BGP with an Adaptive Minimal Route Advertisement Interval

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1 with a Adaptive Miimal Route Advertisemet Iterval Nead Lasković ad Ljiljaa Trajković Simo Fraser Uiversity Vacouver, British Columbia, Caada {laskovi, ljilja}@cs.sfu.ca Abstract The duratio of the Miimal Route Advertisemet Iterval (MRAI) ad the implemetatio of MRAI timers have a sigificat ifluece o the covergece time of the Border Gateway Protocol (). Previous studies have reported existece of optimal MRAI values that miimize the covergece time for various etwork topologies ad traffic loads. I this paper, we propose the adaptive MRAI algorithm for adaptive adjustmet of MRAI values. We also itroduce reusable MRAI timers that idepedetly limit advertisemets of idividual destiatios. The modified is amed with adaptive MRAI (-AM). processig delay used i the evaluatio of -AM is based o reported measuremets. s-2 simulatio results demostrate that -AM leads to a shorter covergece time while maitaiig a umber of update messages comparable to the curret implemetatio. -AM covergece time depeds liearly o the processig delay. 1. Itroductio The Iteret cosists of umerous heterogeeous etworks without a cetralized cotrol. These etworks are clustered i groups called Autoomous Systems (ASs), where each AS is cotrolled by a commo admiistrative etity. Commuicatio betwee ASs requires a commo protocol. Border Gateway Protocol () [1] is the de facto stadard iter-domai routig protocol i today s Iteret. suffers from log covergece time. The covergece time is the time that elapses from the momet whe a chage of a route occurs util all routers accordigly adjust their routig tables [2]. This updatig of route iformatio is called the covergece process. Durig this process, routig tables may cotai obsolete routig iformatio, which may cause iaccessibility of ASs, packet loss, ad additioal This research was supported by the NSERC Grat ad the Caada Foudatio for Iovatio New Opportuities program. overhead to routers [3], [4]. To reduce the overall umber of messages ad the covergece time, limits the rate of messages exchaged betwee routers. Oe of the rate limitig parameters is the Miimal Route Advertisemet Iterval (MRAI) or MRAI roud, which defies the miimum time iterval betwee sedig two cosecutive update messages for the same destiatio. The covergece time is affected by the duratio of MRAI ad the implemetatio of MRAI timers. The default MRAI value (3 s) is used i the majority of today s routers [5]. This value is ot optimal for every etwork topology ad usig smaller values may lead to a sigificat decrease of the covergece time [2]. It has also bee reported that a optimal MRAI value depeds o the etwork topology ad traffic load [2]. Oe proposed solutio for fidig a optimal MRAI value is usig adaptive MRAI timers [4]. No implemetatio details have bee reported [4]. I this paper, we propose a adaptive MRAI algorithm for adjustig MRAI values for every destiatio i each router. The curret implemetatio of MRAI timers (such as per-peer MRAI timers) prologs the covergece time because they impose delay o all route advertisemets regardless of their destiatios. Hece, we propose reusable MRAI timers that idepedetly limit advertisemets of idividual destiatios, while retaiig the efficiecy of per-peer MRAI timers. The proposed modificatio, amed with adaptive MRAI (-AM), employs the adaptive MRAI algorithm ad reusable MRAI timers. A accurate estimatio of the delay due to processig of messages i routers ( processig delay) is importat for aalysis ad simulatio of the dyamic behavior. A commoly used approach for calculatig the processig delay (such as the uiform processig delay [2]) assumes that the average time eeded for processig messages depeds liearly o the umber of received messages. However, recet measuremets [6] idicate that assumig uiform delay leads to urealistically high estimates of processig delay. We use, istead, the empirical processig delay based o reported measuremets [6], [7].

