An Opportunistic Burst Cloning Scheme for Optical Burst Switching over Star Networks

Transcription

1 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July A Opportuistic Burst Cloig Scheme for Optical Burst Switchig over Star Networks Salek Riadi, Adelilah Maach, Driss El Ghaami Computer Sciece Departmet, Mohammadia School of Egieers, Mohammed V-Agdal Uiversity, Raat, Morocco, salek.riadi@gmail.com, maach@emi.ac.ma, elghaami@emi.ac.ma Astract I optical urst switched (OBS) etworks, urst loss is maily due to cotetio that occurs at oth edge ad core ode. At edge ode, cotedig urst may e electroically queued. Whereas at core ode, which lacks of optical memory ad wavelegth coversio capaility, cotedig urst will e dropped. Burst cloig prevets urst loss at core odes y sedig multiple copies of the same urst through OBS etwork simultaeously i order to ehace proaility that at least oe copy will reach destiatio. However, at high load, urst cloig leads to a sigificat urst loss at edge odes, which ecome uale to schedule ew ursts at earliest tolerale departure time. I this paper, we adopt urst cloig scheme with star topology ad we propose a opportuistic urst cloig scheme, which aims to cotrol the extra load of urst cloig i order to reduce urst loss at oth edge ad core ode. We perform oth aalytical ad simulatio aalyses o covetioal OBS, asic urst cloig scheme ad opportuistic urst cloig scheme over star etworks. We oserve that opportuistic urst cloig scheme achieves etter overall etwork performace tha the other approaches. Idex Terms asic urst cloig, opportuistic urst cloig, optical urst switchig, optical star etwork. I. INTRODUCTION Optical Burst Switchig (OBS) has ecome a mature techology to support the curret ad ext geeratio Iteret over ufferless wavelegth divisio multiplexig etworks [1]. It ca e cosidered as itermediate solutio etwee optical circuit switchig, which has a low complexity ut it suffers from low adwidth utilizatio, ad optical packet switchig, which has advatage of high adwidth utilizatio ut at the cost of high complexity [2], [3]. I OBS etworks, a data urst, which cosists of multiple packets, is created at igress ode ad switched y oe or more core odes alog the etwork all-optically util it reaches its destiatio egress ode. Before the start of the urst trasmissio, the igress ode seds a cotrol packet to reserve a wavelegth for the urst at each core ode, where the cotrol packet is suject to optical-electric-optical coversios. If the wavelegth reservatio fails due to the cotetio with aother urst at a core ode, which lacks of optical memory ad wavelegth coversio capaility, the the urst is lost. Loss recovery represets oe of the major challeges that face researchers. Loss recovery Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

