Scalable Link-State Internet Routing

Transcription

1 Scalable Link-State Internet Routing J. J. Garcia-Luna-Aceves and Marcelo Spohn Computer Engineering Department School o Engineering University o Caliornia Santa Cruz, CA 95, USA jj, spohn@cse.ucsc.edu Abstract We present and veriy the Adaptive Link-State Protocol (ALP), a new link-state routing protocol that does not require the state o each link to be looded to the entire internetwork, or to entire areas i hierarchical routing is used. A router in ALP disseminates link-state updates incrementally to its neighbors or only those links along paths used to reach destinations. Link-state updates are validated using time stamps and contain the same inormation used in other link-state protocols. For the case o neighbor routers connected through a broadcast medium, a designated router is distributedly elected or each link state reported over the medium, rather than requiring a designated router to report every topology change over the broadcast medium, like OSPF does. Simulation experiments illustrate that ALP is as eicient as the Distributed-Bellman Ford algorithm when distances to destinations do not increase and resources do not ail, and more eicient than traditional link-state protocols based on looding ater distances increase or resources ail. ALP also outperorms the linkvector algorithm (LVA), which is the only prior routing algorithm based on selective dissemination o link states.. Introduction The majority o the work on routing protocols or internetworks has proceeded in two main directions: distance-vector protocols (e.g., BGP [], IDRP [3], RIP [7], and EIGRP []) and linkstate protocols (e.g., ISO IS-IS [] and OSPF [9]). In a distancevector protocol, routers exchange path inormation (e.g., distance or complete path to one or more destinations) and compute their preerred paths in a distributed manner. Several routing algorithms based on distance vectors have been proposed to eliminate the counting-to-ininity problem that prevents the Bellman-Ford algorithm rom working eiciently in large networks (e.g., [5, 3, ]) and a number o these algorithms have been shown to outperorm the traditional approach used in implementing link-state routing. Most approaches to link-state routing are based on topology broadcast [, ]. Unortunately, disseminating complete link-state inormation to all routers incurs excessive communication overhead. The link-vector algorithm (LVA) [] was recently proposed to avoid the overhead o topology broadcast when using link-state inormation. In LVA, each router updates its neighbors with the state o each o the links it uses to reach a destination through one or more preerred paths, and also inorms them o the links that it stops using to reach destinations. Updates to or deletions o links are propagated incrementally, based on the distributed computation o preerred paths at routers, just like distance inormation propagates in a distance-vector algorithm. Although eicient algorithms have been proposed based on both link-state and distance-vector inormation, link-state routing is more eicient than distance-vector routing when constraints are placed on the paths oered to destinations, which is the case or QoS routing oering paths with required delay, bandwidth, reliability, cost, or other parameters. The communication overhead This work was supported by the Deense Advanced Research Projects Agency (DARPA) under grant F and by Raytheon under a UC MICRO grant. o a link-state protocol increases to the extent that more parameters have to be communicated or each link whose state is updated, i.e., the added overhead is at most linear with the number o link parameters. In contrast, the communication overhead o a distance-vector protocol grows with the number o combinations o values o the link parameters needed to deine the quality o paths. As the Internet continues to evolve to support QoS routing, obtaining more eicient approaches to link-state routing has become an important design and engineering problem. This paper presents a new link-state routing protocol or internetworks called ALP (adaptive link-state protocol). In ALP, a router sends updates to its neighbors regarding the links in its preerred paths to destinations. Each router decides which links to report to its neighbors based on its local computation o preerred paths. In contrast to LVA, a router does not ask its neighbors to delete links; instead, a router simply updates its neighbors with the most recent inormation about those links it decides to take out o its preerred paths. Link states are validated using time stamps and a router accepts only more recent link-state updates. Link-state inormation is aged out at each router just like in traditional link-state protocols. Furthermore, when multiple routers are connected through a broadcast medium (e.g., a LAN), they elect distributedly a designated router or each link reported over the broadcast medium; this reduces the number o updates per link sent over a given network. Unlike OSPF, ALP does not require backbones and can be used with distributed hierarchical routing schemes proposed in the past or distance-vector routing. Because routers in ALP propagate link-state inormation selectively, it incurs less communication overhead than algorithms based on topology broadcast. The ollowing sections introduce the network model assumed throughout the rest o the paper, describe ALP, show that ALP converges to correct paths a inite time ater the occurrence o an arbitrary sequence o link-cost or topological changes, calculate its complexity, and present simulation results comparing ALP s perormance against the perormance o an ideal topologybroadcast algorithm, the distributed Bellman-Ford algorithm (DBF), and LVA.. Network Model In ALP, routers maintain a partial topology map o their network. In this paper we ocus on lat topologies only, i.e., there is no aggregation o topology inormation into areas or clusters. The topology o a network is modeled as a directed graph G = (V; E), wherev is the set o nodes and E is the set o edges connecting the nodes. Each node has a unique identiier and represents a router with input and output queues o unlimited capacity updated according to a FIFO policy. For the purpose o routing-table updating, a Node A can consider another Node B to be adjacent (we call such a node a neighbor ) i there is linklevel connectivity between A and B and A receives update messages rom B reliably. Accordingly, we map a physical broadcast link connecting multiple nodes into multiple point-to-point bidirectional links deined or these nodes. A unctional bidirectional link between two nodes is represented by a pair o edges, one in each direction and with a cost associated that can vary in time but is always positive.

2 Report Documentation Page Form Approved OMB No. 7- Public reporting burden or the collection o inormation is estimated to average hour per response, including the time or reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection o inormation. Send comments regarding this burden estimate or any other aspect o this collection o inormation, including suggestions or reducing this burden, to Washington Headquarters Services, Directorate or Inormation Operations and Reports, 5 Jeerson Davis Highway, Suite, Arlington VA -3. Respondents should be aware that notwithstanding any other provision o law, no person shall be subject to a penalty or ailing to comply with a collection o inormation i it does not display a currently valid OMB control number.. REPORT DATE 99. TITLE AND SUBTITLE Scalable Link-State Internet Routing. REPORT TYPE 3. DATES COVERED --99 to a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) University o Caliornia at Santa Cruz,Department o Computer Engineering,Santa Cruz,CA,95. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES). SPONSOR/MONITOR S ACRONYM(S). DISTRIBUTION/AVAILABILITY STATEMENT Approved or public release; distribution unlimited 3. SUPPLEMENTARY NOTES. ABSTRACT 5. SUBJECT TERMS. SPONSOR/MONITOR S REPORT NUMBER(S). SECURITY CLASSIFICATION OF: 7. LIMITATION OF ABSTRACT a. REPORT unclassiied b. ABSTRACT unclassiied c. THIS PAGE unclassiied. NUMBER OF PAGES 9a. NAME OF RESPONSIBLE PERSON Standard Form 9 (Rev. -9) Prescribed by ANSI Std Z39-

3 An underlying protocol, which we call the neighbor protocol, assures that a router detects within a inite time the existence o a new neighbor, the loss o connectivity with a neighbor, and the reliable transmission o packets between neighbors. All messages, changes in the cost o a link, link ailures, and new-neighbor notiications are processed one at a time within a inite time and in the order in which they are detected. Because o the neighbor protocol, ALP assumes that all messages transmitted over an operational link are received correctly and in the proper sequence within a inite time. Routers are assumed to operate correctly, and inormation is assumed to be stored without errors. 3. Operation o ALP In ALP, each router reports to its neighbors the characteristics o every link it uses to reach a destination through a preerred path. The set o links used by a router in its preerred paths is called the source graph o the router. A router knows its adjacent links and the source graphs reported by its neighbors; the aggregation o a router s adjacent links and the source graphs reported by its neighbors constitute a partial topology graph. The links in the source graph and topology graph must be adjacent links or links reported by at least one neighbor. The router uses one or more local route selection algorithms, the topology graph to generate its own source graph, and a routing table speciying the successor, successors, or paths to each destination. The basic update unit used in ALP to communicate changes to source graphs is the link-state update (LSU). An LSU reports the characteristics o a link; an update message contains one or more LSUs. For a link between router u and router or destination v, router u is called the head node o the link in the u to v direction. The head node o a link is the only router that can report changes in the parameters o that link. The head o a link reports the state o the link in an LSU periodically or when the parameters o the link change. A router w other than the head o link (u; v) sends LSUs about the link when the link is in its source graph and it receives a more recent LSU or the link rom any o its neighbors, when the link is added to its source graph, or when the link that has been removed rom the source graph changes state. Thereore, the LSUs rom a router speciy the state o links that the router currently uses in its source graph and links that are removed rom the source graph. Each router ages the link-state inormation it receives and erases a link rom its topology graph i the age o the link-state inormation reaches a maximum value. Figure illustrates the act that routers in ALP have to maintain only partial topology inormation. For simplicity, this igure and the rest o the paper assume that a single parameter is used to characterize a link in one o its directions, which we will call the cost o the directed link. Furthermore, although any number and type o local route selection algorithms can be used in ALP, we describe ALP assuming that shortest paths are used or routing and that Dijkstra s shortest-path irst is used locally at each router. Figure b through d show the selected topology according to ALP at the routers indicated with illed circles. Solid lines represent the links that are part o the source graph o the respective router, dashed lines represent links that are part o the router s topology graph but not o its source graph. Arrowheads on links indicate the direction o the link stored in the router s topology graph. Router x s source graph shown in Figure b is ormed by the source graphs reported by its neighbors y and z, andthe links or which router x is the head node (namely links (x; y) and (x; z)). From the igure, the savings in storage requirements are clear, even or the small example shown in the igure. We have developed a routing protocol ramework based on the API provided by gated [] or implementation o routing protocols (Figure ). A Hello Protocol is used to detect the presence o new neighbors and the loss o connectivity to them; the Retransmission Protocol is responsible or delivering update messages correctly and in the proper sequence to neighbors, as long as the physical link and network interace are operational. Among other things, the gated API manages the routing orwarding table A y p x B z s q r u g y x z v w C A B s p w C h A q r u g y p x B z s q r u g y x z v v w C A B s p w C h q r u g (d) Figure : Topology as seen by routers indicated with illed circle. Solid lines indicate links in source graph; dashed lines indicate links in topology graph but not in source graph. and relays indications to ALP reporting changes in the parameters o adjacent links, such as link cost changes, link ailures, and link recoveries. In the rest o this paper we describe ALP assuming the services provided by the three underlying modules, which corresponds to the services provided by the neighbor protocol. 3.. Inormation Stored and Exchanged The LSU or a link (u; v) in an update message is a tuple (u; v; l; tod; sn; age) reporting the characteristics o the link, where l represents the cost o the link, tod and sn is the timestampassigned to the LSU, and age corresponds to maximum age the LSU can achieve while in the topology graph. A router i maintains a topology graph TG i, a source graph v h h

4 Neighbor Protocol Service Hello Protocol Retransmission Protocol gated API A L P The head o the link can reset sn whenever j tod - tod o last LSU j. The maximum age assigned to an LSU must not be larger than the maximum value o t, which is reseted every hours. This leads to a sel-stabilizing system because it makes the timestamp look like an unbounded register model. Alternatively, a large linear sequence number space can be used, together with a reset mechanism or the sequence number to guard against malunctions. We opt or the timestamp method in order to make our treatment o ALP simple. Figure : ALP protocol building modules SG i, a routing table, and the set o neighbors N i. The record entry or link (u; v) in the topology graph o router i is denoted TG i(u; v) and is deined by the tuple (u; v; l; tod; sn; age; F; l ; tag; rn), and a parameter p in the tuple is denoted by TG i(u; v):p. TG i(u; v):f contains the set o network interaces through which Node i has received up-to-date link-state inormation or (u; v),andtg i(u; v):f ( ) holds the addresses o the neighbors who have reported up-to-date link-state inormation or (u; v) through interace. In the example shown in Figure, router x s topology graph would have a record or link (s; u) indicating that y and z reported the same link. The link parameters l, tag, and rn are described in the next sections. Avertexv in TG i is denoted TG i(v) and contains a tuple (d; pred) whose values are used on the computation o the source graph. TG i(v):d is the distance o the path i ; v, and TG i(v):pred is v s predecessor in i ; v. The source graph SG i is a subset o TG i. The routing table contains record entries or destinations in SG i, each entry consists o the destination address, the cost o the path to the destination, and the address o the next-hop towards the destination. In our description, we reer to an LSU that has a cost ininity and the age ield is greater than zero as a RESET, and reer to an LSU with an ininity link cost, a zero age, and a timestamp equal to the corresponding entry in the topology graph, as a DELETE. However DELETEs and RESETs are simply LSUs. 3.. Validating Updates Because o delays in the routers and links o an internetwork, update messages sent by a router may propagate at dierent speeds along dierent paths. Thereore, a given router may receive an LSU rom a neighbor with stale link-state inormation, and a distributed termination-detection mechanism is necessary or a router to ascertain when a given LSU is valid and avoid the possibility o LSUs circulating orever. ALP implements the termination-detection mechanism used in several prior link-state protocols based on topology broadcast [9, ], which consists in time stamps. A router receiving an LSU accepts the LSU as valid i the received LSU has a larger timestamp than the timestamp o the LSU stored rom the same source, or i there is no entry or the link in the topology graph. There is a special case in which a router other than the head o the link can change the cost o a link to ininity and report the new cost to the neighbors; this type o LSU will be considered valid under certain circumstances, as discussed in the next section. Each LSU sent by the same source speciies the current timestamp and the maximum age or that LSU (which is in the order o an hour). Every router that accepts an LSU decrements its age by at least one and also decrements the age while the LSU sits in memory. The timestamp o an LSU consists o two values: time-o-the-day (tod), and sequence number (sn). The tod value corresponds to the number o seconds elapsed rom midnight (t) to the moment a timestamp must be assigned to the LSU. The head o a link that generates two or more LSUs with the same tod value uniquely identiies them by assigning dierent sns rom a linear sequence-number space starting at Processing Input Events An update message rom a router k consists o a list o LSUs reporting incremental updates to its source graph and deletion o links rom the topology graph not caused by aging; the procedure Update (Figure 3) is executed when a router i processes an update message. First, the topology graph is updated, then the source graph is updated, which may cause the router to update its routing table and to send its own update message. An LSU or (u; v) updates the topology graph i its timestamp is larger than the timestamp maintained or the same link in the topology graph, or no entry or the link exists in the topology graph, or the entry in the topology graph has the cost set to ininity and the LSU has the same timestamp as the entry in the topology graph but the link cost is not ininity. An LSU is considered outdated not only i it speciies a timestamp that is smaller than the one in the topology graph, but also i the timestamps are the same and the LSU carries a link cost ininity, while the entry in the topology graph has a cost dierent than ininity and the link is in the source graph. The reception o an outdated LSU causes the router to send an LSU with up-to-date inormation to the neighbor that originated the update message. I the LSU is a valid RESET and there is an entry in the topology graph or the link, the LSU is orwarded to the neighbors. A new source graph is computed and the routing table is updated i new link-state inormation is added to the topology graph or links are deleted rom the topology graph. The shortest-path tree is generated by running Dijkstra SPF algorithm on the topology graph. Rather than generating delete updates every time a link is removed rom the source graph, as is the case in LVA, ALP reports to its neighbors the new value o the parameters o a link removed rom the source graph i the cost o the link has increased. For those links that are removed rom the source graph and that had not a cost increase, the node will only announce their removal when it learns that the cost o such links increased. The links stored in the topology graph have a tag that is used to keep track o those links that had the source graph removal announcement postponed, and gives the current state o the link in the state diagram o Figure. The state diagram shows the transition to a new state or a link l =(u; v), given its current state and the type o input event received or the link. The tag o a link (u; v) or Node i is denoted TT i(u; v):tag, and its possible values at time t are the ollowing: : Link (u; v) is not in the source graph at time t i, where t reset t i t and t reset is the time the link last transitioned to State. The tag o a link is set to when the link is inserted into the topology graph or when the cost o the link increases. : Link (u; v) is in the source graph at time t. : Link (u; v) is not in the source graph at time t, but it was in the source graph at time t i,where t reset t i <t. The removal o the link rom the source graph had not been announced. The transition to NIL in the state diagram corresponds to the deletion o the link rom the topology graph. The description o possible input events summarized on the state diagram in Figure are given in Figure 5. In our current implementation o ALP, a link in the topology graph has just one reporting neighbor. This contrasts with

5 Update(k; msg) i ( msg = ; ) changed Update Topology Graph(k; msg); else changed TRUE; i ( changed =TRUE) newsg Build Shortest Path Tree(); Process Cost Increase State (newsg); Process Cost Increase State (newsg); Process Links RemovedFrom SG(newSG); event Update Routing Table(newSG); i (event=newlink or event = PARAMETER CHANGE or event = NEWSG EMPTY ) Compare Source Graphs(SGi ; newsg); g SG i newsg; g i ( k = i ) Send(); g Figure 3: Processing update message msg received rom neighbor k LSU(l) OR RESET(l) OR COST_INCREASE(l) OR VOID_RESET(l) LSU(l) i RESET(l) RESET(l) OR COST_INCREASE(l) Set cost o l to ininity i the node is not the head o the link; RESET(l) NO_INCREASE(l) nil DEL(l) DEL(l) nil RESET(l) OR COST_INCREASE(l) LSU(l) LSU(l) OR LSU(k) LSU(l) LSU(l) OR LSU(k) OR VOID_RESET(l) LSU(l) nil DEL(l) LSU(l) OR LSU(k), AND TG(l).cost is not ininity LSU(l) OR OUTDATED_RESET(l) OR DELETED(l) not rom irst reporting neighbor LSU(l) Figure : State diagram or a link l LVA, which considers a reporting neighbor to be any neighbor that has reported an LSU with sequence number that matches the sequence number or the link in the topology graph. The reporting neighbor or a link (u; v) in the topology graph is denoted TT i(u; v):rn, and consists o the address o the neighbor that last reported a valid LSU or the link i the state o (u; v) is, or the address o the neighbor that is in the shortest-path to u i (u; v) is in the source graph (i.e, the state o (u; v) is ), or the address o the neighbor that was in the shortest-path to u at the time link (u; v) was removed rom the source graph and transitioned to State. The reporting neighbor o a neighbor s adjacent link is the neighbor itsel. LSU(l) : LSU or link l other than RESET(l), VOID RESET(l), OUTDATED RESET(l), COST INCREASE(l), COST INCREASE(l), and DELETE(l). RESET(l) : LSU with cost ininity generated when link l ails or when l transitions rom State to State. VOID RESET(l) : Timestamp o LSU is equal to the timestamp o the link in the topology graph, the cost o the LSU is not ininity, and the cost o the link in the topology graph is ininity. OUTDATED RESET(l) : Timestamp o link in LSU is equal to the timestamp o the link in the topology graph, the cost o the LSU is ininity, the age o the LSU is greater than zero, and link l is in the source graph. COST INCREASE(l) : Cost o link l has increased. COST INCREASE(l) : Cost o LSU is greater than TT i(l):l. DELETE(l) : LSU reporting link l was removed rom the topology graph. DEL(l) : DELETE(l) or there is no reporting neighbor or link l. NO INCREASE(l) : cost o link l in LSU is not greater than TT i(l):l Figure 5: Input events o the state diagram When a link (u; v) is removed rom the source graph SG i and transitions to State, Node i needs to store the current cost o the link in TT i(u; v):l, which is used or checking increases in the cost o the link while (u; v) is in State. Ater computing the new source graph newsg (Figure 3) the router generates link-state updates or those links whose cost has increased and were removed rom the source graph, i.e., the links have transitioned rom State to State (Figure ). Then, the router generates RESETs or those links that had the cost increased while in State. I the router that transitions a link rom State to State is not the head o the link, the cost o the link in the topology graph is set to ininity. Procedure Update then executes Process Links RemovedFrom SG which sets TT i(u; v):l TT i(u; v):l and TT i(u; v):tag or each link (u; v) that was removed rom the source graph and had not the cost increased. The router then compares the new source graph newsg against the current source graph SG i,andlsus are created with the link-state inormation or links that are in newsg but not in SG i, or that are in both graphs but had their timestamp changed. Ater LSUs are generated, newsg becomes the current source graph SG i. The procedure Update is run having as input an empty message when a link-state inormation has been erased rom the topology graph due to aging. I a link cost changes, then its head node is notiied by an underlying protocol. The router then runs Update withthe appropriate message as input; the LSU in the message gets a current timestamp. This holds or simple changes in link cost, as well as or a link ailure. The same approach is used or a new link or a link that comes up ater a ailure. When a router establishes connectivity to a new neighbor, the router sends its complete source graph to the neighbor (much like a distance vector protocol sends its complete routing table). When the link (i; k) to neighbor k ails, the topology graph is updated to erase the neighbor rom the set TT i(i; k):f ( ), and a RESET or (i; k) is transmitted to the neighbors. For each link (u; v) in the topology graph whose reporting neighbor is router k, router i generates a DELETE update or (u; v) and deletes the link rom the topology graph. A router that receives a DELETE update rom a node other than the reporting neighbor transmits to the sender o the DELETE an LSU with the current state o the link i the link is in the source graph. This guarantees that the tree o reporting neighbors or link (u; v) E, ormed by the links (i; T T i(u; v):rn) E, or each Node i V, is updated accordingly. Link-state inormation or ailed links that have a reporting neighbor must be kept in the topology graph in order to validate incoming LSUs or the link. Consider the topology in Figure and assume that link (y; B) increases its cost dramatically (e.g., rom to ). Node y processes the link-cost increase and generates a new source graph;

6 the update message sent by Node y to its neighbors speciies an LSU or the link (y; B) with the new cost and LSUs or links (p; q), (x; z), (z; B) and (w; g), which must now be used to reach all the nodes in the graph. Note that router y does not inorm its neighbors that it removed links (B;z), (B; q) and (u; g) rom its source graph, as would be the case in LVA [], but makes the links to transition rom State to State (see Figure ). An important dierence between ALP and LVA is that in ALP a router inorms its neighbors o a link removed rom its source graph only i it is removed because its cost increased or because there is no reporting neighbor or the link anymore (in which case the cost is set to ininity). LVA reports all deletions to the source graph, and all such deletions represent ininite link costs. 3.. Electing Designated Routers Because routers in ALP communicate partial topology inormation to their neighbors, deining a designated router as in OSPF to be in charge o sending topology inormation over a network connecting multiple neighbor routers cannot be applied. In ALP, a link is assigned a designated router i it needs to be reported by at least one router over a given broadcast medium (a LAN, a network, or a link). The idea o assigning one designated router per link-state update consists o making only one router responsible or reporting the link-state update in a broadcast link. In this way, when an adjacency is ormed with a new neighbor x through a broadcast link, x will receive only one copy o the link-state inormation or a link (u; v) rom the routers that already have adjacencies in the link. To accomplish this, the topology graph entry TG i(u; v) maintains the set o interaces through which Node i has received link-state updates or the link (u; v), aswellasthe list o neighbors attached to the interace that have reported the link-state update. TG i(u; v):f contains the set o interaces, and TG i(u; v):f ( ) is the list o neighbors with adjacencies through interace that have reported a link-state update. When Node i receives a valid LSU rom neighbor x or link (u; v), the LSU or (u; v) is orwarded to all neighbors except x, i then stores neighbor s x s address in the list TG i(u; v):f ( ) TG i (u; v):f ;; TG i (u; v):f TG i (u; v):f [g; TG i (u; v):f() address o xg; I the received LSU (u; v) is not valid, but its timestamp is equal to the one stored in the topology graph, Node i also stores neighbor s x s address in the list TG i(u; v):f ( ),where is the incoming interace i ( = TG i (u; v):f ) TG i (u; v):f TG i (u; v):f [g; TG i (u; v):f() SORT(TG i (u; v):f() [address o xg); When a router i reports an LSU (u; v) through interace, it adds the address o into TG i(u; v):f ( ). The list o neighbors TG i(u; v):f ( ) is always sorted in ascending order o router addresses. The irst router address in the list (TG i(u; v):f ( ):) is the one with the smallest address. When a new adjacency is ormed to a neighbor k through interace, Node i will only report an LSU or link (u; v) to k i i is the head node o the link, or TG i(u; v):f and TG i(u; v):f ( ): equals s address. The procedure DST SET shown in Figure returns the set o interaces through which a link-state update or link (u; v) can be announced, and AN- NOUNCE returns TRUE i Node i can announce an LSU or (u; v) through the interace i has connectivity to neighbor k. For any given link used by a set o routers connected to a LAN, the router with the smallest ID is the only one allowed to send LSUs orthelinkoverthelan. DST SET(u; v) F set o operational interaces; i ( r = i ) or each ( interace TG i (u; v):f ) i ( TG i (u; v):f() = ; and TG i (u; v):f(): = :address ) F F,g; return F ; g ANNOUNCE(k; u; v) announce TRUE; interace attached to k; g i ( r = i and TG i (u; v):f ) i ( TG i (u; v):f() = ; and TG i (u; v):f(): = :address ) announce FALSE; return announce; Figure : Procedures used to determine to which neighbors a linkstate update can be announced When i detects loss o connectivity to a neighbor x attached to a broadcast link through interace, andx was the only router in TG i(u; v):f ( ), router i will announce an LSU or (u; v) in the broadcast link i it has a path to destination v whose successor is not a neighbor in the broadcast link. This guarantees that new neighbors that have not received link-state inormation about (u; v) will get it as soon as i detects lack o connectivity to x.. ALP Correctness In this section we show that routers executing ALP stop disseminating link-state updates and obtain shortest paths to destinations within a inite time ater the cost o one or more links changes and there are no more changes aterwards. For simplicity o exposition, we assume that all links are bidirectional point-to-point links and that shortest-path routing is implemented. Let t be the time when the last o a inite number o link-cost changes occur, ater which no more such changes occurs. The network G =(V; E) in which ALP is executed has a inite number o nodes (j V j) and links (j E j), and every message exchanged between any two routers is received correctly within a inite time. According to ALP s operation, or each direction o a link in G, there is a router that detects any change in the cost o the link within a inite time. The ollowing theorems relay on the use o timestamps as described in Section 3.; the same approach applies i an alternative update validation scheme based on resets is used. We also assume that all routers use the same type o tie-braking rules in computing shortest paths, e.g., i a shortest path to j is obtained through two dierent relays, routers choose the relay with the smallest identiier. Lemma : The dissemination o LSUs in ALP, other than DELETEs, stops a inite time ater t. Proo: A router that detects a change in the cost o any outgoing link must update its topology graph, update its source graph as needed, and send an LSU i the link is added to or is updated in its source graph. Let l be the link that last experiences a cost change up to t,andlett l be the time when the head o link l originates the last LSU o the sequence o LSUs originated as a result o the link-cost change occurring up to t. Any router that receives the LSU or link l originated at t l must process the LSU within a inite time, and decides whether or not to orward the LSU based on its

7 updates to its source graph. A router can accept and propagate an LSU only once because each LSU has a timestamp; accordingly, given that G is inite, there can only be a inite chain o routers that can propagate the LSU or link l originated at t l,andthe same applies to any LSU originated rom the inite number o link-cost changes that occur up to t. Thereore, ALP stops the dissemination o LSUs a inite time ater t. Lemma : The dissemination o DELETEs in ALP stops a inite time ater t. Proo: A router i that detects ailure o the link to the reporting neighbor o a link l in the topology graph must delete l rom the topology graph, update its source graph, and send a DELETE LSU or link l. Let the ailed link be the link that last experiences a cost change up to t,andlett l be the time when Node i originates the last LSU o the sequence o LSUs originated as a result o the link-cost changes occurring up to t. Any router that receives the DELETE or link l originated at t l must process the DELETE within a inite time, and orwards the DELETE ater deleting l rom its topology graph i the sender o the DELETE was the irst reporting neighbor o l. A router can accept and propagate a DELETE only once because the link is deleted rom the topology graph when the DELETE is accepted or the irst time, and a DELETE or link l is not propagated i link l is not in the topology graph o the router processing the DELETE. Given that G is inite, there can only be a inite chain o routers that propagate the DELETE or link l originated at t l, and the same applies to any DELETE originated rom the inite number o link-cost changes that occur up to t. Thereore, ALP stops the dissemination o DELETEs a inite time ater t. Theorem : The dissemination o LSUs in ALP stops a inite time ater t. Proo: The proo is immediate rom Lemmas and. From Theorem, it must be true that there is a time t s when no more LSUs are queued or in transit anywhere in the network. Lemma 3: A router with a tag value o or link l at time t s must be the head o the link or have at least one neighbor with a tag value o or. Proo: The proo is obvious i the router is the head o the link. Assume that router i is not the head o link l and that all o its neighbors have tags equal to at time t s. Because router i is not the head o link l and has link l in its source graph, it must have received an LSU reporting l rom at least one neighbor k at some time t <t s, which required k to have link l in its source graph at that time, i.e., to have a tag value o or l at time t <t s. By assumption, k has a tag equal to or link l, which means that k must have transitioned its tag value rom or to beore time t s. According to ALP s operation, at the time o its transition, k must have sent an LSU reporting an increase in the cost o link l, and it may also have sent LSUs or links that k adds or updates in its source graph. Because by assumption no LSUs are queued at or in transit to router i at time t s, i must have processed the LSU rom k indicating the cost increase or l, as well as any LSUs needed to bring i topology graph consistent with k s source graph. Because none o i s neighbors use link l in their shortest paths, because i has received the LSUs rom k that exclude link l rom being part o any shortest path rom k, and because all routers use the same tie-braking rules or shortest paths, it ollows that router i cannot use l in any o its shortest paths, because k does not. Accordingly, router i must transition to a tag value o or ater processing the LSUs rom k, and the Lemma is true. Lemma : A router with a tag value o or link l at time t s must be the head o the link or have at least one neighbor with a tag value o or. Proo: The proo is obvious i i is the head o link l, because i may have shorter paths to the tail o the link than the link itsel. Assume that router i is not the head o link l and that all its neighbors have tags equal to or link l at time t s. Because router i is not the head o link l and has link l in its source graph, it must have received an LSU reporting l rom at least one neighbor k at some time t <t s. Following the same line o argument used in the proo o Lemma 3, we can show that, at time t s, router i must have processed the LSU rom k indicating the cost increase or l, together with any LSUs needed to bring i topology graph consistent with k s source graph. According to ALP s operation, when router i has a tag value o or link l and receives an LSU reporting a cost increase or l, then it must transition to a tag value o and send an LSU; thereore, the theorem is true. Theorem : In a connected network, and in the absence o link ailures, all routers have the most up-to-date link-states they need to compute shortest paths to all destinations within a inite time ater t s. Proo: The proo is by induction on the number o hops o a shortest path to a destination, and is basically a generalization o the proo or SPTA []. Consider the shortest path rom router s to a destination j at time t s,andleth be the number o hops along such a path. For h =, the path rom s to j consists o one o the router s outgoing links. By assumption, an underlying neighbor protocol provides the correct parameter values o adjacent links within a inite time; thereore, the Theorem is true or h =, i.e., s must have link (s ;j) in its source graph, which means that its tag value or the link is and it must have sent its neighbors an LSU or that link. Assume that that any router with a path o n or ewer hops to j has the correct link-state inormation about all the links in the shortest path to j, and consider the case in which the path rom s to j at time t s is n +hops. Router s has a tag value o or each link in the shortest path to j, because the path belongs to its source graph. For any such link l in the shortest path to j, it ollows rom Lemma 3 that the router has a neighbor that by time t s has reported an LSU it can believe that speciies the up-to-date cost o l. Accordingly, the shortest path rom s to j must be through a neighbor s with a tag value o or or link l, which means that s must send the most up-to-date LSUs it receives or each link in its shortest path to j. The sub-path rom s to j has h, hops and, by the inductive assumption we have made, such a path must be the true shortest path rom s to j by time t s. Because all routers use the same tie-braking rules to choose shortest paths, this also means that that s must have a tag value o or each link in its shortest path to j. Because it is also true that s has the most recent link-state inormation about link (s ;s ), it ollows that s has the most recent inormation about all the links in its chosen path to j. The Theorem is thereore true, because the same argument applies to any chosen destination and router. Theorem 3: In a connected network, and in the absence o link ailures, a tree o reporting neighbors or a link l will be ormed within a inite time ater t s. Proo: For the neighbors o the head o the link l the root o the tree o reporting neighbors is the head o the link. The tree o reporting neighbors consist o routers whose value o the tag or link l can be,, or. Routers that have the tag set to elect as the reporting neighbor or l the next hop in theshortest-path tothe head o the link. Given that the source graph is computed within a inite time ater t s according to Theorem, the subtree o the tree o reporting neighbors that includes the source graph is computed a inite time ater t s. Whenever a valid link-state update or l is processed and l has a tag set to or ater computing the source graph, the reporting neighbor is set to be the router which sent the update message. Together with Lemma, this implies that the Theorem is true. Theorem : All the routers o a connected network have the most up-to-date link-state inormation needed to compute shortest paths to all destinations.

8 Proo: The result is immediate rom Theorem in the absence o link ailures. Consider the case in which the only link that ails in the network by time t is link (s; d). Call this time t t. According to ALP s operation, router s sends an LSU reporting an ininite cost or (s; d) within a inite time ater t ; urthermore, every router receiving the LSU reporting the ininite cost o (s; d) must orward the LSU i the link exists in its topology graph, i.e., the LSU gets looded to all routers in the network that had heard about the link, and this occurs within a inite time ater t.itthan ollows that no router in the network can use link (s; d) or any shortest path within a inite time ater t. DELETE updates will also be propagated by router s or all those links in the topology graph that had router d as the reporting neighbor, as described in the proo o Lemma. A router sends and LSU or a link l to the router that transmitted a DELETE update i l is in the source graph and the router is not the reporting neighbor o l. Accordingly, within a inite time ater t all routers must only use links o inite cost in their source graphs; together with Theorem, this implies that the Theorem is true. Theorem 5: I destination j becomes unreachable rom a network component C at t ; the topology graph o all routers in C includes no inite-length path to j. Proo: ALP s operation is such that, when a link ails, its head node reports an LSU with an ininite cost to its neighbors, and the state o a ailed link is looded through a connected component o the network together with DELETE updates or those links j that are part o the disconnected component to all those routers that knew about the link. Because a node ailure equals the ailure o all its adjacent links, it is true that no router in C can compute a inite-lengthpathtoj rom its topology graph ater a inite time ater t. Note that, i a connected component remains disconnected rom a destination j all link-state inormation corresponding to links or which j is the head node is updated when the network components get connected. The previous theorems show that ALP sends correct routing tables within a inite time ater link costs change, without the need to replicate topology inormation at every router (like OSPF does) or use explicit delete updates to delete obsolete inormation every time the source graph o a router changes (like LVA does). 5. Perormance ALP has the same communication, storage, and time complexity than LVA. However, worst-case perormance is not truly indicative o ALP s perormance advantage over LVA. Because linkstates are deleted rom the topology graph o a router, rather than ater receiving explicit delete updates rom neighbors, ALP incurs less communication overhead than LVA. ALP also compares avorably against recent distance vectors based on source tracing [3] [], or the diusion o distances [5], which do solve the looping problems o RIP and RIP-. Compared to the diusion o distances, ALP disseminates link-state inormation rom only the source o an LSU out to those routers that need the link, while DUAL requires distances to be disseminated rom the source o the update out to those routers whose path included the source o the update, ollowed by replies going back to the source. Hence, when such coordination occurs in DUAL, ALP incurs hal the communication overhead. Compared to source tracing algorithms, it is interesting to observe that in ALP a router notiies its routing tree to its neighbors by speciying each link in the tree, while in a source tracing algorithm the same tree is speciied by reporting, or each node on the tree, the distance rom the root o the tree to the node and the identiication o the previous node on the tree. Clearly, there is an one-to-one mapping between the two representations, which means that the same routers will receive LSUs or distancevectors updates reporting changes to the routing tree. In other words, the communication overhead is the same. Furthermore, in terms o communication overhead, it is not possible to attain a smaller overhead than sending updates (o links or distances) to only those routers whose shortest paths are aected by a topology change, i.e., ALP and source-tracing algorithms make very eicient use o communication, and both amount to a more distributed implementation o Dijkstra s SPF algorithm than protocols using topology broadcast (e.g., OSPF), which replicate SPF runs at each router. In terms o storage overhead, ALP has similar overhead than distance-vector protocols and link-state protocols or the case o shortest-path routing. ALP and other link-state protocols become more attractive than distance-vector protocols when providing multiple paths to the same destinations becomes necessary. Because o the way in which ALP updates link-state inormation, ALP outperorms any topology broadcast protocol. Because ALP does not use delete updates we expect ALP to outperorm LVA, specially when nodes ail or resources recover. Furthermore, because no counting-to-ininity occurs in ALP, ALP should outperorm protocols based on the Bellman-Ford algorithm. To veriy this, we ran a number o simulation experiments to compare its average perormance against DBF, topology-broadcast (called LSA in prior literature), and LVA. We used the same topology and experiment reported in [] in order to compare ALP against the best-perorming published results or other approaches. The perormance metrics consist o the number o steps and update messages that are required or each algorithm to converge (i.e., the algorithm stops sending messages), and the size o these updates. When a router receives an update message, it compares its local step counter with the sender s counter, takes the maximum and increments the count. Update messages are processed one at a time in the order in which they arrive. Like LVA and LSA, ALP uses Dijkstra s algorithm to compute the local shortest-path tree. The results presented are based