1. University of Arizona ECE 478/578 258 Optimality Principle Assume that “optimal” path is the shortest one OP indicates that any portion of any optimal path is also optimal Set of optimal paths from all sources to a given destination forms a tree that is routed at the destination A B C D E F 23 2 12 41  Optimal path between A and F is A-B-C-E-F  Then, the optimal path between B and F is B-C-E-F

2. University of Arizona ECE 478/578 259 Shortest Path Algorithm “Shortest” in the sense of distance (e.g., total delay) Assume that distance is “additive” Two approaches to computing the shortest path: –Dijkstra’s algorithm (basis for link-state routing) –Bellman-Ford algorithm (basis for distance-vector routing)

3. University of Arizona ECE 478/578 260 Dijkstra’s Algorithm Goal: find the shortest path from a given source to all destinations Network is represented by a graph G(V,E), where –V: set of nodes –E: set of links (edges) Assume that each link is associated with a delay value Starting from the source node, the algorithm “discovers” remaining node in the order of their distances from the source

4. University of Arizona ECE 478/578 261 Dijkstra’s Algorithm (Cont.) Each node v  V is associated with a label: –Current best distance from source s to v –Previous node from which distance was obtained Initially, all labels are tentative If the distance is not known yet, it is set to infinity In each iteration, the algorithm chooses a working node from set of nodes with tentative nodes –Working node is one with smallest distance among tentatively labeled nodes –Its label now becomes permanent

5. University of Arizona ECE 478/578 262 Dijkstra’s Algorithm (Cont.) Variables: –V: set of nodes in the graph –s: source node –d ij : link cost from node i to node j (=  if i is not a neighbor of j) –M: set of permanently labeled nodes –U n : current distance from s to node n

6. University of Arizona ECE 478/578 263 Dijkstra’s Algorithm (Cont.) Initialization: –M = {s}, U n = d sn, n  s (=  if n is not a neighbor of s) Repeat until M = V: –Find working node v  V-M such that U v = min U n –M = M  v (v is permanently labeled) –U n = min{U n, U v + d vn } for all n  V-M Worst-case complexity is in the order of n 2 (although, lower complexities can be achieved)

7. University of Arizona ECE 478/578 264 Example

8. University of Arizona ECE 478/578 265 Routing in the Internet Two general types of routing algorithms 1. Distance-vector 2. Link-state Common aspects –Each router knows the address of its neighbors –Each router knows the cost of reaching its neighbors –Router obtains global routing information by exchanging information with its neighbors only  distributed routing

9. University of Arizona ECE 478/578 266 Routing in the Internet (Cont.) Fundamental difference –Distance-vector: a node informs its neighbors of its “distance” to every other node in the network –Link-state: a node tells every other node in the network of its “distance” to its neighbors –Distance can be interpreted in different ways

10. University of Arizona ECE 478/578 267 Distance-Vector Algorithm Developed by Bellman and Ford Each router maintains a distance vector Distance vector: list of [destination,cost] pairs –Cost is the cost of the shortest path from the router to a given destination (initialized to  ) Router periodically broadcasts its distance vector When a router receives the distance vector of a neighbor, it updates its own distance vector

11. University of Arizona ECE 478/578 268 Example A B C D A Initial 014  1011 102 120 B C D  4 1011 2122 014  0122 AB=1 Computation at A when DV from B arrives Cost to go to B from A Cost to destn from B Cost to destn via B Current cost from A MIN Newcost = New DV for A + = BB Next Hop A C B D 1 4 1 1 4

12. University of Arizona ECE 478/578 269 1 Problem with Distance-Vector Routing Formation of loops after a link goes down  count-to-infinity problem B  - A2B B1C A2B B  - A  - B  - A4B B3A A  - A B C COST TO C NEXT HOP INITIAL 1 Link BC GOES DOWN 2 EXCHANGE 3 4 5 STABLE Portion of the RT at A Portion of the RT at B

13. University of Arizona ECE 478/578 270 Variations of Distance-Vector Routing 1. Path-vector routing –Each entry in the distance vector is annotated with the path used to obtain the cost –Count-to-infinity problem is solved –Used in Border Gateway Protocol (BGP) –Drawback: large path vectors (overhead)

14. University of Arizona ECE 478/578 271 Variations of Distance-Vector Routing (Cont.) 2. Split-horizon routing –Router does not advertise the cost of a destination to a neighbor if that neighbor is the next hop to that destination –Solves count-to-infinity problem for two routers –Does not work when three or more routers count to infinity –Variant of split-horizon split-horizon with poisonous reverse used in Routing Information Protocol (RIP)

15. University of Arizona ECE 478/578 272 Variations of Distance-Vector Routing (Cont.) 3. Distance-vector with source tracing –In addition to cost to destination, distance vector includes the address of the router immediately preceding the destination –Router can construct entire path to destination –When router updates costs in its distance vector, it also updates preceding-router field