2 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July mechaisms have ee classified ito two categories, called reactive ad proactive; reactive mechaisms are etter suited whe urst loss is rare ad adwidth utilizatio eeds to e optimized, however proactive mechaisms are etter suited whe cotetio loss is high ad delay eeds to e optimized [4]. Burst cloig is a proactive loss recovery mechaism; the idea is to replicate a urst ad sed duplicated copies of the urst through the etwork simultaeously; if the origial urst is lost, the cloed urst may still e ale to reach the destiatio [5]. To our kowledge, urst cloig is studied oly i mesh topologies whereas star OBS etworks have received cosiderale attetio from researchers ad idustrials [6]-[10]. I this paper, we adopt the urst cloig scheme with star topology ad we demostrate that the urst cloig scheme ca lead to a sigificat urst loss at edge odes, which ecome uale to schedule ew ursts at earliest tolerale departure time especially at high load. I order to overcome this shortcomig, we propose a ehaced scheme, called opportuistic urst cloig scheme, which aims to cotrol the extra load of urst cloig. We aalytically aalyze the covetioal OBS, asic urst cloig scheme ad opportuistic urst cloig scheme over star etworks. The precisio of our aalytical model is verified through simulatio ad the oth aalytical ad simulatio results cofirm that opportuistic urst cloig scheme ca achieve etter overall etwork performace tha the other approaches. The remaider of this paper is structured as follows. I Sectio II, we preset the etwork uder study. I Sectio III, we descrie ad aalyze the covetioal OBS over star etworks. I Sectio IV, we adopt ad aalyze urst cloig scheme with star etworks. I Sectio V, we propose ad aalyze opportuistic urst cloig scheme over star etworks. I Sectio VI, we show the aalytical ad simulatio results. Fially, we coclude this paper i Sectio VII. II. THE NETWOR UNDER STUDY We focus o a class of OBS etworks that use a overlaid-star topology (also called composite-star topology) [6]-[10]. The overlaid-star topology, as show i Fig. 1, forms a logical mesh, where each edge ode is a memer of two or more stars i order to have at least oe recovery path i the evet of core or fier lik failure. A urst traversig the etwork oly passes through oe core ode, resultig i a major simplificatio of the cotrol prolem of esurig that cotetio is rare; furthermore, each of the stars ca e maaged idepedetly of the others [10]. We cosider a star OBS etwork topology with N edge odes, as show i Fig. 2, where each edge ode fuctios as oth the igress ad egress ode ad it is coected to a core ode usig two fiers, oe i each directio. All the fiers have the same umer of trasmissio wavelegths W t, W of them are used for urst trasmissio, called data wavelegths, while the remaiig wavelegths W c are used to trasmit cotrol packets, called cotrol wavelegths: W = W + W. (1) t c Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

3 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July Fig. 1. Overlaid-star topology Fig. 2. Star OBS etwork III. CONVENTIONAL OBS Packets arrivig from cliets are classified accordig to destiatios ad assemled ito varialelegth ursts accordig to hyrid (time ad legth) assemly algorithm. Whe a urst is ready, the edge ode schedules it y usig Earliest Possile Miimum Void with Void Fillig (EPMV-VF) [11]. Where, the edge ode tries firstly to reserve a data wavelegth at offset time usig Latest Availale Uscheduled Chael with Void Fillig (LAUC-VF) schedulig algorithm [12]. If there are o availale data wavelegths at offset time, the the edge ode reserves usig FIFO scheduler a data wavelegth at the earliest time availale after the offset time that leads to icrease the waitig time at edge ode y a additioal delay, called queuig delay. May studies cosider that urst queue of edge ode is ifiite which is urealistic ad ca lead to ureasoale queuig delay whe the load is heavy relative to lik capacity [13]. I order to keep that queuig delay is less tha a maximum tolerale urst queuig delay, we cosider that urst queue is fiite ad, cosequetly, a ew arrivig urst ca e lost if the urst queue is full. If the data wavelegth reservatio success, the edge ode set a cotrol packet to core ode with the duratio of the urst, the offset time ad the data wavelegth. After the propagatio delay etwee the edge ode ad the core ode, the core ode receives the cotrol packet ad it tries to reserve the same data wavelegth, ad if the data wavelegth reservatio fails due to urst cotetio, the urst is fially lost. If the destiatio receives a urst, it disassemles the urst ito idividual packets ad the forwards them to appropriate cliets. We refer Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

