Simple Optical Fabrics for Scalable Terabit Packet Switches

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.

Simple Optical Fabrics for Scalable Terabit Packet Switches R. Gaudino, G. A. Gavilanes Castillo, F. Neri

J. M. Finochietto

Dipartimento di Elettronica, Politecnico di Torino C.so Duca degli Abruzzi, 29 - 10129, Torino, Italy

CONICET - Universidad Nacional de Cordoba Av. V. Sarsfield, 1611 - 5000, Cordoba, Argentina

Abstract— The design of fabrics for Terabit packet switches and routers needs to consider the limitations imposed by the electronic technology; in particular, more and more attention has to be paid to information density and to power consumption and dissipation, as well as to power supply and footprint requirements. These issues make more difficult to package a packet switch in one single rack of equipment; thus, optical links start being used to interconnect the line cards with the switching fabric. In this paper, we consider optical interconnection architectures that exploit wavelength agility at line cards to control switching decisions. The actual feasibility and physical layer scalability of this approach is analyzed by considering different optical fabric alternatives to interconnect the line cards. The main contribution of the paper is the characterization of these optical fabrics in terms of their power budget, and the analysis of the port count and of the aggregate bandwidth offered by these architectures to build Terabit packet switches.

I. I NTRODUCTION Although packet switches with capacities above several Terabits of aggregate bandwidth are currently commercially available, the number of backplane interconnections and the power and information density are reaching physical limits. Indeed, each new generation of commercial routers consumes more power than the previous one, and it is more difficult to package a router in one single rack of equipment. Thus, high-end routers often comprise several racks of equipment: one or more racks host the electronic switching fabric and the control logic, while others racks host the line cards. In this configuration, optical links are typically used to interconnect the fabric and line cards. These solutions occupy valuable space, consume too much power, and pose reliability concerns due to the large number of active components in the switch fabric. Packet switches with optical fabrics can potentially scale better to higher capacities, increase reliability, and at the same time significantly reduce footprint and power consumption [1]. In this paper we consider optical interconnection architectures that make use of wavelength agility at line cards to actually control switching through a passive optical fabric. We consider different alternatives to implement the optical fabric, and evaluate their feasibility and scalability in terms of their maximum port count and aggregate bandwidth. For this purpose, the characterization of the relevant optical components and their power budget/penalty is discussed, resulting in the definition of simple device models that can be used to evaluate the overall scalability of a given optical fabric.

The architectures proposed in this paper take advantage of the extremely high bandwidth that optical technologies offer. At the same time, we must recognize the inherent difficulties in realizing in the optical domain fundamental router functions such as switching, contention resolution, labelling, etc. Indeed, while many optical switching experiments published in the last 10-15 years propose to use optical processing techniques such as wavelength conversion or 3R regeneration, these approaches, although often successfully demonstrated in a laboratory environment, are unfortunately very far from stable commercial applications, since they require optical components that are still either in their infancy, or are still too expensive. In the architectures proposed here we focused on requiring optical components that are today commercially available. The only significant exception are fast tunable lasers that, even though already demonstrated in many experimental projects [1], do not have yet commercial availability. An experimental prototype of a variant of these architectures is being developed at the PhotonLab and LIPAR laboratories of Politecnico di Torino [2], even though it will not be described here for space limitation. The paper is organized as follows. Section II introduces the general optical interconnection architecture and its main features. Section III describes the different alternatives for implementing optical fabrics based mainly on passive optical devices. Section IV discusses the typical transmission characteristics of these devices and propose simple analytical models that are based on the information available from commercial devices. Section V analyzes the actual feasibility and scalability of the proposed optical fabrics in terms of their maximum port count and aggregate bandwidth. Finally, Section VI concludes the paper. II. O PTICAL I NTERCONNECTION A RCHITECTURE The proposed architecture is based upon a WDM (Wavelength Division Multiplexing) all-optical data path that interconnects N line cards, as shown in Fig. 1. Each line card is equipped with one (wavelength tunable) transmitter and one (fixed wavelength) receiver operating in burst mode at the data rate of a single WDM channel. The optical fabric interconnects line cards but does not have any active switching element, thus, packet switching is actually controlled by line cards. By means of fast tunable lasers, each packet is sent on a specific wavelength such that after traversing the optical fabric,

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Fig. 2. Fig. 1.