2 We have implemeted -AM i the s-2 etwork simulator [8]. Simulatio results idicate that -AM leads to a shorter covergece time, with a comparable umber of update messages as the curret implemetatio [1]. The paper is orgaized as follows. dyamic behavior is described i Sectio 2. I Sectios 3 ad 4, we describe reusable MRAI timers ad the adaptive MRAI algorithm, respectively. Simulatio results for two etwork topologies are give i Sectio 5. We coclude with Sectio Dyamic behavior of speakers (routers) [1] exchage a large umber of update messages due to persistet chages of the Iteret topology. Each speaker adds ew ad deletes ufeasible routes to destiatios. Therefore, is characterized by cotiuous chages of routig tables. Durig the covergece process, a speaker may exchage messages with its peers over several iteratios util it fids the best route (coverges). The ed of the covergece process for a sigle destiatio is defied as the istat whe all speakers i a etwork stop geeratig update messages for the specific destiatio. The covergece time for a sigle destiatio is defied as the time elapsed betwee the istat whe the first update message cotaiig a chage of the destiatio reachability is set ad the istat whe all correspodig update messages are received [2]. To miimize the umber of update messages ad adequately react to chages i the Iteret topology, implemets rate limitig by usig MRAI timers. The default duratio of a MRAI roud is 3 s [1] ad it is cotrolled by MRAI timers. However, maufacturers may use other values for the duratio of MRAI roud. For example, Juiper s default cofiguratio sets MRAI to s [6], [9]. The idepedet rate limitig of various destiatios may be achieved by usig per-destiatio MRAI timers, where oe per-destiatio MRAI timer is associated with oe destiatio i a routig table. The routig table i a core Iteret router cotais over 1, destiatios [1] ad the implemetatio of such a large umber of timers is ot feasible. Rather tha usig per-destiatio MRAI timers, RFC 1771 [1] proposes implemetig perpeer timers. Each per-peer MRAI timer is associated with oe peer. The timer is set whe a route advertisemet is set to the correspodig peer, regardless of its destiatio. A advatage of per-peer timers is that their umber is equal to the maximum umber (several hudred) of peers correspodig to oe speaker. A disadvatage is that they limit advertisemets of all destiatios set to the peer (eve those that are advertised for the first time). 2.1 Uiform processig delay processig delay is the delay imposed o a update message i a speaker. It is a importat parameter i the aalysis of the dyamic behavior. It icludes the queuig time of a message ad the time eeded for to process the received message. The uiform processig delay [2] has bee widely used i studies of the covergece time [1] [12]. It has also bee implemeted i SSFNET [13]. It assumes that a speaker processes each update message idepedetly. (Updates are queued ad processed sequetially.) The processig delay of each message is estimated usig a uiformly distributed radom variable from the iterval [p mi, p max ]. Commoly used values are p mi =.1 s ad p max = 1 s [2]. The average processig delay t process (p) for a group of N queued updates is: ( p - mi ) ( ) max p t process p = N. (1) 2 Eq. (1) idicates that the average processig delay depeds liearly o the umber of update messages. Measuremets have show that this umber may exceed 1 messages per secod i the core Iteret routers [1]. This suggests that usig the uiform delay with p mi =.1 s ad p max = 1 s may ot be appropriate i the case of extesive exchage of update messages. Eve for a moderate umber of messages (~2), usig the uiform delay leads to urealistically high values for the average processig delay (~1 s). Recet measuremets o Cisco routers idicated that the average processig delay is much shorter tha predicted by the uiform delay [6]. They revealed that speakers process groups of update messages i costat 2 ms processig cycles. Whe a speaker operates below its maximum CPU utilizatio, it may process most messages that it receives at the ed of a 2 ms cycle. The average processig delay is betwee 11 ad 11 ms. Over 95% messages are processed withi 21 ms. Nevertheless, i the case of high traffic loads, a speaker caot process all received messages i oe 2 ms cycle ad the maximum processig delay may reach several secods. Measuremets of router CPU utilizatio [7] have idicated that i over 99% cases, the core Iteret routers operate uder 5% of their capacity. Processig messages usually has a higher schedulig priority tha other processes i a speaker [6]. Hece, most of the time, routers process all update messages withi oe 2 ms processig cycle, which is sigificatly shorter tha the value estimated by the uiform delay (~1 s). 2.2 Empirical processig delay We propose to use a empirical value for the

3 processig delay. It is based o the reported measuremets of CPU utilizatio of routers [7] ad the average processig delay [6]. We assume that speakers operate uder a usual traffic load ad that they process update messages withi 2 ms cycles. We also assume that a speaker completes processig all received updates at the ed of the 2 ms processig cycle. As a result, the processig delay is idepedet of the umber of updates ad the maximum processig delay of oe update message is 2 ms. However, speakers uder heavy traffic load caot process all received updates i oe 2 ms processig cycle, which leads to loger processig delays [6]. This behavior of speakers may be modeled by usig loger processig cycles, which would result i loger processig delays. To illustrate differeces betwee the empirical ad uiform processig delays, we cosider a simple case whe MRAI timers i all speakers start at the same time, as show i Fig. 1. Show are times whe a speaker receives (dashed lies) ad seds (solid lies) update messages for a sigle destiatio. The istat whe a speaker seds update messages marks the begiig of a MRAI roud. Each MRAI roud cosists of a active ad a idle period. The active period is the segmet of the MRAI roud whe a speaker processes the received update messages. It lasts from the begiig of a MRAI roud util the last message i the roud has bee received. The period betwee the last received message ad the ed of the MRAI roud is called the idle period. Durig the idle period, the speaker does ot receive ew update messages regardig that particular destiatio. Usig the empirical delay value more accurately reflects the behavior of speakers ad reveals that they are ofte idle durig a MRAI roud. These log idle periods icrease the covergece time. Hece, miimizig the idle periods optimizes the covergece time. To achieve the optimal covergece time for oe destiatio, the MRAI value should be chose close to the active period of each MRAI roud. If MRAI rouds do ot start at the same time, the idle period caot be defied as the iterval betwee the last received message ad the begiig of the ext MRAI roud. Istead, we defie the idle period as the logest time iterval betwee two received messages i oe MRAI roud. The active period is the defied as the differece betwee the duratio of a MRAI roud ad the idle period. The optimal covergece time may be achieved by miimizig the idle period of speakers, as i the case whe MRAI rouds start at the same time. Messages received ad set Messages received ad set Active period Idle period Message received Messages set Time (s) (a) Active period Idle period Message received Messages set Time (s) Fig. 1. Duratios of the active ad idle periods whe usig (a) empirical (2 ms cycles) ad uiform (pmi =.1 s ad pmax = 1 s) processig delays. 3. Reusable MRAI timers The mai drawback of per-destiatio MRAI timers is that they use separate timers for each destiatio, eve for destiatios that are advertised at the same time. Istead of associatig oe MRAI timer with each destiatio, we propose usig a sigle reusable MRAI timer for all route advertisemets set durig a certai (short) time iterval. We redefie the rate limitig so that MRAI rouds belog to this iterval (rather tha beig equal to 3 s). The duratio of the iterval defies the graularity of the MRAI roud ad determies the umber of reusable MRAI timers. For example, if MRAI is betwee 29 s ad 3 s, tha the graularity of MRAI is 1 s ad a speaker eeds 3 reusable timers shifted by 1 s, as show i Fig. 2. The reusable Timer starts at t, Timer 1 starts at t 1 = t + 1 s, while the last reusable timer (Timer 29) starts at t 29 = t + 29 s. The etire cycle repeats after Timer expires at 3 s (t +3 s). Timer 29 Timer 1 Timer 1 Timer Timer t Fig reusable MRAI timers with the graularity of MRAI roud equal to 1 s. A speaker eeds to determie which reusable

4 MRAI timer is to be associated with a set route advertisemet. For each advertisemet, the last expired reusable timer is used because it eforces a MRAI roud to last betwee 29 s ad 3 s. Reusable MRAI timers eable to hadle advertisemets idepedetly, as i the case of per-destiatio MRAI timers. The implemetatio of reusable MRAI timers requires storig poiters that associate each ocoverged route with the correspodig timer. Similar to per-peer MRAI timers, reusable MRAI timers maitai oly a list of poiters for o-coverged routes. A core Iteret router usually deals oly with several hudred o coverget routes, while to the etire routig table may cotai over 1, routes [1]. Hece, the overhead for storig poiters to reusable timers is ot sigificat. deviatio equal to zero would leave the secod adaptive MRAI roud without the safety margi if the active period icreases. New update message received at t R idle state Advertisemet of destiatio D set to peers at t Iitializatio(t ) processig state reusable_timer expired at t E No ew updates i the last T s 4. Adaptive MRAI algorithm calculate idle (t R ) calculate idle (t E ) idle state Fidig the optimal MRAI requires kowig the active period durig a MRAI roud. We were uable to use statistical methods to predict the active period because the distributios of the duratios of active period ad iter-arrival times of update messages were ot available. Hece, we estimate the active period i the followig roud usig the average active period of the previous rouds. The fluctuatios of the active period are estimated usig the stadard deviatio. We also itroduce a safety margi to esure that i the case whe a active period icreases, the ext roud ecompasses all set update messages. We choose the margi equal to three times the stadard deviatio of a adaptive MRAI roud. Thus, the duratio of the ext adaptive MRAI roud for destiatio D is estimated as: adaptivemrai + 1( D) = (2) avg_ active ( D) + 3 deviatio ( D), where avg_active ad deviatio are the average duratio ad the stadard deviatio of the active period for destiatio D i the -th roud, respectively. The miimum duratio of the adaptive MRAI roud is determied by the umber of reusable MRAI timers. For example, for 3 reusable MRAI timers, the miimum duratio of the adaptive MRAI roud is equal to 1 s. The adaptive MRAI has idle ad processig states, as show i Fig. 3. The variables are give i Table 1. The algorithm is i the idle state for all destiatios with stable paths. Whe a chage of destiatio reachability causes a chage of the best route, the speaker seds the first update message to its peers. At that istat, the algorithm eters the processig state. This also marks the begiig of the first adaptive MRAI roud. Iitial values of variables are set i the first adaptive MRAI roud. I the first roud, the duratio ad the stadard deviatio are set to the default value of 3 s ad 1 s (rather tha s), respectively. Usig the stadard processig state begiig of ew roud processig state Fig. 3. The adaptive MRAI algorithm. Table 1. Variables of the adaptive MRAI algorithm used for destiatio D i the -th roud. roud -th roud of the covergece process adaptivemrai duratio of the adaptive MRAI roud idle duratio of the idle period active duratio of the active period avg_active the average active period deviatio stadard deviatio of the average active period reusable_timer serial umber of the reusable timer last_received_update time whe the last update message was received Three types of evets may occur i the processig state: i) receptio of a ew update message, ii) expiratio of the reusable timer associated with a destiatio, ad iii) the completio of the covergece process. Whe a speaker receives a ew update message, the algorithm remais i the processig state ad calculates the idle period. The idle period is the logest iterval betwee two update messages i a MRAI roud. The expiratio of the reusable MRAI timer associated with a destiatio idicates the begiig of a ew adaptive MRAI roud. At that time, the speaker recalculates the idle period, the average active period, ad the stadard deviatio of the active period. They are used to predict the duratio of the ext adaptive MRAI roud, as show i Fig. 4. A short idle period durig the previous roud may idicate that the active period is loger tha predicted ad that the previous adaptive MRAI roud should have bee

5 loger. The threshold for determiig the miimum idle period is set to 1 s, which is idetical to the graularity of the adaptive MRAI rouds. If the speaker detects that the idle period is less tha 1 s, it doubles the duratio of the ext adaptive MRAI roud up to the maximum of 3 s. The maximum duratio of adaptive MRAI roud (3 s) is equal to the default MRAI value [1]. Hece, the adaptive MRAI algorithm caot lead to loger covergece time tha the curret implemetatio. At the begiig of a ew MRAI roud, the speaker assigs agai a reusable timer for the destiatio. Differet reusable MRAI timers may be used for the same destiatio i each adaptive MRAI roud. active = adaptivemrai - idle avg_ active = f(avg_ active -1, roud ) deviatio = f(deviatio -1, roud ) o adaptivemrai +1 = avg_ active + 3 x deviatio o begiig of ew roud idle < 1 s adaptivemrai +1 > 3 s yes adaptivemrai +1 = 3 s yes adaptivemrai +1 = 2 x avg_ active reusable_timer +1 = t E + adaptivemrai idle +1 = ; roud +1 Fig. 4. The procedure for calculatig the variables at the begiig of a adaptive MRAI roud. We assume that the speaker has coverged ad that it returs to the idle state if it does ot receive update messages regardig the destiatio withi a certai predefied time period T. The details of the implemetatio i commercial routers are ot publicly available. Hece, we address the feasibility of the adaptive MRAI by estimatig the implemetatio overhead. The adaptive MRAI algorithm depeds o the routes that have ot coverged because the algorithm is used oly whe the best route to a destiatio chages. The size of the iput is the umber of o-coverged routes i a uit of time. The implemetatio of the adaptive MRAI requires the speaker to store four variables for each ocoverged route: roud, avg_active, deviatio, ad last_received_update. roud is a iteger couter, while the remaiig three variables cotai time stamps i millisecods. Hece, it is sufficiet to use four itegers for storage. Other variables listed i Table 1 may be calculated usig these four variables. Therefore, the space complexity of the adaptive MRAI algorithm is O() (a liear fuctio of the iput size). The time complexity of the adaptive MRAI algorithm is O(). It is defied as the umber of operatios performed whe the algorithm is i the processig state, as show i Fig. 3. The idle period ad the variables i Table 1 are calculated whe a reusable timer expires (the begiig of a adaptive MRAI roud). Oly the idle period is calculated whe a ew update message is received. The graularity of MRAI rouds determies the shortest duratio of a MRAI roud. The upper boud o the umber of adaptive MRAI rouds for each route that has ot coverged is equal to the graularity. Thus, the umber of adaptive MRAI rouds depeds liearly o. The time complexity of the calculatio at the begiig of a ew adaptive MRAI roud ca also be expressed as a fuctio of the iput size. For example, if the graularity is 1 s, there is at most oe adaptive MRAI roud per secod for each o-coverged route. Durig oe MRAI roud, a speaker seds up to two update messages (oe advertisemet ad oe withdrawal) regardig each route. A speaker caot sed more tha oe advertisemet due to the rate limitig. It also caot withdraw the same route twice i a sigle MRAI roud. Hece, the maximum umber of received update messages durig oe MRAI roud for oe speaker depeds o the umber of o-coverged routes ad the umber of its peers. Sice the umber of peers is costat for oe speaker, the time complexity of the idle period calculatio is O(). The average active period (avg_active ) i roud is: activei ( D) avg _ active ( ) = D (3) i = avg _ active- 1( D) +, where = active avg_active -1. Hece, the average active period may be calculated usig the curret value of active period (active ) ad the value from the previous roud (avg_active -1 ). The stadard deviatio of the active period (deviatio ) may also be calculated usig the value from the previous roud (deviatio -1 ) ad : deviatio ( D) = ( 2 deviatio -1( D) deviatio 2-1 ( D)). (4)

6 Based o (3) ad (4), the maximum umber of operatios at the begiig of a adaptive MRAI roud for each route is costat: 4 additios, 3 subtractios, 2 multiplicatios, 2 divisios, 2 comparisos, ad 1 square root operatio. Hece, the time complexity of calculatig the variables at the begiig of a adaptive MRAI roud is O(). 5. Performace of the adaptive MRAI We implemeted the adaptive MRAI algorithm, reusable MRAI timers, ad the empirical ad uiform delays i the s-2 etwork simulator (s-2.27) [8] usig the s- 2. [14] module. We use two etwork topologies to evaluate the performace of -AM ad compare it with the curret implemetatio of. The simulatios were performed o a 2.8 GHz Itel Petium 4 processor with 2 GB of RAM usig Liux Red Hat 9. operatig system. The average duratios of oe simulatio for the etwork topology with 11 odes were ~2.5 mi ad ~2 mi, for ad -AM, respectively. The simulated topologies were limited to 11 odes, due to extesive simulatio times. Several simplificatios were adopted i order to observe the effects of the adaptive MRAI algorithm o the covergece time: i) log-term istabilities (route flaps) were ot cosidered because they may cause log route suppressios ad, hece, mask effects of the adaptive MRAI algorithm [15], ii) routig policies were ot applied because they may cause persistet route oscillatios [16], ad iii) each AS cosisted of a sigle speaker i order to limit the umber of speakers i simulatios. Commoly used scearios for aalysis [2], [1] ad measuremets [3], [4] of the covergece time cosist of the up (advertisemet) ad dow (withdrawal) phases. I the up phase, a ew destiatio is itroduced to a etwork. The destiatio is directly coected to a sigle speaker called the origi. The covergece time T up is the time betwee the istat whe the first update message is set from the origi ad the istat whe all speakers have foud the shortest path to the destiatio. At the ed of the up phase, the origi seds a withdrawal of the destiatio. This marks the begiig of the dow phase. The covergece time T dow is the time eeded for all speakers to reach the ew steadystate whe they have o path to the destiatio (the origi is the oly speaker coected to the destiatio). The adaptive MRAI algorithm limits the umber of update messages for each destiatio idepedetly. Hece, we use oly oe destiatio coected to the origi i each simulatio. The impact of other update messages o the average processig delay is modeled by the empirical delay. Each simulatio sceario is repeated 3 times usig 3 uique radom umber geerator seeds to radomly shift the startig times of reusable MRAI timers, per-peer MRAI timers, ad processig cycles of update messages i distict speakers. We assume that per-peer MRAI timers work cotiuously, which mimics the observed behavior of speakers [4]. speakers use the seder side loop detectio (SSLD) mechaism ad limit oly the advertisemets (withdrawal limitig is ot used) [1]. We also assume that the covergece process is completed if o update messages are exchaged betwee speakers withi the chose period T (6 s). If ot otherwise stated, the adaptive MRAI employs 3 reusable MRAI timers (with graularity of 1 s) ad a 2 ms processig cycle for the empirical delay. 5.1 Completely coected graph The simulated etwork is a completely coected graph with 15 odes. This topology, although ot a realistic represetatio of the Iteret, is cosidered as the worst case sceario for the covergece time i the dow phase because it has the maximum umber of possible paths for a give umber of odes [3]. ASs situated i the core of the Iteret are heavily coected ad their itercoectios may be modeled as completely coected graphs [2], [1]. The choice of the origi i a completely coected graph does ot affect simulatio results because of the graph symmetry. The up phase is ot simulated because all odes are directly coected to the origi ad, hece, coverges almost istataeously. The average covergece time for with the default value of MRAI (3 s) is s, as show i Fig. 5(a). It decreases to 45.1 s with -AM. The average umber of update messages is 1,48 ad 1,553 for ad -AM, respectively, as show i Fig. 5. The results for are similar to previously reported [2], [1]. I the case of the adaptive MRAI algorithm, the covergece time ad the umber of update messages are idepedet of the MRAI roud duratio specified i the curret implemetatio (-AM adaptively adjusts duratios of MRAI rouds, whereas the curret uses a costat MRAI roud through the etire covergece process). covergece time for various duratios of the processig cycle is show i Fig. 6(a). The miimum value of the processig cycle of 2 ms correspods to the ormal operatio of a speaker. The maximum value of 3 s correspods to situatios whe speakers ecouter high traffic loads. The average covergece time (dashed lie) does ot deped sigificatly o the duratio of processig cycles. This is to be expected because the default duratio of MRAI provides sufficiet time for speakers to process all received messages. I the case of the adaptive MRAI

7 (solid lie), the average covergece time is a liear fuctio of the processig cycle because the adaptive MRAI adjusts the duratio of MRAI rouds based o the average processig delay. Hece, the covergece time icreases proportioally with the icrease of the average processig delay. The average umber of update messages is similar i both cases (~1,5), as show i Fig. 6. It is cosistet with the values show i Fig. 5. The duratio of the processig cycle does ot sigificatly affect the umber of update messages. Covergece time (s) Number of updates AM with adaptive MRAI s 45.1 s MRAI (s) (a) 4 3 with adaptive -AM MRAI MRAI (s) Fig. 5. Effect of MRAI o the dow phase: (a) covergece time ad the umber of update messages. The average covergece time ad the average umber of reusable MRAI timers for the dow phase are show i Table 2. The umber of reusable MRAI timers determies the graularity of MRAI ad the miimum duratio of the adaptive MRAI roud. Although a fier graularity is desired, decreasig the graularity implies icreasig the umber of timers ad the complexity of the implemetatio. Therefore, the umber of MRAI timers is a trade-off betwee complexity ad performace. Table 2 idicates comparable covergece times for graularities fier tha or equal to 1 s. Usig graularities coarser tha 1 s prologs the covergece time because the maximum active time is at most 1 s. Thus, for this simulatio sceario, the optimal graularity is 1 s. It achieves similar performace with fewer timers tha for graularities of.5 s or.25 s. Usig graularity of 1 s requires oly 3 MRAI timers, comparig to several hudred per-peer MRAI timers eeded i the core Iteret routers [1]. Covergece time (s) Number of updates AM Duratio of processig cycle (s) (a) -AM Duratio of processig cycle (s) Fig. 6. Effect of the processig cycle o the dow phase: (a) covergece time ad the umber of update messages. Table 2. The average covergece time ad the average umber of update messages for various umbers of reusable MRAI timers. Number of timers Graularity (s) Covergece time (s) Number of updates , , , , , Network with 11 odes We also simulated a etwork with 11 odes from the Uiversity of Orego Route Views Project [17]. Simulatio results for up phase ad dow phase are show i Fig. 7 ad Fig. 8, respectively. Simulatios are repeated for every ode as the origi because the covergece time depeds o the legth of paths from the origi to other speakers. The covergece processes last ~4 MRAI rouds for the up phase ad ~2 MRAI rouds for the dow phase, due to the large etwork diameter. Usig the adaptive MRAI algorithm decreases the covergece times from ~12 s to ~35 s i the up phase, as show i Fig. 7(a). It icreases the overall umber of update messages by ~3%, as show i Fig. 7. I the dow phase, the adaptive MRAI decreases the covergece time from ~6 s to ~1 s, as show i Fig. 8(a). The umber of update messages decreases by ~2%, as show i Fig. 8.

8 Covergece time (s) Number of updates AM Node (a) 8 6 -AM Node Fig. 7. Up phase: (a) the covergece time ad the umber of update messages for various origi odes. Covergece time (s) Number of updates AM Node 1.5 x (a) AM Node Fig. 8. Dow phase: (a) the covergece time ad the umber of update messages for various origi odes. 6. Coclusios I this paper, we preseted the adaptive MRAI algorithm that eables speakers to adjust the duratio of MRAI rouds based o the umber of received update messages. The algorithm employs reusable MRAI timers. The proposed -AM algorithm was implemeted i the s-2 etwork simulator. The simulatio results show that adaptive MRAI leads to shorter covergece times i both up ad dow phases for two simulated etwork topologies. The umber of exchaged update messages remais comparable to the curret implemetatio. The covergece time with adaptive MRAI is a liear fuctio of the average processig delay. As i the case of, it depeds o the umber of MRAI rouds required for to coverge. The improvemet of -AM over the curret is particularly oticeable i the case of large etworks i the dow phase, whe the covergece time decreases by ~8%. Refereces [1] Y. Rekhter ad T. Li, A border gateway protocol 4 (-4), IETF RFC 1771, Mar [2] T. Griffi ad B. Premore, A experimetal aalysis of covergece time, i Proc. ICNP, Riverside, CA, Nov. 21, pp [3] C. Labovitz, A. Ahuja, A. Bose, ad F. Jahaia, Delayed Iteret routig covergece, IEEE/ACM Tras. Networkig, vol. 9, o. 3, pp , Jue 21. [4] C. Labovitz, A. Ahuja, R. Wattehofer, ad S. Vekatachary, The impact of Iteret policy ad topology o delayed routig covergece, i Proc. INFOCOM, Achorage, AK, Apr. 21, pp [5] S. Hares ad A. Retaa, 4 implemetatio report, Iteret Draft, Oct. 24. [Olie]. Available: [6] A. Feldma, H. Kog, O. Maeel, ad A. Tudor, Measurig pass-through times, i Proc. PAM, Atibes Jua-les-Pis, Frace, Apr. 24, pp [7] S. Agarwal, C. Chuah, S. Bhattacharyya, ad C. Diot, Impact of dyamics o router CPU utilizatio, i Proc. PAM, Atibes Jua-les-Pis, Frace, Apr. 24, pp [8] s-2 [Olie]. Available: [9] Z. Mao, R. Bush, T. Griffi, ad M. Rougha, beacos, i Proc. IMC, Miami Beach, FL, Oct. 23, pp [1] B. Premore, A aalysis of covergece properties of the Border Gateway Protocol usig discrete evet simulatio, Ph. D. Dissertatio, Dartmouth College, 23. [11] J. Nykvist ad L. Carr-Motyckova, Simulatig covergece properties of, i Proc. ICCCN, Miami, FL, Oct. 22, pp [12] D. Pei, X. Zhao, L. Wag, D. Massey, A. Maki, S. F. Wu, ad L. Zhag, Improvig covergece through cosistecy assertio, i Proc. INFOCOM, New York, NY, Jue 22, pp [13] SSFNET [Olie]. Available: [14] T. D. Feg, R. Ballatye, ad Lj. Trajković, Implemetatio of i a etwork simulator, i Proc. ATS, Arligto, VA, Apr. 24, pp [15] Z. Mao, R. Govida, G. Varghese, ad R. Katz. Route flap dampig exacerbates Iteret routig covergece, i Proc. SIGCOMM, Pittsburgh, PA, Aug. 22, pp [16] K. Varadha, R. Govida, ad D. Estri, Persistet route oscillatios i iter-domai routig, Computer Networks, vol. 32, o. 1, pp. 1 36, Ja. 2. [17] The Uiversity of Orego Route Views Project [Olie]. Available:

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