4 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July to this scheme i the rest of paper as Covetioal OBS (COBS). A. Modelig the edge ode I the studied etwork, the edge ode seds ursts to the other edge odes usig the uiform distriutio. We assume that the ew urst arrival from urst assemler is Poisso process with rate λ ursts per secod ad the duratio of urst is expoetially distriuted with a mea of 1 µ secods. We model urst queue of the edge ode with M/M/W / queue, where the umer of system places is greater tha the umer of servers W. Therefore, the maximum tolerale urst queuig delay is (W µ) 1. Let p e the equilirium proaility of ursts i the system. p is expressed i terms of p 0 as follows: p 1 λ =! µ p 0, for = 1,, W, (2) W W λ p = p0 W! W, for = W +1,,. (3) µ The ormalizatio coditio of the total proaility is expressed as follows: Cosequetly, p 0 is give y: = 0 p = 1. (4) 1 W 1 = 0 = + 1!! W λ W λ + W µ W Wµ p 0 =. (5) The urst Loss Proaility at Edge-ode (LPE) is the proaility that the system is saturated. It ca e computed y: LPE = p. (6) The utilizatio of each outgoig data wavelegth (ρ) is give y: The Queuig Delay (QD) is give ased o Little's law [14]: λ( 1 p ) ρ =. (7) µ W p = 1 QD =. (8) λ 1 p ) ( B. Modelig the core ode The core ode has ot wavelegth coversio capaility, therefore we ca cosider that the data wavelegth umer per iput/output port of the core ode is oe. I order to model the fact that urst trasmissio takes time ad it is ot istataeous, we associate the IDLE-ON process with each iput port [15], [16]. The iput port stays i ON state for the duratio of the urst 1/µ the it moves to the IDLE state ad vice-versa. We assume that IDLE state period is expoetially distriuted with a mea of 1/α. We ca express α i terms of µ ad ρ as follows: Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

5 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July µ ρ α =. (9) 1 ρ Sice there are N edge odes, the urst arrival process from all iput ports is the superpositio of N sigle IDLE-ON process. The urst arrivals are oly possile from the iput ports that are curretly i the IDLE state. Therefore, the core ode model will cosider that the arrival rate of ew ursts to a iput port may e iflueced y the umer of ursts curretly eig switched to all output ports. Also, sice there is o ufferig i the core ode, the model does ot cotai ay queues. Oe of the arrivig ursts through the N iput ports ca e switched to a output port OP i (1 i N) amog of the N output ports, the remaiig ursts are dropped or switched to the other output ports OP j (1 j N ad i j). We model the core ode with a two-dimesioal loss system, as show i Fig. 3. Let (m, ) e the tuple of possile states. If a urst is curretly eig switched to the output port OP i, the m = 1 else m = 0. However, represets the umer of ursts curretly eig switched to the all output ports OP j ad the followig costraits hold: ( N ) 0 1. (10) The umer of ursts curretly eig switched y the core ode is (m+), which meas that (m+) iput ports are i the ON state ad the remaiig (N (m+)) iput ports are i the IDLE state. We ca estimate the arrival rate of ew ursts from the (N (m+)) iput ports to the output port OP i y: m + λ1 ( m, ) = 1 α. (11) N The departure rate from the output port OP i is give y: µ 1 ( m, ) = mµ. (12) The arrival rate of ew ursts to all output ports OP j (j i) is: ( N 1) λ ( m, ) λ2 ( m, ) = 1. (13) The departure rate from all output ports OP j (j i) is: µ 2 ( m, ) = µ. (14) Fig. 3. Two-dimesioal state trasitio diagram for the loss system Sice the followig two flows are equal: clockwise: λ 2 (m,) λ 1 (m,+1) µ 2 (m+1,+1) µ 1 (m+1,), couter clockwise: λ 1 (m,) λ 2 (m+1,) µ 1 (m+1,+1) µ 2 (m,+1). Thus, accordig to Theorem (olmogorov's criteria) [17], the uderlyig state process of the loss system is a reversile process. We deote the proaility of the state (m, ) with P(m, ), the we ca apply the followig equatios locally etwee ay two coected states: Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