Broadcast-and-Select (BS) optical fabric.

Architecture with distributed sequential scheduling.

the destination receiver is reached. Head-of-the-Line (HoL) blocking is avoided since Virtual Output Queuing (VOQ) is utilized at line cards; thus, transmitters queue packets to be inserted on a per destination basis. The architecture is synchronous, with time slotted operation, as depicted in Fig. 1. For this purpose, all line cards are synchronized to a common clock signal that can be distributed either optically or electrically. Receiver contention is solved at transmitters, since packets are scheduled so that at most one packet is sent (on a given wavelength and time slot) to each receiver. When a single receiver per WDM channel is present, and thus the number of available WDM channels W equals the number of line cards N , the architecture can be shown to be equivalent to a distributed crossbar switch, which is able to connect at every time up to N disjoint input-output pairs. In the rest of the paper we always consider the case N = W . Packet scheduling can be implemented in a centralized fashion as in most current packet switches. In this case, an electronic scheduler is required so that, after receiving status information from line cards, it decides a new permutation, i.e., an input-output port connection pattern, for each time slot. Centralized schemes can potentially offer excellent performance in terms of throughput, but the electronic complexity of the scheduler implementation can upper bound the actual performance [3]. Indeed, optimal algorithms such as Maximum Weight Matching (MWM) are impractical because of their complexity, and sub-optimal ones, such as iSLIP [4], are in general preferred. Centralized arbitration schemes require signaling bandwidth to collect status information and to distribute scheduling decisions, and introduce latencies due to the time needed to propagate such information and to execute the scheduling algorithm. In this context, the implementation of a distributed scheduling scheme becomes a crucial issue to assess the actual value of the proposed optical interconnection architecture. Distributed schemes (see, e.g., [5], [6]) have been proposed for our architecture that exhibit fair access among line cards using only locally available information. The scheme requires line cards to decide in a strictly sequential order which wavelength would be used for packet transmission in a given time slot.

For this purpose, the time slot information generated by the clock signal is delayed by a fraction D (sufficient to take an access decision) of the time slot at each line card, as depicted in Fig. 1. To avoid packet collisions (line cards sending packets to the same destination), each line card must indicate which wavelength has been selected so that the remaining line cards can consider only free channels. This information can be written (read) on (from) a specific low bit-rate channel. Despite scheduling decisions are handled sequentially in time, all packets in one time slot must be received in parallel by all receivers. Thus, each line card has a fixed delay associated according to its position that compensates scheduling times (see Fig. 1). These delays, which can be estimated to be in the tens of nanosecond range [2] are easily obtained by (fixed) short spools of fiber, or by electronic delays inside line cards. It can be shown that variations of this basic scheme permit the transmission of variable-size packets despite the slotted behavior of the architecture. In fact, variable-size packets can easily fit in successive time slots without collisions problems, since each input has full control of the channel access during transmission. The scheme has shown good performance in terms of throughput and latency as discussed in [7]. While details on our distributed scheduling schemes are outside the scope of this paper, and are omitted here due to space limitations, the fabric architectures considered herein preserve the capability of sequential scheduling decisions that are the base for our distributed scheduling approach.

III. O PTICAL FABRIC A LTERNATIVES A major issue of this interconnection architecture is the actual implementation of the optical fabric since, as it will be shown in a following section, the physical layer scalability strongly depends on the optical fabric details. In the following subsections we propose five different simple alternatives to implement a hardwired switch suitable for the proposed architecture. Since each architecture makes use of passive optical devices, we derive expressions that account for the input-output optical power loss L[dB] that each alternative introduces, as this will be the key parameter for their scalability.

