Modelling packet insertion on a WSADM ring

Transcription

1 Modelling packet insetion on a WSADM ing A. Gavey, D. Ama, Philippe Gavey, Michel Movan, Bogdan Uscumlic, Dominique Chiaoni To cite this vesion: A. Gavey, D. Ama, Philippe Gavey, Michel Movan, Bogdan Uscumlic, et al.. Modelling packet insetion on a WSADM ing. 22nd Intenational Confeence on Optical Netwok Design and Modeling ONDM 218, May 218, Dublin, Ieland. IEEE, 218 Intenational Confeence on Optical Netwok Design and Modeling ONDM, < /ONDM >. <hal > HAL Id: hal Submitted on 23 Jul 218 HAL is a multi-disciplinay open access achive fo the deposit and dissemination of scientific eseach documents, whethe they ae published o not. The documents may come fom teaching and eseach institutions in Fance o aboad, o fom public o pivate eseach centes. L achive ouvete pluidisciplinaie HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau echeche, publiés ou non, émanant des établissements d enseignement et de echeche fançais ou étanges, des laboatoies publics ou pivés.

2 Modelling packet insetion on a WSADM ing A. Gavey, D. Ama, P. Gavey, and M. Movan IMT Atlantique, Best, Fance fistname.lastname@imt-atlantique.f UMR CNRS 674 IRISA, Fance, UMR CNRS 6285 Lab-STICC, Fance B. Uscumlic and D. Chiaoni Nokia Bell Labs, Pais Saclay, Fance fistname.lastname@nokia-bell-labs.com Abstact The WDM slotted Add/Dop Multiplexe WSADM technology elies on time slotted WDM ings, whee a slot can cay a single WDM packet. All stations can inset and eceive these WDM packets. This diffes fom pevious achitectues in which packets wee caied ove a single wavelength, while multiple packets could be caied in a single slot, thus taking advantage diffeently of the WDM dimension. The WSADM achitectue is expected to educe costs by exploiting low cost technologies. We popose mathematical models fo evaluating the pefomance offeed by WSADM optical packet ings, unde two diffeent packet insetion policies. In the slot esevation mode, a station can only use the slots that ae peiodically eseved fo its exclusive usage. In the oppotunistic insetion mode, a station can use any slot that is neithe eseved, no aleady occupied. These modes ae bench-maked with a channel esevation mode in which each wavelength is dedicated to a single station. eywods Wavelength Division Multiplexing, Optical Packet Switching, Metopolitan Aea Netwok, Netwok Pefomance I. INTRODUCTION The distibution/aggegation netwok segment, also called Metopolitan Aea Netwok MAN, is expected to be paticulaly impacted by the cuent taffic gowth. Diffeent taffic souces, vaying fom small Digital Subscibe Line Access Multiplexes DSLAMs to lage data centes, geneate highly vaiable types of taffic, which favos using packetbased tanspot technologies in MANs. Ethenet ings with specific potection potocols ae often consideed. The main issues with opaque netwoks ae, on the one hand thei high enegy consumption, and on the othe hand the Ethenet packet ganulaity that is convenient fo Meto Access aeas, but too fine fo Meto Coe ones. Optical Packet/Bust Switching OPS/OBS technologies have been fo many yeas consideed as potential options fo combining sub-wavelength ganulaity and optical tanspaency but the lack of viable optical buffeing technologies has pecluded implementating them. Howeve, time-slotted OPS ings such as TWIN o POADM have been shown to povide both an efficient use of tansmission esouces and caie-gade pefomance without optical packet buffeing. Nevetheless, these technologies ely on custom optical components in paticula on fast-tunable bust-mode emittes that ae not cuently commecially available. In ode to ely on moe widely available components, the WDM slotted Add/Dop Multiplexe WSADM technology has been ecently poposed [1]. The key optical devices equied in a WSADM ae integated multi-wavelength lase souces that ae fully in line with the tend of optoelectonic industy, and Semiconducto Optical Amplifies SOA gates that ae natually suited to opeate on WDM packets because of thei wide optical bandwidth. Peliminay CAPEX compaisons have suggested that WSADM technology could compete favoably with existing electonic packet technologies and othe OPS/OBS options [1], [2]. To the best of ou knowledge, the netwok pefomance of WSADM technology has yet to be assessed. The pesent pape poposes a set of models fo assessing WDM packet insetion pefomance in a WSADM ing. Packet insetion has a stuctuing impact on the global pefomance, as all inseted packets tavel tanspaently till thei destination, esulting in loss-less tansfe and deteministic latency once packets ae inseted. The intoduction of WSADM aises seveal questions. Fo example, the compaison between a puely oppotunistic insetion mode and a fully o patially deteministic one: how do these modes impact on netwok pefomance, in paticula on latency and what is the impact of the numbe of wavelengths on thei espective meits? Moe geneally, the stingent equiements on latency, notably in the famewok of futue 5G deployments, make woth pefoming a detailed analysis of the packet insetion pocess in a candidate technology fo futue meto/aggegation netwoks. Section II descibes the netwok achitectue consideed in this wok. Section III pesents the vaious mathematical models developed fo WSADM netwoks. A patial validation by simulation of the models is pesented in the next section. The main pefomance assessments ae summaized in section V and conclusions ae dawn in section VI. II. NETWOR ARCHITECTURE We conside WDM packets as descibed in [1]. Multiple Sevice Data Units SDU ae aggegated within a single Packet Data Unit PDU; a typical SDU is e.g. an Ethenet Fame. To be tanspoted ove the optical ing, the PDU is split ove wavelengths. The netwok is contolled by both a fast i.e. eal time contol ealized in line, and a slowe, although dynamical, contol ealized thanks to a SDN contolle. The fast contol is implemented though a contol channel caied ove a sepaate wavelength, and synchonized with the data channel: duing a time slot, both a contol packet and a data packet which caies, o not, a PDU ae tansmitted. The SDN contolle povides a povisioning oiented type of contol: it is in chage of station povisioning, of specifying the contol infomation associated to PDUs befoe insetion and of specifying the opeation eception, pass-though, easue associated with PDUs caied ove the ing. A simila povisioning oiented contol has been descibed in a diffeent context in [3]. As the pesent pape focuses on tansfe plane pefomance, it shall not povide a detailed specification of the SDN contol.

3 We assume that each station pesents a single D Mbit/s inteface typically, in a meto netwok, D = 1 Gbit/s, which is equal to the ate of a single wavelength. Let Z be the size, in bytes, of a PDU. Z should be lage enough to contain many Ethenet fames, in ode to avoid segmentation/eassembly and to limit the popotion of esouces wasted due to the fixed ovehead necessay fo each packet guad-band, peamble and faming. On the othe hand, Z should not be too lage. Indeed, in ode to limit the latency due to the netwok, the time taken to fill a PDU by SDUs shall most likely be limited by a time, unless it is filled befoe the time uns out. Wee Z too lage, eithe latency would be negatively impacted by an ovely long time value, o PDUs would be systematically sent patially filled, times having un out befoe the PDU was full, thus wasting esouces. Fo the sake of geneality, define T = Z/D to be the time it takes to fill a PDU at ate D. T is split into slots, whee is the numbe of channels ove which a packet is split to be tansmitted; T/ is thus slot duation. Stations ae oganized into a single uni-diectional ing, in which each station can both inset and extact PDUs fom the optical packet ing. Once a PDU is inseted, it cannot be lost till it is eceived by the final destination station, as it is passed tanspaently though the tansit stations; theefoe, PDUs ae not lost within the netwok; a PDU could howeve be lost within a station, due to insetion buffe oveflow. Endto-end PDU latency is the sum of the sojoun time in the insetion buffe and of the fixed popagation delay between souce and destination stations typically in the ode of.1-1 ms. The pefomance offeed to PDUs is thus mostly chaacteized by the pefomance of the PDU insetion pocess. The pefomance offeed to SDUs also depends on how SDUs ae aggegated in PDUs, and on whethe time-based policies ae implemented, o not, in ode to contol latency. This is not consideed in the pesent pape which focuses on the pefomance offeed to PDUs in tems of latency and jitte. III. MODELLING PACET INSERTION Insetion pefomance is fist diven by the PDU aival pocess. As we conside a meto netwok, whee each station aggegates the taffic of thousands of customes, it is justified to assume that PDUs aive accoding to a Poisson pocess with paamete Λ. Let γ j x be the pobability that j PDUs aive duing an inteval of duation x: Λx Λxj γ j x = e j! The numbe of aivals duing an inteval of duation x is thus Poisson with paamete Λx. Insetion pefomance also depends on slot availability, chaacteized by the insetion mode applied to PDUs. We shall benchmak two slot insetion modes, slot esevation and oppotunistic insetion, with a classical channel esevation mode, in which each wavelength is dedicated to a station. A. Slot Resevation Mode In the slot esevation mode, the PDU can be inseted only on a slot that is maked as being available fo its class. It is assumed that thee is a eseved slot evey R slot. Let a esevation peiod stat at the beginning of a eseved slot, and end just befoe the next eseved slot. If at least one PDU is in the system at the beginning of the esevation peiod, 1 thee is an exit at the end of the eseved slot. Othewise, no PDU is seved duing the peiod. We assume that system capacity is finite of size B. In the following, we shall deive the distibution fo N, numbe of PDUs in system at the beginning of a esevation peiod, M, numbe of PDUs seen by an aiving PDU, Ploss, the pobability that an aiving PDU finds B PDUs in the system and W, sojoun time of a PDU which entes the system. We fist deive the tansitions pobabilities fo N. As system capacity is B, N vaies between and B, and the tansitions ae as follows: RT P, i = γ i B 1 i RT P, B = γ j j=b RT P n, i = γ i1 n B n >, B 1 i RT P n, B = γ j B n > j=b n1 Let π = {πi, i B 1} be the pobability distibution fo N ; π is numeically deived by solving π P = π. In ode to deive the distibution fo M, let us conside the pobability that, knowing that a PDU aives duing [, RT/[, it aives in the inteval [x, xdx[, and that exactly j othe PDUs aived befoe it, in the same esevation peiod. As the aival pocess is Poisson, within a esevation peiod of length RT/, the pobability that the PDU aives duing an inteval of length dx is dx/rt. The date of aival x and the numbe of aivals between the beginning of the peiod and x ae elated as follows: P tagged aival in [x, x dx[, j aivals duing [, x[ = dx RT γ jx The pevious joint pobability is independent fom the state of the system at the beginning of the peiod. M depends both on N numbe of PDUs in the system at the beginning of a peiod, and on whethe the tagged PDU aives befoe the end of the eseved slot, o not. Indeed, if the the tagged PDU aives afte the end of the eseved slot, and if N >, one PDU has been seved befoe the aival of the tagged PDU; on the othe hand, if it aives duing [, T/[ it sees all the PDUs pesent in the system at time. Let νk be the pobability fo {M = k}. Fo k smalle than B, νk = RT k [ RT/ π T/ k1 RT/ T/ γ k ydy γ k n ydy ] γ k n1 ydy

4 which yields, afte integating 1: ν k = [ ΛRT k1 πk1 π k1 γ j RT j=k n2 k1 T γ k n1 γ j RT The loss pobability Ploss is ν B, and can be deived similaly: Ploss = [ ΛRT B B j=b n1 i=b n2 π i=b1 γ j T/ ] i Bγ i RT/ 2 i n B 1γ i RT/ ] 3 The numbe of PDUs seen by an aiving PDU which is not lost is distibuted as νk /1 ν B k < B. The mean sojoun time of such a PDU is then deived using Little s fomula: B 1 1 EW = Λ1 νb kνk 4 k= In ode to deive the distibution fo W, let U be the time between the aival of the tagged PDU and the end of the esevation peiod. Let also A R U be the numbe of PDUs aiving befoe the tagged PDU in the same esevation peiod. The distibution fo W depends on both N and U. If N is null, the tagged PDU is delayed only by the PDUs aiving befoe it, in the same esevation peiod. If N is positive, it is also delayed by the N 1 PDUs aived in pevious esevation peiods one PDU is seved duing the esevation peiod. W is thus equal to the sum of the time till the end of the esevation peiod duing which it aived U, k esevation peiods, whee k is the numbe of PDUs which ae in system when the PDU aives, and which ae not seved duing the esevation peiod duing which the tagged PDU aived, and its own sevice time T/. By conditioning on N and on the numbe of othe PDUs that aived befoe a tagged PDU, in the same peiod which ae independent, we can diectly obtain the distibution [ [ fo W, valid fo k smalle than B 1 and x in [ P W kr1t, RT. x, kr1t dx RT 1 ν B k1 [ x dx = π γ k RT/ x γ k n1 RT/ x Fo k = B 1 we need to ensue that the tagged PDU is not lost, which could occu fo x lage than R 1T/. The 5 [ next esult is thus only valid fo x in [ P W B 1R1T = dx RT 1 ν B, R 1T x, B 1R1T π γ B 1 RT/ x B γ B n RT/ x [ : [ x dx Lastly, the sojoun time in a system of capacity B is uppe bounded by BRT/ which implies that: [ T P W [x, x dx[ = x /, BRT ] 7 B. Oppotunistic Insetion Mode Unde the oppotunistic insetion mode, once the station decides that a PDU should be inseted, it insets the PDU on the fist available slot. A slot is unavailable eithe because it aleady caies a PDU, o because it is eseved to be used by anothe PDU class. In ode to obtain a tactable model fo oppotunistic insetion, we assume that slot availability is modelled by a Benoulli pocess with paamete q. A PDU which aives and finds an empty system only stats its sevice at the beginning of the next slot; if a slot is available, the sevice finishes at the end of the slot with pobability q ; othewise, the sevice lasts at least anothe slot. Moe pecisely, the sevice time is equal to l, l > with pobability q 1 q l 1 geometic distibution with paamete q. In the following, we shall deive the distibution fo N o, numbe of PDUs in system just at the end of a slot, M o, numbe of PDUs seen by an aiving PDU, Ploss o, the pobability that an aiving PDU finds B PDUs in the system and W o, sojoun time of a PDU which entes the system. As system capacity is B, N o cannot be lage than B. Tansition pobabilities ae as follows: P o, i = γ i T/ i B 1 P o, B = γ j T/ j=b P o n, i = 1 q γ i n T/ q γ i n1 T/ 1 n B, i B 1 P o n, B = 1 q γ j T/ q j=b n j=b n1 γ j T/ 6 1 n B P o n, i = {i > B} {n > B} Let π o = {πi o, i B 1} be the pobability distibution fo N o ; π o is numeically deived by solving π o P o = π o. M o diffes fom N o, as PDUs can aive befoe x, aival time of a tagged PDU, in the same slot. Howeve, thanks to the fact that a Poisson pocess is memoy-less, the aival pocess of PDUs afte the beginning of the slot is independent fom N o. We can thus deive ν o k, the pobability fo {M o = k}, by

5 summing on n and integating on x. Fo k smalle than B: ν o k= T = ΛT k n= k n= π o n π o n T/ γ k n xdx i=k n1 γ i T/ The loss pobability Ploss o is νo B and can be deived similaly: νb= o B T/ o γ j xdx T = ΛT n= B j=b n o n= i=b n1 8 γ i T/i B n 9 The numbe of PDUs seen by an aiving PDU which is not lost is distibuted as νk o/1 νo B fo k < B. Little s fomula yields the mean sojoun time of such a PDU: B 1 1 EW o = Λ1 νb o kνk o 1 k= In ode to deive the distibution fo W o, let U o denote the time elapsed between the aival of the tagged PDU and the beginning of the next slot. W o is equal to the sum of U o, of the tagged PDU s sevice time, and of the time it takes to seve the PDUs which ae in system when the PDU aives, and whose sevice does not stop at the end of the tagged slot. In paticula, this implies that W o is lage than T/. P W o [x, x dx[= x < T/ Note that if N o =, no PDU can be seved duing the slot, even if PDUs aive befoe the tagged PDU in the same slot. Othewise, a PDU is cuently being seved and its sevice can finish at the end of the slot with pobability q. Let S k be the sevice fo the k th PDU to be seved, S be the sevice fo the tagged PDU and S 1 be the emaining sevice time fo the PDU cuently being seved at the beginning of the slot, if any. The sojoun time W o of an aiving PDU which is not lost is thus deived as follows: P W o [it/ x, it/ x dx[ 1 = 1 νb o minb 1,i 1 P N o =, j= j aivals duing [, T/ x[, U o [x, x dx[, S 1 S 2.. S j S = it/ minb 1,i j P N o = n, j=1 j n aivals duing [, T/ x[, U o [x, x dx[, S 1 S 2.. S j S = it/ S 1, S k and S ae independent. S k and S ae identically distibuted, but S1 follows a diffeent distibution. Due to the memoy-less popety of the geometic distibution, S1 is equal to l, l, with pobability q 1 q l. Thanks to the memoy-less popety of the Poisson Pocess and of the geometic distibution, we know that what happens befoe the beginning of the slot which detemines N o, what happens duing the slot which detemines U o and potential aivals duing [, T/ U[, and what happens afte the slot which detemines the value fo the sum of geometically distibuted sevices ae independent. We finally obtain: P W o [it/ x, it/ x dx[ = minb 1,i 1 j= minb 1,i j=1 i 1 πγ o j T/ x j 1 1 ν o B 11 q j1 1 q i 1 j j i γ o j n T/ x q j1 j 1 q i j C. Channel Resevation Mode A typical benchmak coesponds to dedicating each data channel to a single station. The behaviou of this system is modelled by an M/D/1 queue, with load ρ = ΛT = λ. Both the M/D/1 and the M/D/1/B queues ae well known models. In paticula, the distibution fo the numbe of PDUs seen in the system by an aiving custome M c which is also the stationay numbe of customes N c in the M/D/1 queue thanks to the PASTA popety is given below see section 5 in [4]. π c = 1 λ π1 c = πe c λ 1 12 n 1 [ ] jλ =π c c e nλ 1 n j e jλ n j n j! jλn j 1 n j 1! j=1 if n 2 Moeove see section in [4], the distibution fo the sojoun time W c in the station can also be explicitly deived: P W c t=1 λ k i=1 e ΛiT t i 1 it ti 1 Λ i 1! t [kt, k 1T [, k 1 = t < T 13 The mean sojoun time is given by λ EW c = T 1 21 λ 14 IV. VALIDITY OF QUEUEING MODELS Thee is no need to check the validity of the slot esevation, as long as an exact esevation peiod can be maintained in a eal life scenaio. Note that this may not always be possible as all esevations have to be oganized into a single schedule, which may not always ensue a pefect peiodicity fo all esevations. Futhe studies ae equested to assess the impact of the schedule design. The validity of the oppotunistic insetion model is howeve moe questionable as slot availability depends on the activity of the othe stations wheeas it is modelled in Section III-B by a Benoulli pocess with paamete q. A ns3 simulation softwae has been developed in ode to assess the global pefomance of a WSADM netwok. A WSADM ing is simulated, with a vaying numbe of stations link length between two stations = 4 km. Each station geneates PDUs accoding to a Benoulli pocess. PDUs

6 7 6 Aggegation simulation Any-to-any simulation Model fo Oppotunistic Insetion 6 5 Mean Sejoun Time in µs Mean Sejoun Time in µs Lambda Fig. 1: Mean Sojoun Time: model vesus simulations ae stoed in a finite buffe of size B = 99. T and ae espectively equal to 1µs and to 1. Each simulation uns duing 1 second. Fig. 1 compaes the mean sojoun times obtained by the model of Section III-B with the sojoun times measued by simulation in two scenaios. In the any-to-any scenaio, the sojoun time is measued in one station of a WSADM ing of 2 stations, exchanging taffic in an any-toany scenaio. In the aggegation scenaio, the sojoun time is measued in a station, which sees the taffic aggegated fom 1 othe stations. In the model and the simulations, a station offes the same taffic λ = ΛT, and expeiences the same mean slot availability. Fig.1 shows that the model is quite close to simulation esults, although it is slightly pessimistic as low load, and athe optimistic at high load. It is also close to the any-to-any case than to the aggegation case. V. ASSESSING PACET INSERTION PERFORMANCE This section povides a pefomance analysis of a WSADM ing based on the pevious models. We focus on taditional MAN scenaios, in which WSADM ings link stations that aggegate the taffic of a lage numbe of customes at least seveal tens of thousands of customes fo a MAN access ing, up to seveal hundeds of thousands of customes fo a MAN coe ing. Although MANs ae usually statically dimensioned, data cente inteconnection may necessitate a moe dynamic opeation of these netwoks in the futue. This is why the flexible contol plane consideed fo WSADM could be beneficial, compaed with a static channel esevation case. A. Impact of the numbe of WDM channels Conside a station geneating PDUs accoding to a Poisson pocess with paamete Λ. Two cases ae shown below: in the fist case ΛT =.8, a full wavelength channel allocation makes sense, wheeas in the second case ΛT =.4, it would epesent a significant ove-allocation. Both WSADM insetion modes offe the same amount of esouces to the station, i.e. R = 1/q. We assume that B ensues that the loss pobability is negligible. The mean sojoun times in the thee models given espectively in equations 4, 1, 14 epesent the mean time taken to inset a PDU on the MAN fo the thee consideed modes. Actually, if the buffe is infinite, a closedfom fomula fo the mean sojoun time in slot esevation mode is given by EW = T 1 R 2 Rλ 15 Mean Sejoun Time in µs 1 Oppotunistic Insetion Channel Resevation Slot Resevation Numbe of Wavelength Channels Fig. 2: Mean Sojoun Time vesus ; high station load Oppotunistic Insetion Channel Resevation Slot Resevation Numbe of Wavelength Channels Fig. 3: Mean Sojoun Time vesus ; low station load Indeed, the slot esevation model waiting time is quite close to an M/D/1 queue with a sevice time equal to the esevation peiod RT/; howeve, as the sevice in the WSADM model is povided only at the beginning of the esevation peiod, statistically, it is necessay to add half a esevation peiod, and lastly to add the sevice time T/. Fig. 2 and Fig. 3 epesent the mean sojoun times vesus, fo inceasing WSADM capacity but fixed offeed taffic and povided esouces i.e. Λ and q = /R fixed. The channel esevation mode is obviously independent fom, as a single channel is dedicated to the station, whateve is ; the λ 21 λ sojoun time is constant, equal to T 1. Moeove, the mean sojoun time deceases with in the slot esevation mode while it inceases with in the oppotunistic mode. In Fig2, the sojoun time fo slot esevation mode is smalle than the one fo channel esevation mode except fo = 1 in this paticula case, both oppotunistic and slot esevation cases can use each slot, but as sevice is slotted, the mean sojoun time exceeds the M/D/1 sojoun time by T/2. In both figues, the mean sojoun time vaies quickly fo small values of, but the vaiation is smalle fo lage values of. The limit value fo the sojoun time in the oppotunistic case coesponds to the M/M/1 sojoun time, as a geometically distibuted sevice conveges to an exponential sevice, and as

7 Allocated Ressouces Oppotunistic Insetion Channel Resevation Slot Resevation Lambda Fig. 4: Resouces ensuing P W > 25µs smalle than 1 3 vesus λ fo = 1 slotting sevice times has little impact fo a small slot size; in T the pesent case, this limit value is /R λ. Using equation T 15, we see that the limit value fo EW s is 2/R λ which is half the limit value fo the oppotunistic insetion case. We also see that the slot esevation mode at high load is almost equivalent to the channel esevation mode. At a low station load, channel esevation is an inefficient use of optical esouces, although it povides of couse a bette pefomance than both esevation and oppotunistic modes. B. Suppoting tanspot level pefomance We addess hee the dimensioning issue, i.e. identifying the amount of esouces needed to suppot offeed taffic. Pefomance objectives fo Ethenet Fames ae povided by the MEF fo diffeent pefomance ties [5]. The pefomance deliveed by a WSADM netwok to SDUs is not fully assessed in the pesent pape as the aggegation of SDUs within PDUs is not taken into account. Howeve, it is possible to dimension the netwok, fo the vaious modes, by setting some objectives fo PDU tansfe that ae significantly smalle than the pefomance objectives set fo Ethenet Fames fo the Meto Pefomance Tie PT1, i.e. spanning up to 25km. In the following table, the fist line is extacted fom [5], wheeas the second line coesponds to the tagets set fo the WSADM netwok. Dimensioning is pefomed by identifying the amount of esouces ensuing P W > 25µs is smalle than 1 3 vesus λ the 99.9 pecentile is selected as in [5]. The case = 1 is consideed, as advocated by [1]. One-way Pefomance Objectives fo the Meto Potion Loss Delay Jitte MEF ms 3ms [5] WSADM 2.5ms popagation.25ms PDU level.25ms insetion insetion Fig. 4 depicts dimensioning fo vaying λ. The benchmak cicuit allocation case coesponds to the hoizontal line, as a full channel is allocated fo all λ values. Using 13, it is assessed that channel allocation suppots the set taget up to λ =.86. Oppotunistic and slot esevation insetion modes ae in most cases moe efficient than channel esevation, especially fo medium and small λ values; they ae also moe flexible due to thei sub-wavelength ganulaity. The slot esevation mode is moe efficient than the oppotunistic insetion mode, especially fo small λ values. If the constaint is elaxed i.e consideing a lage taget delay fo the quantile, this diffeence would howeve decease. VI. CONCLUSION Models fo assessing the tansfe plane pefomance in a WSADM netwok have been deived. They focus on the PDU o slot level pefomance that is govened by the PDU insetion pocess, as PDUs expeience neithe loss no jitte once inseted. The models assume that PDU aive accoding to a Poisson pocess, which is a ealistic assumption in a meto netwok. Slot esevation and oppotunistic insetion have been consideed, and bench-maked with channel allocation. Both modes have been shown to easily suppot MEF pefomance tagets, and to pesent significant esouce allocation gains compaed to a classical channel allocation. As we assume a constant channel bit ate, the global ing capacity is popotional to. This implies that, as insetion latency is less impacted by, selecting should be mainly be detemined by techno-economic issues. As an example, a ing with 1-channel tanspondes would have the same capacity as 1 ings with single-channel tanspondes and would delive a simila insetion latency slightly shote when using a esevation mode and slightly lage in case of oppotunistic insetion. Howeve, the cost benefits of using integated WDM tanspondes and a single SOA fo the 1-wavelength band, as discussed in [2], togethe with the benefit of managing a single ing, clealy favou WSADM. Regading WSADM, the esevation mode slightly outpefoms the oppotunistic mode in tems of insetion latency and esouce usage. Howeve, dimensioning fo the oppotunistic mode is quite simple: it only implies ensuing that enough esouces ae available fo each station. On the othe hand, dimensioning fo the slot esevation mode is moe complex as it elies on building a global schedule taking into account all flows, each with its own peiod. Howeve, the two modes ae not exclusive as the oppotunistic mode only uses slots that ae neithe aleady occupied, no eseved, which makes the WSADM technology quite flexible. ACNOWLEDGMENT The wok has been caied out in the famewok of the N- GREEN poject ANR-15-CE25-9-x, suppoted by the Fench Reseach Agency. REFERENCES [1] D. Chiaoni and B. Uscumlic, Potential of WDM packets, 217 Intenational Confeence on Optical Netwok Design and Modeling ONDM 217, Budapest, May 217. [2] A. Tiki, A. Gavey, P. Gavey and M. Movan Long-Tem CAPEX Evolution fo Slotted Optical Packet Switching in a Metopolitan Netwok, 217 Intenational Confeence on Optical Netwok Design and Modeling ONDM 217, Budapest, May 217. [3] L. Sadeghioon, A. Gavey, B. Uscumlic, P. Gavey and M. Movan, Full featued and lightweight contol fo optical packet meto netwoks, IEEE/OSA Jounal of Optical Communications and Netwoking, volume 7, numbe 2, A235-A [4] D. Goss, J. Shotle, J. Thompson, and C. Hais, Fundamentals of Queueing Theoy, 28. [5] MEF, Implementation Ageement MEF 23.2 Caie Ethenet Class of Sevice Phase 3, 216.