16. University of Arizona ECE 478/578 273 Example DESTN NEXT LAST 1 --- --- 2 2 1 3 3 1 4 2 2 5 2 4 6 2 5 Path = 1,2,4,5,6 Table for Node 1 1 2 4 3 5 6 Assume unit link costs Compute path from Node 1 to Node 6

17. University of Arizona ECE 478/578 274 Link-State Routing Principles –Each router discovers its neighbors (using “Hello” packets) –Each router learns the cost of all links in the network (using topology/state dissemination) –Each router computes the best path to every destination (using Dijkstra's shortest path algorithm) Topology dissemination –Routers generate link-state packets (LSPs), which contain Router's ID Neighbor's ID Cost of link to the neighbor

18. University of Arizona ECE 478/578 275 Link-State Routing (Cont.) LSPs are distributed using controlled flooding –Routers send LSPs to neighboring routers –Routers maintain copies of LSPs –Duplicate LSPs are not forwarded

19. University of Arizona ECE 478/578 276 Example C AD B 4 1 4 1 1 A B 1 A C 4 Two LSPs CREATED BY Node A A’s B’s COST ID

20. University of Arizona ECE 478/578 277 Example (Cont.) A creates two LSPs:  A,B,1  and  A,C,4  Consider LSP  A,B,1  When B receives LSP, it forwards it to C and D When C receives LSP from B, it forwards it to A and D A does not forward the LSP any further If D gets the LSP from B before it gets it from C, it only forwards it to C. Otherwise, it forwards it to B

21. University of Arizona ECE 478/578 278 Sequence Numbers in Topology Dissemination LSP consistency problem when a link/router goes down Solution: use a sequence number for every LSP LSP with a higher sequence number overwrites an LSP with lower number Wrap-around problem

22. University of Arizona ECE 478/578 279 Solutions to Wrap-Around Problem 1. Aging –LSP contains an “age” value –When LSP is first created, its age is set to MAX_AGE –When a router receives an LSP, it copies its current age to a per-LSP counter –Counter is periodically decremented at router –If age reaches zero, router discards the LSP 2. Lollipop sequence space

23. University of Arizona ECE 478/578 280 Link State Versus Distance Vector Arguments in favor of link-state algorithms 1. Stability (no loops at steady state) 2. Multiple routing metrics can be used 3. Faster convergence than distance vector algorithms Counter arguments 1. Transients loops can form 2. Modified distance-vector algorithms are also stable and can support multiple metrics

24. University of Arizona ECE 478/578 281 Link State Versus Distance Vector (Cont.) Arguments in favor of distance-vector algorithms 1. Less overhead to maintain database consistency 2. Smaller routing tables Counter arguments –These advantages disappear when using modified distance-vector algorithms (e.g., path vector approach) Internet uses both approaches –OSPF: link-state protocol –BGP: path-vector protocol

25. University of Arizona ECE 478/578 282 Hierarchical Routing For large networks, state dissemination poses a scalability problem Solution: cluster routers hierarchically into several peer groups (domains) Summarized reachability information is advertised outside a group Grouping can be done at multiple levels

26. University of Arizona ECE 478/578 283 Example (ATM PNNI) PEER GROUP LEADER OF PG(A.2) LOGICAL LINK PG(A.2) PG(A.1) PG(A.4) PG(A.3) PG(B.1) PG(B.2) PG(C) BORDER NODE LOGICAL NODE A.3.1 A.3.2 A.3.3 A.3.4 A.2.3 A.2.1 A.2.2 A.1.3 A.1.2 A.1.1 A.4.1 A.4.2 A.4.3 A.4.4 A.4.6 A.4.5 B.1.2 B.1.3 B.1.1 B.2.1 B.2.2 B.2.3 B.2.4 B.2.5 C.1C.2

27. University of Arizona ECE 478/578 284 Traffic Management & Control Goals: –Guarantee applications QoS requirements –Provide congestion control –Utilize resources efficiently Above goals sometimes conflict with each other Common approach to traffic management: –Map applications QoS into few service classes –Guarantee QoS associated with these classes

28. University of Arizona ECE 478/578 285 How Many Classes of Service? One class –Based on the most demanding traffic –Simple traffic management –Poor bandwidth utilization Many classes –Better utilization –Traffic management is more complicated

29. University of Arizona ECE 478/578 286 1. Reactive control – Action is taken after congestion is detected – Essentially, closed-loop flow control – Network instructs users to reduce their rates end-to-end flow control (similar to TCP) link-by-link flow control –Problems Too slow in a high-speed switching environment Overreaction to temporary congestion Fairness issues Types of Traffic Control

30. University of Arizona ECE 478/578 287 Types of Traffic Control (Cont.) 2. Preventive control –Prevent the occurrence of congestion by means of call admission control (CAC) traffic policing (usage parameter control) –Appropriate for real-time traffic (e.g., voice and video)

31. University of Arizona ECE 478/578 288 1. Connection admission control (CAC) 2. Traffic policing and shaping 3. Resource management – Scheduling – Buffer management – Priority mechanisms – Bandwidth allocation 4. Flow control Traffic Control Functions

32. University of Arizona ECE 478/578 289 Also known as usage parameter control (UPC) Goals of UPC: –Ensure compliance with traffic contract  protect QoS of ongoing connections –Traffic shaping (done by users and/or network) –User identity verification Reasons for traffic violations: –Equipment malfunctioning –Economical advantage (greedy users) –Malicious behavior (degrade QoS of others) Traffic Policing

33. University of Arizona ECE 478/578 290 Traffic Policing (Cont.) Several levels of policing (VC, link, etc.) Actions taken when violations are detected –Packet discarding, or –Packet tagging (marking packets with lower priority) Other possible actions at the connection level –Punitive charging –Connection termination –Problems with connection-level actions long reaction time drastic penalty

34. University of Arizona ECE 478/578 291 Traffic Policing (Cont.) Locations at which traffic policing takes place –Entry nodes (network side of user-network interface) –Boundaries between different networks Commonly policed parameters: 1. Peak cell rate (PCR) 2. Sustained cell rate (SCR) 3. Maximum burst size (MBS)

35. University of Arizona ECE 478/578 292 Issues in Traffic Policing Limitations of current set of traffic parameters How do users estimate their traffic parameters? Traffic parameters may change within CPE before reaching the policing function  tolerance levels are needed

36. University of Arizona ECE 478/578 293 Ideal Requirements in a Policing Mechanism Availability Online operation High probability of detecting violations Transparency to conforming connections  very low probability of a wrong decision Short reaction time

37. University of Arizona ECE 478/578 294 Set of traffic parameters describing a source Used as basis for traffic contract Often based on a traffic envelope –Time-invariant bound on number of arrivals –Often, it represents the worst-case (deterministic) behavior –Also known as “traffic constraint function” –Examples: peak rate ( ,  ) model linear bounded arrival processes (LBAP) Traffic Descriptor

38. University of Arizona ECE 478/578 295 ( ,  ) Traffic Envelope Let A[t, t +  ] = no. of arrivals in interval [t, t +  ] Traffic envelope is the function A*(  ) s.t. A[t, t +  ]  A*(  ),  t > 0 In the ( ,  ) model, A*(  ) =  +   –  : burstiness parameter –  : rate parameter

39. University of Arizona ECE 478/578 296 ( ,  ) Traffic Envelope (Cont.) Cumulative Number of Arrivals Window Size slope =  

40. University of Arizona ECE 478/578 297 LBAP Envelope Several, cascaded ( ,  ) envelopes Cumulative Number of Arrivals Window Size slope =  1 11 22 33 slope =  2 slope =  3

41. University of Arizona ECE 478/578 298 Properties of a good traffic descriptor 1. Representativity 2. Verifiability 3. Preservability 4. Usability

42. University of Arizona ECE 478/578 299 Common Policing Mechanisms 1. Leaky bucket 2. Jumping window 3. Moving window 4. Triggered jumping window 5. Exponentially weighted moving average

43. University of Arizona ECE 478/578 300 Leaky Bucket Mechanism Tokens are generated at rate r Token pool of size b (for unused tokens) Input buffer (optional) For simplicity, assume that packets are of fixed size A packet must obtain a token to enter the network Output traffic conforms to ( ,  ) envelope Can be implemented using two counters

44. University of Arizona ECE 478/578 301 Leaky Bucket Mechanism (Cont.) network token generator (rate r) token bank (size b) buffer (optional) input traffic

45. University of Arizona ECE 478/578 302 Jumping Window Mechanism Time is divided into fixed-length windows Number of packets per window less than or equal N Worst-case burst length = 2N Can be implemented using two counters

46. University of Arizona ECE 478/578 303 Moving Window Mechanism Time window is continuously sliding Number of packets per window at any time  N Each packet is remembered for exactly one window Worst-case burst length = N Higher implementation complexity than JW

47. University of Arizona ECE 478/578 304 Composite Policing Mechanisms Previous mechanisms enforce simple envelopes To enforce more representative traffic envelopes, composite policing mechanisms can be used A composite mechanism consists of several basic policing mechanisms connected in cascade Example: Composite Leaky Bucket (i.e., LBAP)

48. University of Arizona ECE 478/578 305 Composite Leaky Bucket Window size Accumulated No. of Packets compliance region LB1 LB2 LB3

49. University of Arizona ECE 478/578 306 Adopted by ATM Forum for traffic policing Based on continuous-state leaky bucket Characterized by two parameters –Increment (I) –Limit (L) Generic Cell Rate Algorithm (GCRA)

50. University of Arizona ECE 478/578 307 Y< 0 ? Y = X - (T(k) - LCT) Non-conforming packet X = Y + I LCT = T(k) Packet conforming Yes No Y = 0 T(k): arrival time of kth packet LCT: last compliance time Initial conditions: X = 0 LCT = T(1) Y> L ? Yes No Implementation of GCRA

51. University of Arizona ECE 478/578 308 Example GCRA(I,L) with I = 1/PCR = 2 , L = 4 Time T(k) Y X