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Fig. 3.

Couple-and-Demultiplex (CD) optical fabric.

Fig. 4.

Couple-and-Amplify (CA) optical fabric.

A. Broadcast-and-Select (BS) A broadcast-and-select (BS) architecture can be used to implement the optical fabric as shown in Fig. 2. The architecture uses a N × N passive star, i.e., a wavelength independent N -input, N -output coupler. This device is used to combine all optical signals from transmitters and broadcast them to all output ports. By means of a suitable optical filter before each receiver, tuned to a specific wavelength, only one wavelength reaches each receiver. As a result, each output receiver is associated with a specific wavelength that tunable transmitters select when sending packets to this destination. The distributed scheduling enforces that at most one transmitter is tuned to a given wavelength in each time slot. The power loss of the BS architecture LBS (N ) can be expressed in logarithmic scale as: LBS (N ) = LStarcoupler (N ) + LF ilter

(1)

where LStarcoupler (N ) is the power loss of a star coupler with N ports, and LF ilter the loss of a single channel optical filter. B. Couple-and-Demultiplex (CD) Since N ×N star couplers have so far only few commercial applications, standard 1 × N splitters/couplers can be considered, as they are fabricated today with much larger port counts due to their use in Passive Optical Networks (PON), which also make their cost much lower, due to mass production. The resulting architecture, dubbed Couple-and-Demultiplex (CD), is shown in Fig. 3. A N × 1 coupler is used to combine all inputs on a single fiber, and a WDM demultiplexer (such as a 1 × N AWG [1]) distributes each wavelength to a specific receiver. With respect to the previous architecture, the optical filtering function is implemented by the WDM demultiplexer itself, and no further filtering is required. The power loss in dB of the CD architecture LCD (N ) can be expressed as: LCD (N ) = LSplitter (N ) + LDemux (N )

(2)

where LDemux (N ) is the loss of a 1×N WDM demultiplexer. C. Couple-and-Amplify (CA) In order to overcome the significant power loss introduced by the splitter in the CD architecture, an Erbium Doped Fiber Amplifier (EDFA) can be used to amplify all wavelengths

Fig. 5.

Couple-Amplify-Couple (CAC) optical fabric.

before entering the WDM demultiplexer. The resulting architecture, dubbed Couple-and-Amplify (CA), is shown in Fig 4. For this case, as will be shown later, it is useful to consider separately the power loss before and after the EDFA, which can be expressed as follows: LSplitter (N ) before EDFA (3) LCA (N ) = LM ultiplexer (N ) after EDFA D. Couple-Amplify-Couple (CAC) The Couple-Amplify-Couple (CAC) architecture, shown in Fig 5, is a simpler alternative to CA, being amplified (and we limit our attention in this paper to one amplifier per architecture), but using simpler components such as couplers and filters instead of the WDM demultiplexer, which is about 10 times more expensive today for the same number of ports. Wavelength uniqueness is required since there are no filtering devices until each receiver input. Transmitter tuneability is always required over N wavelengths. The power loss behavior can be described by: LSplitter (N ) before EDFA (4) LCA (N ) = LSplitter (N ) + LF ilter after EDFA E. Wavelength Routing (WR) A well-known alternative to implement hardwired switches is the use of an N ×N Arrayed Waveguide Grating (AWG) [1]. Indeed, the inherent cyclic property of N × N AWGs enables the routing of packets by tuning the transmitter to a proper



Fig. 6.

