The Problem: Finding Paths Spring 2011 Lecture #19. Forwarding. Shortest Path Routing

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1 The Problem: Finding Paths Spring 20 Lecture # addressing, forwarding, routing liveness, advertisements, integration distance-vector routing routing loops, counting to infinity 6.02 Spring 20 Lecture, Slide #1 Link costs ddressing (how to name nodes?) Unique identifier for global addressing Link name for neighbors Forwarding (how does a switch process a packet?) Routing (building and updating data structures to ensure that forwarding works) Functions of the network layer 6.02 Spring 20 Lecture, Slide #2 Forwarding Shortest Path Routing Switch 1 ore function is conceptually simple lookup(dst_addr) in routing table returns route (i.e., outgoing link) for packet enqueue(packet, link_queue) send(packet) along outgoing link nd do some bookkeeping before enqueue ecrement hop limit (TTL); if 0, discard packet Recalculate checksum (in IP, header checksum) ach node wants to find the path with minimum total cost to other nodes We use the term shortest path even though we re interested in min cost (and not min #hops) Several possible distributed approaches Vector protocols, esp. distance vector (V) Link-state protocols (LS) (ssume all costs 0) 6.02 Spring 20 Lecture, Slide # Spring 20 Lecture, Slide #

2 node Routing Table Structure 1 estination Link (next-hop) ost ROUT 18 Self Spring 20 Lecture, Slide # istributed Routing: ommon Plan etermining live neighbors ommon to both V and LS protocols HLLO protocol (periodic) Send HLLO packet to each neighbor to let them know who s at the end of their outgoing links Use received HLLO packets to build a list of neighbors containing an information tuple for each link: (timestamp, neighbor addr, link) Repeat periodically. on t hear anything for a while link is down, so remove from neighbor list. dvertisement step (periodic) Send some information to all neighbors Used to determine connectivity & costs to reachable nodes Integration step ompute routing table using info from advertisements ealing with stale data 6.02 Spring 20 Lecture, Slide #6 istance-vector Routing V advertisement Send info from routing table entries: (dest, cost) Initially just (self,0) V integration step [ellman-ford] For each (dest,cost) entry in neighbor s advertisement ccount for cost to reach neighbor: (dest,my_cost) my_cost = cost_in_advertisement + link_cost re we currently sending packets for dest to this neighbor? See if link matches what we have in routing table If so, update cost in routing table to be my_cost Otherwise, is my_cost smaller than existing route? If so, neighbor is offering a better deal Use it update routing table so that packets for dest are sent to this neighbor V xample: round 1 { : (None,0) Node : update routes to, Node : update routes to,, Node : update routes to,,, Node : update routes to,, Node : update routes to, { : (None,0) 1 { : (None,0) { : (None,0) { : (None,0) Subscript indicates node that gave better route 6.02 Spring 20 Lecture, Slide # 6.02 Spring 20 Lecture, Slide #8

3 V xample: round 2 { : (None,0), : (,), : (,) Node : update routes to,, Node : update routes to, Node : no updates Node : update routes to Node : update routes to, { : (,), : (None,0), : (,), : (,) 1 { : (,), : (,), : (None,0), : (,1), : (,) { : (,), : (,1), : (None,0), : (,) { : (,), : (,), : (None,0) Node : no updates Node : no updates Node : no updates Node : no updates Node : no updates V xample: round 3 { : (None,0), : (,18), : (,), : (,22), : (,12) { : (,18), : (None,0), : (,), : (,), : (,16) 1 { : (,), : (,), : (None,0), : (,1), : (,) { : (,22), : (,), : (,1), : (None,0), : (,) { : (,12), : (,16), : (,), : (,), : (None,0) 6.02 Spring 20 Lecture, Slide # Spring 20 Lecture, Slide #10 V xample: reak a Link { : (None,0), : (,18), : (,), : (,22), : (,12) When link breaks: eliminate routes that use that link. { : (,18), : (None,0), : (,), : (,), : (,16) 1 { : (,), : (,), : (None,0), : (,1), : (,) { : (,22), : (,), : (,1), : (None,0), : (,) { : (,12), : (,16), : (,), : (,), : (None,0) V xample: round { : (None,0), : (,18), : (,), : (,22), : (,12) Node : update cost to Node : update routes to,, Node : update routes to Node : no updates Node : update routes to { : (None, ), { : (,22), : (None,0), : (,), : (None, ), : (,1), : (,), : (None,0), : (None, ) : (,) 1 { : (,), : (None, ), : (None,0), : (,1), : (,) { : (,12), : (,16), : (,), : (,), : (None,0) 6.02 Spring 20 Lecture, Slide # 6.02 Spring 20 Lecture, Slide #12