6 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July P( m, ) λ1( m, ) P( m + 1, ) =, (15) µ ( m + 1, ) 1 P( m, ) λ 2( m, ) P( m, + 1) =. (16) µ ( m, + 1) Therefore, we ca express P(0,) ad P(1,) i terms of P(0,0) as follows: 2 1 α P( 0, ) = 1 CN P(0,0), (17) N µ N α 1 α P( 1, ) = 1 CN P(0,0). (18) N µ N µ The urst Loss Proaility at Core ode (LPC) is the proaility of the data wavelegth reservatio failure at core ode. Sice the urst arrivals are state-depedet, we ca otai the LPC ased o the state proailities i comiatio with the appropriate arrival rate: LPC ( N = = 1 m= 0 1) 0 1 ( N 1) = 0 1 Usig Newto's iomial formula, we ca simplify (19) that ecomes: λ (1, ) P(1, ). (19) λ ( m, ) P( m, ) α( N 1) LPC =. (20) µn + 2α ( N 1) C. Overall etwork performace The etwork performace metrics of iterest here are the Burst Loss Proaility (BLP) of etwork, the Normalized Throughput (NT) of etwork ad the Burst Delay (BD). The BLP is give y: BLP = LPE + ( 1 LPE)LPC. (21) The NT defied as the asolute throughput divided y the total availale adwidth ad we ca calculate the NT y the followig formula: ( BLP) λ 1 NT = W µ. (22) The Burst Delay (BD) depeds o offset time (OT), QD ad ed-to-ed Propagatio Delay (PD). BD is give y: BD = OT + QD + PD. (23) IV. BASIC BURST CLONING SCHEME The idea of urst cloig scheme is to sed multiple copies of the same urst through the OBS etwork simultaeously i order to ehace the proaility that at least oe copy will reach destiatio [5]. I this scheme, which is proposed for mesh etworks, the oth edge ad core ode ca do cloig. Each copy ca traverse the mesh etwork alog a idepedet path, which leads to sed a cotrol packet for each copy. The edge ode ca receive multiple copies of the same urst ut oe copy of them will e cosidered. I this paper, we adopt the urst cloig scheme with star etworks ad we refer to the ew scheme as Basic Burst Cloig Scheme (BBCS). The implemetatio of Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

7 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July BBCS is less complex. The cloig ca e doe oly at the edge odes i electroic or optical domai. The data wavelegth reservatio at edge ode for each copy is processed as i COBS; therefore, the copies of the same urst ca e trasmitted with differet data wavelegths at differet departure times. The edge ode seds oly oe cotrol packet for all copies of the same urst with the duratio of the urst, the offset time of each copy ad the data wavelegth of each copy. Whe the core ode receives the cotrol packet, it tries to reserve the data wavelegth for first arrivig copy; ad if the reservatio fails, the it tries for secod arrivig copy; ad if the reservatio fails, the it tries for third arrivig copy ad so o util a successful reservatio. The the core ode disales the other reservatios i order to esure that oe copy ca leave the core ode to its destiatio edge ode. If all reservatios fail, the the urst is fially lost. A. Modelig the edge ode We shall ow propose the queueig model of the urst queue of a edge ode i BBCS. To arrive at this model, we first make a simplifyig cosideratio, which is the oth W ad are divisile y the umer of copies of the same urst (R). Cosequetly, we ca model the urst queue of edge ode with M/M/V/Q queue with the same parameters λ ad µ, where the umer of server V is W /R ad the umer of system places Q is /R. The equilirium proaility p is give as i COBS. Here, the LPE is give y: ρ is computed y: QD is expressed as follows: LPE = p Q, (24) λ( 1 p Q ) ρ =, (25) Vµ Q p = 1 QD =. (26) λ 1 p ) ( Q B. Modelig the core ode Let f e the proaility of a data-wavelegth reservatio failure. Sice the th reservatio will e cosidered oly after the 1th reservatio failure. Therefore, the load (l) may e cosidered as: R (1 f ) ρ l =. (27) (1 f ) R We model the core ode as i COBS such as α is give y: Therefore, we ca express f as follows: µ l α =. (28) 1 l α( N 1) f =. (29) µn + 2α ( N 1) It is clear, that to otai f we eed l ad to otai l we eed f, which leads to a iterative algorithm. We propose the followig iterative algorithm. I the iitializatio step, we assume that f is ull. I the Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