Wavelength Routing (WR) optical fabric.

wavelength. Therefore, by means of a N × N AWG, a Wavelength Routing (WR) architecture can be considered as shown in Fig 6. In the previous architectures, an unique wavelength is associated with each receiver; thus, all transmitters use the same wavelength to reach a given destination. Since the scheduling guarantees that no packet collisions may occur, on a given time slot all transmitters select different wavelengths to send packets. However, in the WR architecture the actual routing of packets through the N × N AWG depends also on the input port. The scheduling scheme still guarantee that a single packet is routed in each time slot to the same output (i.e., to one receiver), but the received wavelength depends on the current transmitter. The power loss of the WR architecture can be formulated as: LW R (N ) = LAW G (N )

(5)

where LAW G (N ) is the power loss of an N ×N AWG device. IV. PASSIVE O PTICAL D EVICES The characterization of the passive optical devices used in the previous section becomes crucial to effectively assess their performance. In performing our study, we observed that first order scalability assessment based on theoretical insertion loss values give unrealistic results. As a clear example, the WR architecture has an insertion loss that ideally does not depend on the number on input-output ports, thus leading to a theoretical “infinite scalability”. Clearly, we need a more accurate second order assessment taking into account also other important effects, such as polarization dependence, excess losses, channel uniformity, and crosstalk, that characterize commercial devices. Despite their different nature, all these effects can be expressed as an input-output equivalent power penalty which accounts for both actual physical power loss and the equivalent power penalty introduced by other second order transmission impairments, as described in the following. A. Power Penalties Insertion Loss (IL): We indicate as Insertion Losses the total worst case power loss, which includes all effects related to internal scattering due to the splitting process and non ideal splitting conditions, such as material defects, or manufacturing inaccuracies. In the case of N -port splitters, the splitting

process gives a minimum theoretical loss increasing with 10 log(N ) dB, but extra loss contributions due to non ideal effects, often referred as Excess Losses (EL), must also be considered. Uniformity (U): Due to the high wavelength range typically covered by multiport devices, different transmission coefficients exist for different wavelengths. On the WDM comb, the propagation conditions vary slightly from center channels to border ones. This difference is taken into account by the U parameter, which is often referred to as an IL variation over the full wavelength range. Polarization Dependent Loss (PDL): The attenuation of the light crossing a device depends on its polarization state due to construction geometries, or to material irregularities. Losses due to polarization effects are counted as a penalty in the worst propagation case. Crosstalk (X): When considering a signal out of a WDM demultiplexing port, there is always an amount of power, other than the useful one, belonging to other channels passing through the device. This effect is generally referred as crosstalk, and it is usually classified as out-of-band or inband crosstalk [8]. In general, the contribution to crosstalk from adjacent channels XA is high, while the contribution from non-adjacent channels XN is lower, but it increases with the number of ports. Thus, the overall crosstalk, expressed in dimentionless linear units, can be approximated as follows: X(N ) = 2XA + (N − 3)XN

(6)

Out-of-band crosstalk (OX), also called incoherent crosstalk, takes into account the power from other wavelengths interfering a certain channel. This effect is present mainly on filtering devices, such as WDM demultiplexers, 1 × N AWGs, and optical filters, due to the fact that their ability to transmit/reject out-of-band signals does not behave as an ideal step transfer function. For single port filters, incoherent crosstalk is present as there are WDM channels; in this case, the number of WDM channels can be considered instead of the number of ports. The previous Equation (6) can be transformed into an equivalent OX power penalty (in dB) following the approximations presented in [9], giving rise to (remember that X(N ) is defined in linear units): OX(N ) = 10 log10 (1 + X(N ))

(7)

In-band crosstalk (IX), or coherent crosstalk, is due to interference from other channels working on the same wavelength as the channel under consideration. In our proposed architectures, In-band crosstalk is only relevant for the WR architecture, in which the same wavelength can simultaneously enter all input ports. The impact of this crosstalk is typically high given its in-band characteristics, and the equivalent IX power penalty (in dB) for optimized decision-threshold in the receiver can be estimated [10] by IX(N ) = −10 log10 (1 − X(N )Q2 )

(8)



where Q is the target quality factor in linear units, determining the target Bit Error Rate (BER) (typically Q lies in the range from 6 to 7 in linear scale for BER between 10−9 and 10−12 ).

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B. Device Characterization LStarcoupler [dB]

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Power penalties for N × N star coupler devices.