on simulations or the DOE-ESNET topology [] which was used in order to simply use published simulation results or the competing approaches. The graphs in Figure 7 show the results or every single link changing cost rom to ; in Figures and 9 or every link ailing and recovering; as well as every node ailing and recovering again (Figures and ). All changes were perormed one at a time, and the algorithms had time to converge beore the next change occurred. The ordinate o Figures 7,, and 9 represent identiiers o the links, and the ordinate o Figures and represent the identiiers o the nodes that are altered in the simulation. ALP, DBF, and LVA propagate updates to only those routers aected by single link-cost changes (Figure 7). In contrast, LSA shows almost constant behavior because the same link-state update must be sent to all routers; ALP is the most eicient o the our algorithms. Each update message contains one link-state update in LSA, and an average o. links in ALP; the average number o messages transmitted in ALP is 3.3,.7 in LVA, and 57.5 in DBF. Figure depicts DBF suering rom counting to ininity in some cases. There is a small dierence in the average number o updates and synchronization steps required in ALP and LVA. The average size o an ALP message is.. When a ailed link recovers, ALP is superior to all three algorithms. The average number o messages in LVA is 7% more than in ALP; LSA exhibits the same behavior as with link-cost changes, and in average more than three times the number o update messages generated by ALP. With an average o 5.5 steps, ALP is twice as ast as LSA, and 5% aster than LVA. Messages in LSA are no longer one-link long due to the packets containing complete topology inormation sent over the recovering link. ALP also shows to have the best perormance o the our algorithms or ailing nodes. DBF always suers rom counting to ininity. ALP needs to send 3% ewer updates than LSA, and % less the amount experienced by LVA. For recovering nodes, ALP shows to be more eicient than LVA, DBF, and LSA, both in terms o the amount o inormation sent through the network and speed o convergence. The simulation results show that ALP has better overall average perormance than LVA, LSA, and DBF. ALP behaves better than DBF and LVA when link cost changes and is always aster and produces less overhead traic than LVA and LSA when resources are added to the network, and behaves better than the

9 ideal LSA when links or routers ail. This is precisely the desired result, and indicates that ALP is desirable even i multiple constraints are not an issue.. Conclusions We have presented ALP, which we believe is the irst example o a link-state protocol that has been shown to be more eicient than topology broadcast and recent distance-vector routing approaches. ALP is currently running in a small testbed implemented with PCs running gated, and the very same code was used in the reported simulation experiment. The size o ALP s executable code including the Hello Protocol and the Retransmission Protocol (Figure ) is 9 Kbytes, compared to the Kbytes o OSPF. A novel eature in ALP is the use o designated routers per link or each broadcast medium, rather than a designated router or the entire medium, and its ability to accommodate partitioned areas and multi-hop or partitioned IP subnets, which makes it adaptable to ad hoc networks. Simulations using the actual code or ALP corroborate the act that ALP achieves the most eicient way o disseminating update inormation in a routing protocol compared to topology broadcast, the distributed Bellman-Ford algorithm, and LVA. ALP addresses the complexity o today s approach to link-state routing by making the computation o routing trees using link-states costs a distributed computation and establishes link-state routing as the more eicient approach or the Internet, in terms o communication overhead and the ability to support eicient types o paths to destinations, which well become more important as QoS support emerges in the Internet. 7. Reerences [] Y. Rekhter and T. Li, A Border Gateway Protocol (BGP- ), RFC 5, July 99. [3] Y. Rekhter, Inter-Domain Routing Protocol (IDRP), Internetworking: Research and Experience, Wiley, Vol., No., June 993, pp. -. [] Merit GateD Consortium, updates Number o updates or link changes Size o updates or link changes ALP DBF LSA LVA [] R. Albrightson, J.J. Garcia-Luna-Aceves, and J. Boyle, EIGRP A Fast Routing Protocol Based on Distance Vectors Proc. Networld/Interop 9, Las Vegas, Nevada, May 99. [] D. Bertsekas and R. Gallager, Data Networks, Second Edition, Prentice-Hall, Inc., 99. [3] C. Cheng, et al, A Loop-Free Extended Bellman-Ford Routing Protocol without Bouncing Eect, Proc. ACM SIGCOMM 9, Austin, TX, September 99. [] E. Gani, Generalized Scheme or Topology-Update in Dynamic Networks, Lecture Notes in Computer Science (G. Goos and J. Hartmanis, Eds.), No. 3, pp. 7-9, 97. [5] J.J. Garcia-Luna-Aceves, Loop-Free Routing Using Diusing Computations, IEEE/ACM Trans. Networking, Vol., No., 993. [] J.J. Garcia-Luna-Aceves and J. Behrens, Distributed, scalable routing based on vectors o link states, IEEE Journal on Selected Areas in Communications, Vol. 3, No., 995. [7] C. Hedrick, Routing Inormation Protocol, RFC 5, Network Inormation Center, SRI International, Menlo Park, CA, June 9. [] International Standards Organization, 99: Intra-Domain IS-IS Routing Protocol, ISO/IEC JTC/SC WG N33, September 99. [9] J. Moy, OSPF Version, RFC 53, Network Working Group, March 99. [] R. Perlman, Fault-Tolerant Broadcast o Routing Inormation, in Computer Networks, North-Holland, Vol. 7, pp , 93. [] B. Rajagopalan and M. Faiman, A New Responsive Distributed Shortest-Path Routing Algorithm, Proc. ACM SIG- COMM 9, Austin, TX, September 99. size o updates steps Number o steps or link changes Figure 7: Links changing cost; number o update messages, average size o messages, and number o steps or convergence.