8 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July iterative step, we calculate l usig (27); we calculate α usig (28); ad the we calculate f y (29). We repeat the iterative step util f coverges. The urst is lost oly if all reservatios fail. Therefore, LPC is give y: R LPC = f. (30) C. Overall etwork performace BLP, NT ad BD are give as i COBS. If origial load λ(w µ) 1 is less tha R 1, the BBCS ca reduce urst loss at the core ode with very low loss at edge odes; else, BBCS ca lead to saturatio state of urst queue of edge ode ad, cosequetly, a sigificat urst loss at edge odes. V. OPPORTUNISTIC BURST CLONING SCHEME Whe the load is low, the most ursts are expected to reach their destiatio; cosequetly, the urst loss at the core ode ca e miimized sufficietly y just sedig two copies of the same urst. Whe the load is high, the cloig mechaism leads to a sigificat urst loss at edge odes eve if the umer of copies of the same urst is oly two. Istead of cloig all ew arrivig ursts as i BBCS, our Opportuistic Burst Cloig Scheme (OBCS) aims to cotrol the extra load due of urst cloig mechaism i order to avoid the prolem of urst queue saturatio. I OBCS, o more tha two copies of the same urst ca e set through the etwork. Furthermore, the edge ode either eales or disales the cloig of a ew urst accordig to the curret state of its urst queue. Whe the urst queue size is less tha a preset threshold, the edge ode eales the cloig mechaism ad seds two copies of the same urst; however, whe the urst queue size reaches the preset threshold, the edge ode disales the cloig mechaism ad seds oly oe copy. This techique is similar to the cocept of Early Radom Drop (ERD) [18], which used for cogestio avoidace i packet switched etworks. Whe the queue size reaches a drop level, the source i ERD egis to drop all ew arrivig packets with a fixed proaility. I OBCS, whe the urst queue size reaches the preset threshold, the edge ode drops also all ew arrivig copies with a fixed proaility of 0.5 ut i a fairly maer ecause it keeps a opportuity for each urst to reach its destiatio. If the urst cloig is ealed, the edge ode seds a cotrol packet for two copies as i BBCS; else, it seds a cotrol packet for oe copy as i COBS. The core ode processes the cotrol packet for two copies as i BBCS ad processes the cotrol packet for oe copy as i COBS. A. Modelig the edge ode We model the urst queue of edge ode queue with the Markov chai show i Fig. 4, where T deotes the threshold. Based o the gloal alace equatio for the cut etwee states ( 1) ad, we ca express p for 1 as follows: p λ p 1 = p 0, for = 1, µ (31) λ ( p 1 2 ) mi(, ) p, for = 2,,T, W µ (32) = Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

9 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July p λ = p 1 mi( W, ) µ, for = T+1,,. (33) Fig. 4. State trasitio diagram for urst queue of a edge ode i OBCS Based o (31), (32), (33) ad the ormalizatio coditio of the total proaility, we ca calculate ay state proaility p. We propose the followig way for computig all state proailities of the system: we deote the u-ormalized proaility of the state with u ; we iitialize u 0 to oe; for 1, we calculate u as i (31), (32) ad (33); fially, we calculate p as follows: LPE is give y: ρ is give y: p u = i = 0 u i, for = 0,,. (34) LPE = p, (35) = 1 mi( W, ) p ρ =, (36) W if the urst is ot lost at edge ode, the it will e cloed with the proaility (c): QD is give ased o Little's law as follows: W µ ρ c = 1. (37) λ(1 p ) = p QD = 1. (38) W µρ B. Modelig the core ode We calculate the data-wavelegth reservatio failure (f) as i BBCS except that the load (l) may e cosidered as: ( 1+ cf ) ρ l =. (39) 1+ c If the urst is cloed, the it is lost oly whe the oth data wavelegth reservatios are failed. However, if the urst is ot cloed, the the urst is lost whe oe data wavelegth reservatio is failed. Therefore, LPC is give y: LPC + 2 = ( 1 c) f cf. (40) C. Overall etwork performace BLP, NT ad BD are give as i COBS. OBCS ca reduce urst loss at the core ode without leadig to saturatio state of urst queue of edge ode eve at high load. Cosequetly, OBCS ca improve sigificatly the ormalized throughput while maitaiig a small queuig delay through a simple techique to disale/eale urst cloig mechaism. Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

10 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July VI. NUMERICAL RESULTS I order to evaluate the precisio of our aalytical model, we implemeted COBS, BBCS ad OBCS over Optical Burst Switchig - etwork simulator (OBS-s) that developed at the Optical Iteret Research Ceter (OIRC) [19] o the asis of s-2 [20]. I performig the simulatios, we cosider a star OBS etwork with 15 edge odes (i.e. N = 15). A dual-fier was estalished etwee each edge ode ad the core ode. We assume that all the dual-fiers are 200m i legth, i other words, the Propagatio Delay (PD) of each dual-fier is 10 3 s. The umer of data wavelegths is 8 per sigle fier (i.e. W = 8). We assume that there are o cotrol packet losses. The capacity of each wavelegth (C) is 10Gps. The core ode has ot wavelegth coversio capaility ad has ot fier delay lies. The iitial offset time etwee the cotrol packet ad its correspodig urst is 10 5 s. The urst assemler geerate ursts with a average urst legth of 1Mytes (i.e. µ 1 = s). Cosequetly, we ca set the load (L) geerated y each urst assemler y adjustig the rate λ: λ L =. (41) W µ The maximum tolerale urst queuig delay (W µ) 1 is s (i.e. = 24). I Figures 5, 6, 7, 8 ad 9, we plot respectively the results of LPE, LPC, BLP, NT ad BD, which are otaied from aalytical model ad simulatio, as fuctio of L for COBS, BBCS with R = 2 ad OBCS with T = 16. The results show i Figures 5, 6, 7, 8 ad 9 demostrate that, the precisio of our aalytical model is good. Fig. 5. Burst delay (BD) I Fig. 5, we oserve that, the ed-to-ed urst delay (BD) of the COBS remais less tha that of oth BBCS ad OBCS for every load. It remais close to 0 util the load reaches 0.5; after this poit, the BD of COBS egis to icrease as we icrease the offered load. However, whe the load is elow 0.3, the BD of the OBCS is similar to that of the BBCS ad icreases slowly. Whe the load is aove 0.3, the BD of BBCS cotiues to icrease more rapidly tha that of OBCS. The aove results ca e iterpreted ased o equatio (23). Sice OT ad PD remai costat, the variatio of BD is due to Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

11 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July QD. For BBCS, as the load icreases the extra load, due to urst cloig mechaism, icreases, however, OBCS reduces the ratio of the extra load as the load icreases. Thus, OBCS ca also reduce QD ad, cosequetly, BD more tha BBCS. Fig. 6. Burst loss proaility at edge ode (LPE) I Fig. 6, we oserve that, the urst loss proaility at edge-ode (LPE) of BBCS remais close to 0 util the load reaches 0.3; after this poit, the LPE egis to icrease rapidly as we icrease the load. The LPE for the OBCS remais close to 0 util the load reaches 0.5; after this poit, the LPE egis to icrease slowly as we icrease the load. The LPE for the COBS remais close to 0 util the load reaches 0.7; after this poit, the LPE egis to icrease slowly as we icrease the load. The aove results ca e iterpreted as follows. For the BBCS, as the load icreases the extra load icreases util urst queue of edge ode is almost full which leads to a sigificat urst loss at edge ode. However, the OBCS disales urst cloig mechaism whe the urst queue is ear to saturatio state. Cosequetly, the OBCS ca keep very reasoale LPE relative to that of COBS eve at very high load. I Fig. 7, we oserve that, the urst loss proaility at core-ode (LPC) of COBS remais greater tha that of oth BBCS ad OBCS for every load. Whe the load is elow 0.4, the LPC of the OBCS is very similar to that of the BBCS ad icreases slowly. Whe the load is aove 0.4, the LPC of BBCS cotiues to icrease slowly util the load reaches 0.6, after this poit, it remais almost costat. However, whe the load is aove 0.4, the LPC of OBCS ecomes greater tha that of BBCS ad cotiues to icrease as we icrease the load. The aove results ca e iterpreted as follows. For the BBCS, as the load icreases the urst loss at edge odes icreases which meas that the load to the core ode is reduced i additio to almost all icomig ursts to core ode are cloed ad, cosequetly, BBCS achieves etter LPC. For the OBCS, as the load icreases the extra load, due to the urst cloig mechaism, reduces that explais that whe the load is low the LPC of OBCS is ear to that of BBCS ad whe the load is high the LPC of OBCS ecomes ear to that of COBS. Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

12 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July Fig. 7. Burst loss proaility at core ode (LPC) Fig. 8. Burst loss proaility (BLP) of etwork I Fig. 8, we oserve that, the urst loss proaility (BLP) of etwork of OBCS remais less tha that of oth BBCS ad COBS for every load. Whe the load is elow 0.4, the BLP of OBCS is very similar to that of the BBCS ad icreases slowly. Whe the load is aove 0.4, the BLP of BBCS cotiues to icrease rapidly ad ecomes greater tha that of COBS whe the load is 0.7. However, whe the load is aove 0.4, the BLP of OBCS ecomes less tha that of BBCS ad cotiues to icrease slowly as we icrease the load. I Fig. 9, it is clearly that the OBCS ca achieve etter ormalized throughput (NT) of etwork tha oth COBS ad BBCS for every load. Whe the load is elow 0.4, the NT of the OBCS is very similar to that of the BBCS ad icreases as we icrease the offered load. Whe the load is aove 0.4, the NT of BBCS cotiues to icrease slowly ad ecomes less tha that of COBS whe the load reaches 0.7, after this poit, it remais almost costat. However, whe the load is aove 0.4, the NT of OBCS ecomes greater tha that of BBCS ad cotiues to icrease as we icrease the load. We ca explai the aove results as follows. The COBS Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

13 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July have etter LPE ut worse LPC. The BBCS have worse LPE ut etter LPC. The OBBS ca e cosidered as a itermediate solutio etwee COBS ad BBCS; it ca get the optimal solutio for equatio (21). Cosequetly, the OBCS achieves etter BLP ad NT. Fig. 9. Normalized throughput (NT) of etwork VII. CONCLUSION I this paper, we adopted the urst cloig scheme with star topology ad we demostrated that the urst cloig scheme ca lead to a sigificat urst loss at edge odes, which ecome uale to schedule ew ursts at earliest tolerale departure time especially at high load. I order to overcome this shortcomig, we proposed a opportuistic urst cloig scheme, which aims to cotrol the extra load of urst cloig. We aalytically aalyzed the star topology with covetioal OBS, asic urst cloig scheme ad opportuistic urst cloig scheme. The precisio of our aalytical model was verified y simulatio ad the oth aalytical ad simulatio results cofirm that opportuistic urst cloig scheme achieves etter overall etwork performace tha the other approaches. REFERENCES [1] I. Baldie, G. N. Rouskas, H. G. Perros, ad D. Steveso, JumpStart: a just-i-time sigalig architecture for WDM urst-switched etworks, IEEE Commuicatios Magazie, vol. 40, o. 2, pp , Feruary [2] C. Qiao ad M. Yoo, Optical urst switchig (OBS) A ew paradigm for a Optical Iteret, Joural of High Speed Networks, vol. 8, o. 1, pp , Jauary [3] S. Yao, B. Mukherjee, ad S. Dixit, Advaces i photoic packet switchig: a overview, IEEE Commuicatios Magazie, vol. 38, o. 2, pp , Feruary [4] Vokkarae, V.M. ad Q. Zhag, Forward redudacy: A loss recovery mechaism for optical urst-switched etworks, Proceedigs of the third IEEE/IFIP Iteratioal Coferece o Wireless ad Optical Commuicatios Networks, WOCN 2006, Bagalore, Idia, April [5] X. Huag, V.M. Vokkarae, ad J.P. Jue, Burst cloig: A proactive scheme to reduce data loss i optical urstswitched etworks, Proceedigs of IEEE Iteratioal Coferece o Commuicatios (ICC), Seoul, South orea, May [6] R. Vickers ad M. Beshai, PetaWe architecture, Networks 2000 Symposium, Toroto, Caada, Septemer [7] F.J. Bloui, A.W. Lee, A.J.M. Lee, ad M. Beshai, Compariso of two optical-core etworks, Joural Optical Networkig, vol. 1, o. 1, pp , Jauary [8] X. Moutrouidou, V. S. Puttasuappa, H. G. Perros, A zero urst loss architecture for star OBS etworks, Net- Co 06, (part of the IFIP World Computer Cogress 2006), Sadiago, Chile, August [9] A. Reiert, B. Sasò ad S. Secci, Desig optimizatio of the Petawe architecture, IEEE/ACM Trasactios o Networkig, vol. 17, o. 1, pp , Feruary Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN

14 Joural of Microwaves, Optoelectroics ad Electromagetic Applicatios, Vol. 12, No. SI-2, July [10] G. Bochma, M. J. Coates, T. J. Hall, L. Maso, R. Vickers ad O. Yag, The agile all-photoic etwork: A architectural outlie, Quee's 22d Bieial Symposium o Commuicatios, May [11] Hailog Li ad Ia Li-Ji Thg, Edge ode uffer usage i optical urst switchig etworks, Photoic Network Commuicatios, vol. 13, o. 1, pp , Jauary [12] Y. Xiog, M. Vaderhoute, ad H. C. Cakaya, Cotrol architecture i optical urst-switched WDM etworks, IEEE Joural o Selected Areas i Commuicatios, vol. 18, o. 10, pp , Octoer [13] A. Agustí-Torra, G. Bochma, ad C. Cervelló-Pastor, Retrasmissio schemes for optical urst switchig over star etworks, Proceedigs of the 2d IFIP Iteratioal Coferece o Wireless ad Optical Commuicatios Networks, WOCN 2005, Duai, UAE, March [14] J.D. Little, A Proof for the Queueig Formula L = λw, Operatios Research, vol. 9, pp , [15] T. Battestilli ad H. G. Perros, Ed-to-ed urst loss proailities i a OBS etwork with simultaeous lik possessio, Proceedigs of the Third Iteratioal Workshop o Optical Burst Switchig, WOBS3, Sa Jose, CA, Octoer [16] S. Riadi ad A. Maach, A Accurate Loss Model for A Star Optical Burst-Switched Network, Joural of Commuicatios ad Computer Egieerig, vol. 2, o. 3, pp , [17] F. P. elly, Reversiility ad Stochastic Networks, Wiley, [18] E. S. Hashem, Aalysis of radom drop for gateway cogestio cotrol, Report LCS TR-465, Laoratory for Computer Sciece, MIT, Camridge, MA, August [19] OIRC OBS-s Simulator, 2009 [Olie]. Availale: [20] s-2 Network Simulator, 2009 [Olie]. Availale: Brazilia Microwave ad Optoelectroics Society-SBMO received 24 Fe 2013; for review 1 May 2013; accepted 21 Jue 2013 Brazilia Society of Electromagetism-SBMag 2013 SBMO/SBMag ISSN