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The previously described power penalties enable the characterization of passive optical devices in terms of the overall power penalty L(N ) they introduce for a given number of ports N . A detailed study has been carried out in order to find reasonable values for realistic commercial devices. To achieve this, a large number of commercial device datasheets [11]– [14] have been used to collect typical realistic values of each parameter for the different devices. Moreover, linear and logarithmic regression methods have been used to derive analytical formulas that well fit on datasheet values and can estimate unknown ones. For the same device type, the values reported in datasheets from different vendors are usually very similar, since the reported values are those that allows to meet the specification of some relevant international standard. For instance, most commercial 1 × N splitters have values that are set by the current PON/GPON/EPON standards. Thus, the values that we have considered in this paper can be assumed as fairly general and consistent among different vendors. Results of this study for the star coupler and splitter devices are shown in Fig. 7 and Fig. 8 respectively. These plots report the contribution of each of the individual effects described in Section IV-A, and the resulting total equivalent power penalty. In both cases, the ideal log(N )-like loss dominates over the contributions of other parameters like U, PDL and EL. However, as the number of ports increases, so does the relative contribution of these second order parameters. For instance, 20 ports contribute with 3-4 dB of additional penalty with respect to the ideal case. The characterization of WDM demultiplexers and AWGs is shown in Fig. 9 and Fig. 10. Ideally, the power penalty of these devices should be independent from the number of ports due to the wavelength routing property. However, in both cases the IL values that we inferred from datasheets show a dependency on the number of ports that contributes logarithmically to the power penalty. Crosstalk has a significant impact only on the power penalty of the N × N AWG, since the presence of in-band crosstalk increases exponentially the power penalty, limiting the realistically useful size of the AWG device to about 10-15 ports (13-18 dB). This rather strong limit is in contrast with frequent assumptions of AWG-based designs. Finally, single-input single-output optical filters, such as those requested by the BS architecture, are typically quite ideal devices, with attenuation of adjacent channels in excess of 40 dB, so that we simply assumed an IL value of 3 dB [15] and negligible crosstalk.

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Total Penalty IL

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V. S CALABILITY A NALYSIS In this Section, we consider the feasibility and scalability of the optical fabric architectures described in Section III when taking into account the device characterization proposed in

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Power penalties for 1 × N WDM demultiplexers devices.



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Section IV. With this scope, we still need to introduce some other parameters/assumptions for the transmitter/receiver pair. For the transmitter, a typical average transmitted power PT X of 3 dBm is assumed. This is consistent with typical tunable laser output of the order of +10 dBm, and with the 6-7 dB equivalent loss introduced by an external modulator (3 dB due to on-off keying, and 3-4 dB due to additional insertion loss). For the receiver, we assume a target BER TBER = 10−12 , for which the best receivers at 10 Gbps have today a typical reference receiver sensitivity PS around −26 dBm (for the case without any optical amplification). Since we wanted to address scalability at different bit rates, we looked for a suitable model on how receiver sensitivity scales with the bit rate Rb . This is a non trivial task, and we followed the excellent analysis presented in [16] which, inferring from many different commercial datasheets, proposes a sensitivity slope vs. Rb of 13.5 dB/decade. Following this model, the receiver sensitivity in dBm can be determined as follows: Rb (9) PS (Rb )|dBm = −26 + 13.5 log 10 Gbps Finally, including other possible effects, such as component ageing, a power margin µ of 3 dB was considered. Given all the assumptions and models presented so far, the power budget analysis for the completely passive optical fabrics (architectures BS, CD and WR) can be quite simply evaluated by imposing that, for a given N , the received power PRX must satisfy PRX ≥ PS including the margin, i.e., in logarithmic scale: PT X − L(N ) − µ ≥ PS . In the case of amplified architectures, due the presence of the EDFA, the analysis should be treated in a different way. We first observed that for most optical transmission systems, the performance are usually bounded by either the optical signalto-noise ratio (OSNR) at the EDFA output (due to Amplified Spontaneous Emission (ASE) noise), or by the useful signal power at the input of the receiver photodiode. Consequently, a typical system is limited by either the lowest acceptable OSNR at the output of the EDFAs present in the system, or by the receiver sensitivity. For this purpose, we assume a (com-

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Fig. 11.