4 Update cost V xample: round { : (None,0), : (, ), : (,), : (,22), : (,12) Node : update route to Node : no updates Node : no updates Node : no updates Node : no updates { : (,), : (None,0), : (,), : (,), : (,1) 1 { : (,), : (,), : (None,0), : (,1), : (,) { : (,22), : (,), : (,1), : (None,0), : (,) { : (,12), : (,1), : (,), : (,), : (None,0) Node : no updates Node : no updates Node : no updates Node : no updates Node : no updates V xample: final state { : (None,0), : (,), : (,), : (,22), : (,12) { : (,), : (None,0), : (,), : (,), : (,1) 1 { : (,), : (,), : (None,0), : (,1), : (,) { : (,22), : (,), : (,1), : (None,0), : (,) { : (,12), : (,1), : (,), : (,), : (None,0) 6.02 Spring 20 Lecture, Slide # 6.02 Spring 20 Lecture, Slide #1 orrectness & Performance Optimal substructure property fundamental to correctness of both ellman-ford and ijkstra s shortest path algorithms Suppose shortest path from X to Y goes through Z. Then, the sub-path from X to Z must be a shortest path. Proof of ellman-ford via induction on number of walks on shortest (min-cost) paths asy when all costs > 0 and synchronous model (see notes) Harder with distributed async model (not in 6.02) How long does it take for distance-vector routing protocol to converge? Time proportional to largest number of hops considering all the min-cost paths Partitioning the Network { : (None,0), : (,), : (None, ), : (None, ), : (None, ) Node : delete routes to,, Node : delete routes to,, Node : update routes to, Node : update routes to, Node : update route to, cost to { : (,), { : (,22), : (None,0), : (None, ), : (None, ), : (,1), : (None, ), : (None,0), : (None, ) : (,) 1 { : (None, ), : (,), : (None,0), : (,1), : (,) { : (,12), : (,1), : (,), : (,), : (None,0) 6.02 Spring 20 Lecture, Slide # Spring 20 Lecture, Slide #16

5 V xample: round 6 { : (None,0), : (,) Node : no updates Node : no updates Node : update costs to, Node : update route to, cost to Node : update routes to, { : (,), : (None,0) 6.02 Spring 20 Lecture, Slide #1 1 { : (,1), : (,22), : (None,0), : (,1), : (,) { : (,2), : (,30), : (,1), : (None,0), : (,) { : (,3), : (None, ), : (,), : (,), : (None,0) Nodes,, and each update their costs in response to earlier updates by neighbors. osts spiral upwards towards " remove route when cost reaches self.infinity ounting to Infinity { : (None,0), : (,) { : (,), : (None,0) 6.02 Spring 20 Lecture, Slide #18 1 { : (,0), : (None, ), : (None,0), : (,1), : (,) { : (,38), : (None, ), : (,1), : (None,0), : (,) { : (,22), : (,2), : (,), : (,), : (None,0) { : (None,0), : (,) Suppose sends a packet to : forwards to forwards to repeat rop packet when TTL is decremented to 0 Routing Loop { : (,), : (None,0) 6.02 Spring 20 Lecture, Slide # 1 { : (,0), : (None, ), : (None,0), : (,1), : (,) { : (,38), : (None, ), : (,1), : (None,0), : (,) { : (,22), : (,2), : (,), : (,), : (None,0) ventually all the unreachable nodes are removed from routing table and all routing loops are resolved. ventual Final State { : (None,0), : (,) { : (,), : (None,0) 6.02 Spring 20 Lecture, Slide #20 1 { : (None,0), : (,1), : (,) { : (,1), : (None,0), : (,) { : (,), : (,), : (None,0)