Coursehero >> California >> Berkeley >> L&S 17

Course Hero has millions of student submitted documents similar to the one below including study guides, homework solutions, papers, exam answer keys and textbook solutions.

Algorithms Distributed in Networks EECS 122: Lecture 17 Department of Electrical Engineering and Computer Sciences University of California Berkeley The Internet is a HUGE Distributed System Nodes are local processors Messages are exchanged over various kinds of links Nodes contain sensors which sense local changes Nodes control the network jointly Method for doing this is a distributed algorithm Example: Routing Time taken to solve the problem has two components: Computation time taken for local processing Communication time for messages to be received over the links March 21, 2006 AKP: EECS122 Lecture 17 2 1 Solving Global Problems in a Distributed Setting Examples: Minimum Spanning Tree Shortest Path Leader Election Topology Broadcast Much easier to think in terms of centralized algorithms Creativity needed to convert to the distributed case March 21, 2006 AKP: EECS122 Lecture 17 3 Network Protocols often have unintended effects TCP Example 1 TCP connections detect congestion after it has happened May cause packet drops from uncongested well behaved flows Non congested flows back off Example 2 Two TCP flows sharing the same router get uneven bandwidths because one has a much smaller RTT than the other Routing Oscillation and countless other pathologies It is very difficult to avoid these unintended effects March 21, 2006 AKP: EECS122 Lecture 17 4 2 Today Focus on protocol design issues How to move from Centralized to Distributed Alg. Synchronous and Asynchronous computation Why does the Asynchronous Bellman Ford converge? Selfish behavior distributed systems March 21, 2006 AKP: EECS122 Lecture 17 5 The Network is Heterogeneous Speed Dialup to terabit fiber Reliability Hosts: Distributed Server farms to 486 PC Links: Noisy wireless to virtually error free fiber Congestion Trustworthiness What is a general enough model to cover all of this? March 21, 2006 AKP: EECS122 Lecture 17 6 3 Consensus over an Unreliable Link A and B in a connection over an unreliable link They both want to terminate the connection only if they are certain that no more packets will arrive from the other user A B A won t terminate unless it knows that B knows it is about to terminate. B won t terminate unless it knows that A knows it is about to terminate March 21, 2006 AKP: EECS122 Lecture 17 7 Consensus Problem Suppose B tells A it can terminate and A receives this message, say M A can terminate, but B will never know if A actually received M and so it can t terminate A B A sends ACK(M) to B, but then A needs to makes sure that B received this message, so it must wait for ACK(ACK(M)) A never terminates. In fact, NO protocol exists to solve this problem! Worth convincing yourself of this fact. March 21, 2006 AKP: EECS122 Lecture 17 8 4 Link model Error correction Assume that errors can eventually corrected Propagation Delay Fixed Variable but no more than d Variable with no upper bound Other components of delay Queueing Delay Transmission Delay Packet order FIFO Can be delivered in arbitrary order March 21, 2006 AKP: EECS122 Lecture 17 9 Maintaining accurate topology information A B Whenever a link goes down/up, its end points send messages to all their neighbors who then flood. slow link C D March 21, 2006 AKP: EECS122 Lecture 17 10 5 Maintaining accurate topology information A B Whenever a link goes down/up, its end points send messages to all their neighbors who then flood 1. CD fails Down C Down D March 21, 2006 AKP: EECS122 Lecture 17 11 Maintaining accurate topology information Down A B Whenever a link goes down/up, its end points send messages to all their neighbors who then flood. 1. CD fails A marks the link down Down C D March 21, 2006 AKP: EECS122 Lecture 17 12 6 Maintaining accurate topology information Up A B Down Whenever a link goes down/up, its end points send messages to all their neighbors who then flood. 1. CD fails A marks the link down 2. CD comes back up Up C Up D March 21, 2006 AKP: EECS122 Lecture 17 13 Maintaining accurate topology information Up A B Down Whenever a link goes down/up, its end points send messages to all their neighbors who then flood. 1. CD fails A marks the link down 2. CD comes back up Up C D March 21, 2006 AKP: EECS122 Lecture 17 14 7 Maintaining accurate topology information Up A Down B Up C Whenever a link goes down/up, its end points send messages to all their neighbors who then flood. 