Port count performance for different bit rates.

monly accepted) target OSNR TOSN R = 17 dB constraint, together with the previously introduced constraint on receiver sensitivity. As a result, two constraints are considered (for CA architecture, again assuming logarithmic units): PT X − LCA (N ) − (hvRb )|dBm − F − µ ≥ TOSN R PEDF A − 10 log(N ) − LCA (N ) − µ ≥ PS (10) The first equation considers the minimum signal power at the input of the EDFA that can guarantee an OSN R ≥ 17 dB, where (hvRb )|dBm is the equivalent channel in-band ASE noise in dBm at the input of the EDFA, F is the EDFA noise figure, h is the Planck constant and v is the optical signal center frequency. The EDFA is assumed to have a noise figure F = 5 dB and to operate in constant output power regime with a total output power of PEDF A = 17 dBm. This output power, when all N WDM channels are simultaneously active, is evenly distributed among the N WDM channels, giving rise to a power per channel of PEDF A − 10 log(N ) dBm. A. Port Count The output of our scalability study is reported in Fig. 11, which shows for all architectures the received power PRX vs. the number of ports N . On the same graph, we report the received signal threshold PS for bit rates of 2.5, 10 and 40 Gbps. These thresholds are usable also for the CA architecture, since it turned out that for all reasonable cases, the limits set by Equations (10) are crossed in the path from transmitters to EDFA input, and thus are limited by OSNR. The CAC architecture instead is limited by OSNR only at 2.5 Gbps, while at higher bit rates the receiver sensitivity limit is reached first (i.e., with less ports). Fig. 11 clearly shows that the CA architecture overperforms all others (with the exception of power-only limited BS at 2.5 Gbps), reaching for instance about 150 ports at 40 Gbps (6 Tbps). Within passive architectures, BS shows the best performance, although it is able to support less than 20 ports at 40 Gbps (0.8 Tbps), and more than 200 ports at 2.5 Gbps (0.5 Tbps). Crosstalk penalties are relevant in the WR architecture, so that port count is limited to less than 20 for



Aggregate Bandwidth [Tbps]

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all bit rates. Note that these (expected) results are in contrast with many studies on switching architectures, in which AWGs are indicated as a very promising component for the design of large optical switches. We observe here that tunable transmitters must support fast wavelength agility over the whole WDM comb. When the number of wavelengths N is very high, it is clear that the actual port count of these architectures can be limited by the laser tunability range, and can thus result in values lower than those shown in Fig. 11. Though it is out of the scope of this paper to address these issues, we mention that we recently started to study multi-plane solutions that make use of relatively simple spatial switching at the transmitter to reduce the wavelength agility requirements. B. Aggregate Bandwidth Fig. 12 shows the maximum aggregate bandwidth that each architecture can support vs. the individual channel bit rates. As the bit rate increases, the CA architecture increments its bandwidth, offering 3.52 Tbps at 40 Gbps, and reaching a maximum of about 6.5 Tbps at 100 Gbps. For all bit rates, the CAC capacity is limited by OSNR. All other architectures support nearly 1 Tbps of aggregate bandwidth. The WR architecture can offer a maximum of almost 1 Tbps at 100 Gbps, while BS can reach about 0.7 Tbps at 2.5 Gbps. For the BS architecture, the larger the bit rate, the lower the aggregate bandwidth, since the increase on the receiver sensitivity strongly penalize the maximum number of ports on the star coupler. This is compensated in the CAC architecture, since the EDFA power gain is useful when less channels (ports) are present, and the per-channel gain is reasonably high. The behavior of the CAC architecture is lower-bounded by CD, depending on the EDFA output power, and top-bounded by the CA architecture (with an enhanced power budget having only Demux losses). Similarly, but with a passive approach, the WR architecture increases its aggregate bandwidth with the bit rate since the main limitation of this architecture is the maximum number of ports of the AWG (about 10).

