddressing Recall from Lecture that routers maintain routing tables to forward packets based on their IP addresses To allow scalability, IP addresses are assigned based on location, similarly to phone numbers [area,zone,number]

4 Location-ased ddressing Location-based addressing helps reducing the number of entries in routing tables: IP addresses with the same prefix can share the same entry in a routing table routing table maps prefixes of input IP addresses to output ports Given a destination IP address, the router finds the longest matching prefix in the routing table

5 xample Packet with destination address is sent to output port, as.8.00.xxx is the longest prefix matching packet s destination address xxx.8.xxx.xxx.8.00.xxx

6 utonomous Systems (S) The Internet is grouped into about 40,000 utonomous Systems (S) or domains Groups of hosts/routers under a single administrative entity ach S is assigned a unique identifier 6 bit S Number (SN)a network under a single administrative entity utonomous System or omain

7 Two-Level Routing Routing is performed at two levels: Routing within a domain is called intra-domain routing Routing across domains is called inter-domain routing Reasons: Routing within a domain requires microscopic knowledge of local network topology omains are managed by different companies/institutions Intra-domain routing driven by optimal performance Inter-domain driven by economic trade-offs

8 Routing Protocols Internet routing protocols are responsible for constructing and updating the routing tables at the routers Routing protocols use shortest path algorithms to establish good paths between nodes. Two classical algorithms: Link State: ased on ijkstra s Shortest Path lgorithm istance Vector: ased on ellman-ford lgorithm Routing Protocols used in practice: Intra-domain routing: Open Shortest Path First (OSPF) (link state), Routing Information Protocol (RIP) (distance vector) Inter-omain routing: order Gateway Protocol (GP)

9 Network Representation as a Graph Routing algorithms model the network as a graph Routers are graph vertices and links are edges dges have an associated cost (e.g., distance, queue delay, cost) F Goal: Find a least-cost path from any two vertices

10 Link State vs istance Vector Link State (LS): ach node learns the complete network map (global information) ach node computes shortest paths independently and in parallel istance Vector (V): No node has the complete picture (local information) Nodes cooperate to compute shortest paths in a distributed manner LS uses global information, while V is asynchronous, and distributed. LS has higher messaging overhead and higher processing complexity, but is less vulnerable to looping

11 Link-State!

12 Link State Routing ach node maintains its local link state (LS) i.e., a list of its directly attached links and their costs Host (N,N) (N,N4) (N,N) Host Host N N N N Host N4 Host N6 N7

13 Link State Routing ach node maintains its local link state (LS) ach node floods its local link state on receiving a new LS message, a router forwards the message to all its neighbors other than the one it received the message from Host Host Host (N,N) (N, N4) (N, N) N N4 (N,N) (N, N4) (N, N) (N,N) (N, N4) (N, N) (N,N) (N, N4) (N, N) (N,N) (N, N4) (N, N) N N (N,N) (N, N4) (N, N) (N,N) (N, N4) (N, N) N (N,N) (N, N4) (N, N) Host Host (N,N) (N, N4) (N, N) N6 (N,N) (N, N4) (N, N) N7

14 Link State Routing ach node maintains its local link state (LS) ach node floods its local link state Hence, each node learns the entire network topology an use ijkstra s to compute the shortest paths between nodes Host Host Host N N N N Host N4 Host N6 N7

15 ijkstraʼs Shortest Path lgorithm INPUT: Network topology (graph), with link costs OUTPUT: Least cost paths from one node to all other nodes Iterative: after k iterations, a node knows the least cost path to its k closest neighbors

16 Notation c(i,j): cost 0 from node i to j ( if i and j are not neighbors) (v): total cost of the current least-cost path from source to destination v p(v): v s predecessor along path from source to v S: set of nodes whose least cost path is known Source! F