1. CD fails A marks the link down 2. CD comes back up A marks the link up 3. A marks the link down D March 21, 2006 AKP: EECS122 Lecture 17 15 Maintaining accurate topology information Up Down A B Up msg lost Up C This can be fixed with sequence numbers, but then other problems emerge Whenever a link goes down/up, its end points send messages to all their neighbors who then flood. 1. CD fails A marks the link down 2. CD comes back up A marks the link up 3. A marks the link down 4. CA fails Up message lost A thinks CD is down when it is actually up! D March 21, 2006 AKP: EECS122 Lecture 17 16 8 Synchronous v/s Asynchronous Algorithms Synchronous algorithms can be described in terms of global iterations. The time taken for a given iteration is the time taken for the slowest processor to complete that iteration: time driven E.g. TDM or SONET Asynchronous algorithms execute at a processor based on received messages and internal state: event driven E.g. IP protocols which must run over heterogeneous systems March 21, 2006 AKP: EECS122 Lecture 17 17 Slotted Time Slotted system 1,2, ,3 All nodes agree on slot boundaries Have access to a global clock Helps to co-ordinate the nodes Every node can run the same algorithm Proving correctness is generally tractable if the centralized algorithm is analyzable Easier to understand the sequence of communication between nodes March 21, 2006 AKP: EECS122 Lecture 17 18 9 Synchronous Bellman-Ford (SBF) Every node runs the same algorithm Time is slotted and in every tick each node sends its distance vector. At time h, node i has as an estimate of the shortest path to node 1 that has <= h+1 hops Dh+1(I,j) = mink N(i) {Dh(k,j) + c(i,k)} 1 2 3 3 1 1 1 5 2 1 4 4 4 6 1 1 1 2 1 6 4 March 21, 2006 2 1 6 4 4 1 3 1 6 3 1 5 2 2 3 3 5 2 2 1 6 3 3 4 5 2 19 4 6 3 5 AKP: EECS122 Lecture 17 Synchronous Timing 1 1 2 3 3 1 1 2 4 4 Great when links are reliable and similar idle 1 2 idle 3 idle 4 6 1 5 Node 1 1 2 3 Node 6 March 21, 2006 AKP: EECS122 Lecture 17 20 10 Synchronous Timing 1 1 2 3 3 1 1 2 4 4 But what when some links are much faster? idle 1 2 idle 3 idle 4 6 1 5 Node 1 1 2 3 Node 6 1 idle 2 idle 3 idle Node 5 Node 5 suffers penalty synchronization March 21, 2006 AKP: EECS122 Lecture 17 21 Synchronization Penalty 1 1 2 3 3 1 1 2 4 4 Slow nodes can create a penalty as well idle 1 2 idle 3 idle 4 6 1 5 Node 3 1 2 3 Node 4 1 idle 2 idle 3 idle Node 5 Penalty can be huge! March 21, 2006 AKP: EECS122 Lecture 17 22 11 Implementing a Synchronous Algorithm Suppose the slowest process can complete an iteration in time Tp Link delay is always less than Tl Then a slot size of Tp+Tl or more is sufficient But most processors may be idle most of the time What if Tp and or Tl are not known? March 21, 2006 AKP: EECS122 Lecture 17 23 Locally Synchronous Computation Forget about fixed slots When a node has received all round k-1 messages from its neighbors, it computes and sends out its round k message Worst-case: As slow as synchronous computation Generally much faster Any synchronous algorithm that isn t using time as a part of the computation will also work when run in a locally synchronous manner. March 21, 2006 AKP: EECS122 Lecture 17 24 12 Local Synchronization 1 1 2 3 3 1 1 2 4 4 Send update k after you ve heard update k-1 from all neighbors. idle 1 2 idle 3 idle 4 6 1 5 Node 3 1 2 3 Node 4 1 idle 2 idle 3 idle Node 5 March 21, 2006 AKP: EECS122 Lecture 17 25 Compare with Synchronous 1 1 2 3 3 1 1 2 4 4 Slot size is affected by the slow node 4 idle 1 2 idle 3 idle 4 6 1 5 Node 3 1 2 3 Node 4 1 idle 2 idle 3 idle Node 5 March 21, 2006 AKP: EECS122 Lecture 17 26 13 Asynchronous computation 1 1 2 3 3 1 1 2 4 4 No notion of slot size at all! 4 6 1 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Node 1 1 2 3 Node 6 1 idle 2 idle 3 idle Node 5 Why should this work? March 21, 2006 AKP: EECS122 Lecture 17 27 Why bother with Asynchronous Algorithms To reduce the synchronization penalty Difficult to get the synchronous algorithm to start The network is dynamic Flows Topology Think of the algorithm having to restart with a new set of initial conditions, every time there is a failure Changes create events which may or may not have global impact Event-driven algorithms better suited March 21, 2006 AKP: EECS122 Lecture 17 28 14 Asynchronous Bellman Ford (ABF) Don t even wait to hear from all neighbors! Use most recent information to compute new distance vectors i.e. use last