VI. C ONCLUSIONS In this paper we analyzed simple optical interconnection architectures for use inside high-capacity packet switches. These architectures make use of simple and mainly passive optical components, and are conceived in a manner that enables distributed packet scheduling algorithms. We studied their scalability properties using simple models for the optical components which however could capture the significant behaviors of real commercial devices. The best results are obtained by the CA architecture, that is shown to be able to support 6.5 Tbps at 100 Gbps using 65 wavelengths (OSNR limited port count to 65). We believe this is a very promising result, considering the extremely low complexity of the proposed interconnection architectures. Even assuming a more reasonable limitation on the fast tunable laser to, say, 40 wavelengths, this still would give rise to a 4.0 Tbps aggregate capacity with ample power margin. As an extension of this work, we are currently working on multi-plane versions of the described architecturs, in which space diversity is exploited to increase scalability without going too close to the limits of wavelength agility requirements. ACKNOWLEDGMENT This work was partially supported by the Italian project OSATE and by the FP7 European NoE e-Photon/ONe. R EFERENCES [1] J. Gripp, et al., “Optical switch fabrics for ultra-high-capacity IP routers”, J. of Lightwave Technology, vol. 21, no. 11, Nov. 2003, pp. 2839-2850. [2] A. Antonino, R. Birke, V. De Feo, J. M. Finocchietto, R. Gaudino, A. La Porta, F. Neri, M. Petracca, “The WONDER Testbed: Architecture and Experimental Demonstration”, Prooc. ECOC 2007, Berlin, Germany, Sept. 2007. [3] N. McKeown, “Optics inside Routers”, Proc. ECOC 2003, Rimini, Italy, Sep. 2003. [4] N. McKeown, “The iSLIP Scheduling Algorithm for Input-Queued Switches”, IEEE/ACM Trans. on Networking, vol. 7, no. 2, Apr. 1999, pp. 188-201. [5] M. Ajmone Marsan, A. Bianco, E. Leonardi, L. Milia, “RPA: A Flexible Scheduling Algorithm for Input Buffered Switches”, IEEE Trans. on Communications, vol.47, no.12, Dec. 1999, pp. 1921-1933. [6] A. Bianco, et al., “Multi-Fasnet Protocol: Short-Term Fairness Control in WDM Slotted MANs”, Proc. IEEE GLOBECOM 2006, Nov. 2006. [7] A. Bianco, E. Carta, D. Cuda, J. M. Finochietto, F. Neri, “An Optical Interconnection Architecture for Large Packet Switches”, 9th International Conference on Transparent Optical Networks (ICTON) 2007, vol. 3, 1-5 July 2007, pp. 226-229. [8] R. Ramaswami, and K.N. Sivarajan, Optical Networks - A Practical Perspective, Morgan Kaufman, 1988. [9] G. P. Agrawal, Fiber-optic communication systems, New York, John Wiley & Sons, 2002 [10] H. Takahashi,K. Oda,H. Toba, “Impact of crosstalk in an arrayedwaveguide multiplexer on NN optical interconnection”, J. of Lightwave Technology, Vol.14, Iss.6, Jun 1996, Pages:1097-1105 [11] JDSU, WDM Filter 100 GHz Multi-channel Mux/Demux Module, Product Datasheet, http://www.jdsu.com [12] FUTUREX, Single Mode Standard Star Coupler Module, Product Datasheet, http://www.futurexusa.com [13] ACCELINK, 100GHz DWDM Module, Product Datasheet, http://www.accelink.com [14] ANDevices, N × N AWG multiplexers and demultiplexers Router Module, Product Datasheet, http://www.andevices.com [15] JDSU, WDM Filter 100 GHz Single-channel, Product Datasheet, http://www.jdsu.com [16] E. Sackinger, Broadband Circuits for Optical Fiber Communication New York, John Wiley & Sons, 2005