17 ijkstras lgorithm c(i,j): link cost from node i to j Initialization: S = {}; for all nodes v 4 if v adjacent to then (v) = c(,v); 6 else (v) = ; 7 8 Loop 9 find w not in S such that (w) is a minimum; 0 add w to S; update (v) for all v adjacent to w and not in S: if (w) + c(w,v) < (v) then // w gives us a shorter path to v than we ve found so far (v) = (w) + c(w,v); p(v) = w; 4 until all nodes in S; (v): current cost source v p(v): v s predecessor along path from source to v S: set of nodes whose least cost path definitively known

18 xample: ijkstras lgorithm! Step 0 4 set S (),p(), (),p(), (),p(), (),p() (F),p(F) F Initialization: S = {}; for all nodes v 4 if v adjacent to then (v) = c(,v); 6 else (v) = ;

19 xample: ijkstras lgorithm! Step 0 4 set S (),p(), F (),p(), (),p(), (),p() (F),p(F) 8 Loop 9 find w not in S s.t. (w) is a minimum; 0 add w to S; update (v) for all v adjacent to w and not in S: If (w) + c(w,v) < (v) then (v) = (w) + c(w,v); p(v) = w; 4 until all nodes in S;

20 xample: ijkstras lgorithm! Step 0 4 set S (),p(), (),p(), F (),p(), (),p() (F),p(F) 8 Loop 9 find w not in S s.t. (w) is a minimum; 0 add w to S; update (v) for all v adjacent to w and not in S: If (w) + c(w,v) < (v) then (v) = (w) + c(w,v); p(v) = w; 4 until all nodes in S;

21 xample: ijkstras lgorithm! Step 0 4 set S (),p(), F (),p (),p(),, 4, (),p(), (F),p(F) 8 Loop 9 find w not in S s.t. (w) is a minimum; 0 add w to S; update (v) for all v adjacent to w and not in S: If (w) + c(w,v) < (v) then (v) = (w) + c(w,v); p(v) = w; 4 until all nodes in S;

22 xample: ijkstras lgorithm! Step 0 4 set S (),p(), F (),p(), 4,, (),p(), (),p(), (F),p(F) 4, 8 Loop 9 find w not in S s.t. (w) is a minimum; 0 add w to S; update (v) for all v adjacent to w and not in S: If (w) + c(w,v) < (v) then (v) = (w) + c(w,v); p(v) = w; 4 until all nodes in S;

23 xample: ijkstras lgorithm! Step 0 4 set S (),p(), F (),p(), 4,, (),p(), (),p(), (F),p(F) 4, 8 Loop 9 find w not in S s.t. (w) is a minimum; 0 add w to S; update (v) for all v adjacent to w and not in S: If (w) + c(w,v) < (v) then (v) = (w) + c(w,v); p(v) = w; 4 until all nodes in S;

24 xample: ijkstras lgorithm! Step 0 4 set S (),p(), F (),p(), 4,, (),p(), (),p(), (F),p(F) 4, 8 Loop 9 find w not in S s.t. (w) is a minimum; 0 add w to S; update (v) for all v adjacent to w and not in S: If (w) + c(w,v) < (v) then (v) = (w) + c(w,v); p(v) = w; 4 until all nodes in S;

25 xample: ijkstras lgorithm! Step 0 4 set S F (),p(), F (),p(), 4,, (),p(), (),p(), (F),p(F) 4, 8 Loop 9 find w not in S s.t. (w) is a minimum; 0 add w to S; update (v) for all v adjacent to w and not in S: If (w) + c(w,v) < (v) then (v) = (w) + c(w,v); p(v) = w; 4 until all nodes in S;

26 xample: ijkstras lgorithm! Step 0 4 set S F (),p(), (),p(), 4,, (),p(), (),p(), (F),p(F) 4, F To determine path (say), work backward from via p(v)

27 The Routing Table Running ijkstra at node gives the shortest path from to all destinations We then construct the routing table F estination Link (,) (,) (,) (,) F (,)

28 lgorithmic omplexity How many messages needed to flood link state messages? O( N ), where N is no. nodes; is no. edges in graph Processing complexity for ijkstra s algorithm? O( N ), because we check all nodes w not in S at each iteration and we have O( N ) iterations more efficient implementations: O( N log( N ))

29 ijkstra in action

30 ijkstra in action