received values of D() and d Whenever ready, each node i computes D (i) = mink N(i) [D(k) + c(i,k)] Sends the result to each of its neighbors No notion of global iterations In general, nodes are using different and possibly inconsistent estimates March 21, 2006 AKP: EECS122 Lecture 17 29 Asynchronous Bellman Ford Regardless of how asynchronous the nodes are, the algorithm will eventually converge to the shortest path Links can go down and come up but as long as the topology is fixed after some time t, the algorithm will eventually converge to the shortest path Why? There s some hope because the D(j) can only go up if one of j s neighbors estimates has gone up. March 21, 2006 AKP: EECS122 Lecture 17 30 15 Idea There are too many different runs of ABF, so lets try to bound the range of distance estimates of D(j) over time Do this by two different runs of Synchronous BF Set different initial estimates One run U, uses the familiar ones, i.e. estimate is infinity if no edge The other, L, uses -1if no edge! One bounds the estimates from above, one from below and both find the correct the shortest paths eventually For every iteration k of the two SBF runs Lk(j) Lk+1(j) D*(j) Uk+1(j) Uk (j) For any asynchronous run, A, it is possible to show that for any k, there is a time t such that Lk(j) Lk+1(j) At(j) Uk+1(j) Uk (j) Since both lower and upper runs converge to the optimal, so will ABF eventually March 21, 2006 AKP: EECS122 Lecture 17 31 Soft State State with Time-Out Example: A host joins a group by sending a join message to a host manager . The manager adds the host to the group for the next T seconds. If the host wants to stay in the group it must send a refresh message within T seconds to the manager. Otherwise it is dropped. Advantage: Manager robust to host failure Disadvantage: Too many messages Most internet protocols use this way of communicating Trades of simplicity of correctness with complexity of communication March 21, 2006 AKP: EECS122 Lecture 17 32 16 The nature of asynchronous distributed protocols Generally non-intuitive Limited theory to work with Correctness extremely hard to prove Robustness hard to analyze Networking gurus have a vast knowledge of special cases that can lead to strange behaviors Misconfiguration is a big cause of errors Soft state helps a lot, but wastes many messages! What about just broadcasting topology information accurately so that these problems go away March 21, 2006 AKP: EECS122 Lecture 17 33 Trustworthiness Three levels Honest: Always in conformance of the protocol Selfish: May lie to get better performance out of the protocol (BGP) Malicious: Unpredictable Internet Protocols (for the most part) assume Honest protocol agents Unreliable infrastructure Infrastructure has gotten more reliable, and agents have gotten less honest Braess s Paradox: Example of how Greediness and distributed algorithms can lead to suboptimality March 21, 2006 AKP: EECS122 Lecture 17 34 17 Congestion Sensitive Routing Depends on traffic R x 1 Weights are delays/bit 1 unit of traffic from s to t u bits on the upper path S x 1 T 1-u bits on the lower path Q March 21, 2006 AKP: EECS122 Lecture 17 35 Each Node is Greedy Depends on traffic R x 1 Weights are delays/bit 1 unit of traffic from s to t u bits on the upper path S x 1 T 1-u bits on the lower path Q Node S minimizes Total delay = u(u+1) + (1-u)(2-u) = 2(u^2 u +1) Delay minimized at u=.5 So Total Delay = 1.5 s March 21, 2006 AKP: EECS122 Lecture 17 36 18 Greediness leads to suboptimality S still sends .5 on each path .5 x R 1 Weights are delays/bit 1 unit of traffic from s to t u bits on the upper path S 0 T x 1-u bits on the lower path 1 .5 Q BRAESS S PARADOX R is greedy R diverts all .5 units on to the new link March 21, 2006 Now total delay is 2! AKP: EECS122 Lecture 17 37 Conclusions Distributed Algorithms are not intuitive There is no systematic way to design them Active research area is making some progress Until then use Hacking Abilities Simulation Control Theory Optimization Graph Theory Game Theory . Greedy and malicious users complicate the protocol design problem even more Another active research area making progress This is why it is hard to build networks March 21, 2006 AKP: EECS122 Lecture 17 38 19

Find millions of documents here - Study Guides, Homework Solutions, Papers, Exam Answer Keys and more. Course Hero has millions of course related materials that will enable you to learn better, faster and get an A in all your courses.
Below is a small sample set of documents: