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DOI 10.1007/s11107-010-0299-2

Analysis of delay mean and variance of collision-free WDM rings

with segment recirculation of blocked traffic

Isaac Seoane · Gerson Rodríguez de los Santos ·

José Alberto Hernández · Manuel Urueña ·

Ricardo Romeral · Ángel Cuevas · David Larrabeiti

Published online: 30 October 2010

© Springer Science+Business Media, LLC 2010

Abstract In Tunable-Transmitter Fixed-Receiver (TT-FR)

-based Wavelength Division Multiplexed (WDM) ring topol-ogies, each node is provided with a dedicated wavelength (home channel) for reception, which must be shared by the upstream nodes willing to communicate with it. Thus, to avoid channel collisions, it is necessary to define a Medium Access Control (MAC) mechanism that arbitrates access to a given destination wavelength. This work proposes and analy-ses a simple MAC mechanism that avoids channel collisions by recirculating traffic on the upstream ring segment where congestion was detected. Essentially, whenever a given node has got any traffic to transmit, it must first block access to in-transit traffic, which is reflected back to the upstream node over a second optical fibre. Such blocked traffic is given a second chance to pass through the congested node after a round segment delay, thus making use of the ring topology as buffering units. This work analyses the performance oper-ation of such a MAC protocol under two policies applied to recirculated traffic: (1) recirculation bypass and (2) recircu-lation store-and-forward.

Keywords Optical WDM Rings·Tunable-Transmitter

Fixed-Receiver · Collision-free WDM metro rings ·

Teletraffic analysis·Delay mean and variance

1 Introduction and related work

The ever-increasing bandwidth demands of users and appli-cations have made the research community agree that only

I. Seoane·G. R. de los Santos·J. A. Hernández (

B

)·M. Urueña·

R. Romeral·Á. Cuevas·D. Larrabeiti

Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid, Spain

e-mail: josealberto.hernandez@uc3m.es

optical fibres and Wavelength Division Multiplexing (WDM) may provide the solution to meet such demands in the next-generation Internet. In light of this, WDM-based architec-tures have already been proposed for the access, the metro and the backbone area networks. Concerning the metro area, the most widely used architecture at present comprises Son-et/SDH rings which combine optical transmission with Time Division Multiplexed (TDM) switching on every node in the ring. Thanks to the advent of Reconfigurable Optical Add-Drop Multiplexers (ROADMs), more cost-effective WDM ring technologies have been proposed over the last decade to replace legacy Sonet/SDH nodes where transit traffic need not suffer Optical-Electronic-Optical (OEO) conversion and switching on every intermediate node, but can just traverse them all-optically. Such architectures require the definition of new Medium Access Control (MAC) mechanisms to arbi-trate channel access since, in most cases, a single wavelength (or channel) is shared by multiple source nodes and collisions may occur. This is the case of the so-called Tunable-Trans-mitter Fixed-Receiver (TT-FR) rings, where each node has got a dedicated home wavelength for the reception of traffic and, at the same time, is provided with a fast tunable laser that allows it to transmit traffic on the dedicated home channel of other nodes [1,2].

In TT-FR topologies, receiver collisions can never occur since destination nodes are always listening on their dedi-cated channel, but transmission collisions may do, since mul-tiple source nodes must compete for accessing the dedicated home channel of other destination nodes. In this case, the need for a MAC mechanism that arbitrates channel use is mandatory to avoid such collisions.

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were provided with channel inspection capabilities such that they were able to identify the status (available or occupied) of forthcoming time-slots and decide whether or not to trans-mit on them. For instance, the “WDM Multirings” studied by the authors in [3], proposed a collision-free MAC proto-col whereby each node maintains as many separate logical queues as destination nodes such that, a Synchronous Round Robin (SRR) protocol scans them sequentially for packet transmission. This solution reduces the so-called Head-Of-the-Line (HOL) blocking which arises at nodes with a single FIFO for all destinations where the packet at the head of the queue blocks access to all wavelengths because it is destined to a node whose wavelength is always busy. Never-theless, the authors identified some starvation situations that may occur and further defined a fairness protocol on top of SRR to guarantee equal opportunities in accessing the ring. Such mechanism was further extended in [4] to allow service differentiation of multiple QoS classes. This architecture and MAC protocol was finally implemented in a laboratory under the name of RingO testbed [5].

In parallel, another TT-FR optical ring proposal, called Hornet, was tested by the authors in [6]. Hornet was origi-nally conceived to employ CSMA/CA as MAC protocol to avoid transmission collisions [7], but this was soon replaced by a dedicated control-channel-based MAC whereby a token advertises the availability of the next time-slots in the future. Fairness issues are resolved here by limiting the number of reservations that a given node may make on the token passing through the out-of-band control channel.

Nevertheless, both RingO and Hornet required slotted-time bandwidth partitioning. Recently, a new MAC protocol proposed for the Dual Bus Optical Ring Network (DBORN for short [8]) has shown that it is possible to employ CSMA with variable packet sizes using cheap passive components, thus simplifying the optical ring architecture at moderate cost [9]. This MAC protocol relies on the idea that each node is provided with a detection window created by delaying transit traffic by one maximum frame duration using a fibre delay line (FDL). This gives the node an amount of time enough to decide whether or not there is a suitable gap in the transit traffic to schedule the next packet waiting in its local queue. While this technique is very effective, the fact that transit traf-fic is given priority over local one may bring serious HOL problems to downstream nodes, since they can only use the gaps left in between transit packets.

This work proposes and analyses a novel MAC protocol that solves channel collisions based on recirculating blocked traffic over upstream ring segments. In this ring, priority is given to local traffic over in-transit traffic and, when con-tention occurs, incoming traffic from upstream nodes are reflected back to the previous node over a separate fibre in the opposite direction of data transmission. This way, ring seg-ments are used somehow as buffering devices since blocked

traffic is given a second chance to traverse the node found blocked in the previous attempt. Essentially, giving priority to local traffic over in-transit traffic gives worse-than-average access to distant nodes, which translates here to an increase in the experienced delay. However, as noted before, the opposite may cause starvation to nodes closely located to the destina-tion node since the available gaps left by transit traffic, after multiplexed from many source nodes, may be too small to allocate large packets.

The remainder of this work is thus organised as fol-lows: Sect.2explains in detail the proposed architecture and its operation principles. Sect. 3 analyses the performance achieved by recirculating traffic over upstream ring seg-ments from a teletraffic perspective. This includes the analy-sis of the blocking probabilities and delay mean and variance observed by the packets originated from each node of the ring. Section4validates the performance equations derived with a Simulink-based experiments and shows a few illus-trative example cases. Finally, Sect.5concludes this work reviewing its main contributions and findings.

2 Collision avoidance by recirculating blocked traffic

This section explains the principles of operation of the bi-directional WDM ring with recirculation of blocked traf-fic. Figure1shows a four-node example of such a bi-direc-tional ring where traffic is assumed to circulate on the clock-wise direction over the solid line. Without loss of generality, let node n0 be the destination node for local traffic loads

ρi,i=1,2,3 generated by the three upstream nodesn1,n2 andn3. Following the TT-FR architecture, such traffic is in-jected by the transmission nodes on wavelengthλ0, and re-moved from the ring by the reception noden0, which is the only one capable of listening onλ0. Additionally, we refer to links 1+,2+and 3+(solid lines in the figure) to the optical fibres connecting node pairs 0–1, 1–2 and 2–3 respectively in the clockwise (regular transmission) direction, and denote 1−,2− and 3− (dashed lines in the figure) the optical fi-bres connecting the same node pairs 0–1, 1–2 and 2–3 in the counter-clockwise direction. Finally, it is clear that traffic in-jected on the ring by noden3must first traverse nodesn2and

n1respectively to reach its destination noden0; traffic gener-ated at noden2must go through noden1before reaching the destination node, and traffic generated at noden1does not traverse any intermediate node, since it is directly attached to noden0by segment 1+.

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Fig. 1 A four-node WDM ring with recirculation of blocked traffic. Notation of traffic flow intensities

previous node through the counter-clockwise fibre (dashed fibre link). Such blocked and redirected traffic, when arriving at the previous (upstream) node can be treated following one of two different policies, as illustrated in Fig.2a, b:

Recirculation bypass (Fig.2a): In this case, recirculated

traffic has got priority over local traffic and it bypasses the previous node directly to the blocked node without any OEO conversion. In case there is local traffic waiting for transmission, this must wait.

Recirculation store-and-forward (Fig.2b): In this case,

recirculated traffic is converted to the electronic domain and must wait in queue together with local traffic. No priority is given to recirculated traffic.

Clearly, packets are expected to experience less end-to-end delay in the first case since they do not suffer OEO con-version upon reaching a blocked node. However, too many recirculations of traffic may cause the signal to noise ratio degrade significantly with subsequent data loss. Essentially, recirculation bypass of blocked traffic is preferred at low loads (few recirculation times) but, at high loads, when data packets are expected to recirculate several times, conversion to the electronic domain might be mandatory. Additionally, when segment lengths are too large with subsequent high attenuation losses, store and forward might be preferred for signal’s regeneration purposes. Nevertheless, in both cases, the ring segments act somehow as optical buffering elements. The next section studies the delay mean and variance expe-rienced in both cases.

3 Analysis

LetN+1 refer to the number of nodes in the ring of Fig.1, and letni,i = 0, . . . ,N be used to label each node in the optical ring. Without loss of generality, the aim is to study the delay experienced by the packets injected by any source nodeni withi =1, . . . ,N to the destination noden0, both under the recirculation bypass and the recirculation store-and-forward policies. The following blocking analysis holds for both policies.

3.1 Blocking analysis

As previously stated, each node is provided with a dedicated home channel for reception, in this case, noden0 continu-ously listens on wavelengthλ0. Thus, upstream nodes must compete for accessingλ0. Now, letρirefer to the traffic load that nodenioffers to wavelengthλ0(that is, destined to node

n0). In addition to this,ρi,o f f refers to the total amount of traffic offered on segmenti+, which basically comprises a sum of traffic load intensities. Owing to the flow conservation law on each node, the sum of incoming flow intensities must equal the sum of outgoing flow intensities. This translates to the following set ofN+1 equations:

Fig. 2 Recirculation bypass (left) and store and forward

(right).aRecirculation Bypass

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ρout +ρ1,o f fB0=ρ1,o f f ⇒ ρout =ρ1,o f f(1−B0) nodei and blocked at this node (with probabilityBi).

It can be easily shown from the equations above that:

ρout =ρ1,o f f(1−B0)=ρ1+ρ2,o f f(1−B1)

which confirms that no data is lost (flow conservation law), that is, all traffic injected in the network eventually arrives at noden0.

This information is very useful for computing the block-ing probabilities Bi experienced by transit traffic on each nodeni, using the well-known Erlang-loss equations. Essen-tially, the blocking probability experienced by transit traffic on every node follows:

Bi =EBii,o f fBi−1,1), i =1, . . . ,N (3)

where EB(ρ,M)refers to the Erlang-B loss equation ofρ units of traffic to be served byM circuits. Remark that:

EB(ρ,M)=

with B0 = 0 since the destination node is never blocked because it never injects traffic onλ0.

Thus, given a set of traffic intensitiesρi destined to node n0, it is very easy to compute the blocking probabilitiesBi from Eq.5 recursively, that is: starting from B0 =0, then

B1 = ρ1+ 1−BB00 iN=1ρi =ρ1, and so on. The next step is to derive the amount of time required by each packet to successfully arrive at the destination node following the two recirculation policies: (1) store and forward and (2) bypass.

3.2 Delay analysis

3.2.1 Recirculation store-and-forward

In this case, data frames arriving at a blocked node need to travel back to the previous node in the ring, where they suffer OE conversion and wait in queue together with the node’s traffic load. Thus, assuming infinite buffer queues, no buffer overflow occurs and all data frames eventually arrive at their destination. However, data frames may need to recircu-late several times certain segments if these are usually found blocked, with subsequent unbounded delay. Thus, it is impor-tant to study both the delay mean and its variance to give an idea of not only the average delay experienced on the ring but also the jitter.

Under the assumption of unlimited electronic buffering, the results of queueing theory for M/M/1 systems apply to derive the average delay experienced at each node’s queue, namelyE(Qi),i=1, . . . ,N. This value is given by:

E(Qi)= E(S)

1−ρi

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whereE(S)is the average service time of a data frame of size

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Now, let loop jrefer to the segments j+and j−. Thus, a given packet originated at nodenl and destined to noden0 experiences the following delay:

Dl =Ql+Reo+ l

j=1

Lj+Roe (7)

which accounts for the queueing delay experienced until it is injected on the ring plus the amount of timeLj spent on each intermediate loop j, with j =0, . . . ,l−1. Addition-ally, the EO and OE conversion delays (ReoandRoein Eq.2) suffered when entering and exiting the ring respectively are also considered in the model.

Now, consider loop j only: If the packet finds node nj free (which occurs with probability 1−Bj), then the packet only suffers propagation delay Rj. Otherwise, this packet is reflected back to nodenj+1, converted to electronic, and stored in the queue of nodej+1 (this occurs with probability Bj). In the next attempt, if the packet finds nodenjfree, then the packet has experienced a total delay of 2Rj+Qj+1+Rj (this is with probabilityBj(1−Bj)). If the packet is suc-cessfully transmitted on the third attempt (with probability

B2j(1−Bj), then such packet experiences a total delay of 4Rj +2Qj+1+Rj, and so on. Following this reasoning, the total delay experienced by a packet traversing loop j is given by:

wheremis a geometrically distributed random variable with parameter Bj. Essentially, m gives the number of extra attempts required for the successful transmission of a given packet over loop j, characterised by the probability Bj to find the next nodenjblocked in the end-to-end path. In other words:

P(m=k)=(1−Bj)Bkj, k=0,1, . . . (9)

Additionally, it is worth remarking from Eq.8that pack-ets must suffer OE and EO delay whenever they find the next node blocked, since they must be electronically buffered on the immediate upstream node.

The mean delay for loopLj is given by:

E(Lj)=E(Rj)+E(m)E(2Rj+Roe+Qj+1+Reo) value given by the fibre length and the speed of light on the optical fibre (typically 2·108m/s). The same applies to

the OE and EO conversion which are fixed quantities, i.e.

E(Roe)= Roeand E(Roe) = Roe. The loop’s delay vari-Finally, the end-to-end delay experienced by a packet orig-inated at nodenlhas got the following mean and variance:

E(Dl)=

under the assumption of node independency.

As shown, at low load levels, a given packet originated at nodelwould ideally experience a delay ofE(Ql)+l−j=10Rj.

3.2.2 Recirculation bypass

In this case, the same Eq.2as above applies here:

Dl =Ql+Reo+ l

j=1

Lj +Roe (14)

However, the computation ofQlandLjis rather different. First of all, the delay experienced on the j-th loop,Lj, does not include queueing delay since, recirculated traffic does not suffer OEO conversion and queueing on the previous nodes. Thus:

1 Remark that the variance of a random sum of N iid random

vari-ablesXi,i=1,2, . . .is given by:V ar(iN=1Xi)=E(N)V ar(X1)+

E2(X

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In addition, the average queueing delay experienced by the packets before entering the ring is also different from the previous case:

E(Qi)=

E(S) (1−ρi)(1−Bi−1)

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Since the capacity observed by the queue on node ni is only the remaining one left by the recirculated traffic, that is,

C(1−Bi−1).

Thus, the mean delay and variance experienced by packets on loopLjare given by:

Finally, the end-to-end delay mean and variance for pack-ets under the recirculation bypass strategy is given by:

E(Dl)=

again under the assumption of node independency.

4 Numerical examples

This section aims to validate the analytical equations derived above and perform a few simulation scenarios to determine what aspects have a greater impact on delay and jitter in the ring. The scenario considers a 60- km ring withN+1 nodes

labelledn0tonNwith noden0acting as destination node. The size of packets injected in the ring is exponentially-distrib-uted with meanE(B)=1250 bytes, thus giving an average

service time: E(S) = 1250×8

10·109 = 1µs on aC = 10 Gbps

interface. Additionally, nodes are assumed to aggregate traf-fic from multiple users, leading to traftraf-fic profile injected in the ring that follows a Poisson process with rateλ=ρ/E(S),

whereρdenotes the input queue load. Finally, both OE and EO delays have been assumed Roe=Reo=25µs.

To give an example with real numbers in the recircula-tion store-and-forward policy, let the ring compriseN+1=

8 nodes equally spaced on a 60 km long ring. Also, let all nodes operate under the same traffic loadρ=0.05, then the queueing delay experienced by a packet to enter the ring is given by:

E(Q)= 1µs

1−0.05 =1.0526µs

and suffer the following propagation delay per segment:

R= 60/8 km

105km/s =37.5µs

Clearly, the total delay depends on the number of segments that a given packet must traverse until reaching its destination (its relative position in the ring) and the number of times that such a packet must recirculate each segment (which depends on the blocking probabilities) before reaching their desti-nation. Additionally, the values of Roe and Reo may also comprise a significant portion of it.

The next section explores such average delay and its var-iance on different topologies and under uniform and non-uniform traffic loads.

4.1 Analysis validation via simulation

This first experiment validates the delay equations derived through the analysis section with simulation. The simula-tion was developed in Matlab’s Simulink for a 60- km ring withN +1 =8 nodes at different input loads, and

assum-ing the values of capacity C = 10 Gbps, E(B) = 1250

bytes andRoe=Reo=25µs, as described above. It is also worth remarking that the maximum input load per node is

ρmax =1/(N+1), since the maximum offered load on the last segment must not exceed unity.

Figure3shows both the analytical and simulated results for such a ring, assuming both policies upon blocked traf-fic: Recirculation store-and-forward (top) and recirculation bypass (bottom). For brevity purposes, only the delay experi-enced by the first and the last nodes in the ring, together with the node in the middle, are depicted. As noted, both analyti-cal and simulated values accurately match one another both in terms of delay mean (dots) and standard deviation (error bars), at different traffic loads. The reader must note that the error bars represent the standard deviation of delay (not con-fidence intervals) in units of time. In this case, the maximum input load per node isρmax =1/(N+1)=0.125.

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0 0.02 0.04 0.06 0.08 0.1 0.12 0

100 200 300 400 500 600 700

N=8, Recirculation Store−and−Forward

Load ρ

E2E delay (

µ

s)

0 0.02 0.04 0.06 0.08 0.1 0.12 0

100 200 300 400 500 600 700

N=8, Recirculation Store−and−Forward Simulated

Load ρ

E2E delay (

µ

s)

0 0.02 0.04 0.06 0.08 0.1 0.12 0

100 200 300 400 500

N=8, Recirculation Bypass Simulated

Load ρ

E2E delay (

µ

s)

0 0.02 0.04 0.06 0.08 0.1 0.12 0

100 200 300 400 500

N=8, Recirculation Bypass

Load ρ

E2E delay (

µ

s)

Last node Half−distant node First node

Fig. 3 Analysis validation with Matlab’s Simulink for a network withN =8 nodes. Analytical results (on theleft) and Simulation results (on the

right) are obtained assuming recirculation Store-and-Forward (top) and recirculation bypass (bottom)

4.2 Delay analysis for different values ofN

This experiment provides a comparison between the two pol-icies when the number of nodes in the ring varies. Remark that the ring length is 60- km fixed and the values forE(B)=

1250 bytes,C =10 Gbps andRoe = Reo =25µsare the same as before. Two cases are considered: (a)N+1=8 and

(b)N+1 =32. In the first case, the propagation delay per

segment is R = 60·103/8

2·108 = 37.5µswhereas in the second

case this isR=60·103/32

2·108 =9.37µs. The average delay and

variance is given in Fig.4for the two cases at different link loads. Again for brevity, only the first, last and a node in the middle of the ring are plotted.

As shown in the figure, there is a great performance dif-ference (in terms of delay mean and variance) between the recirculation bypass and the recirculation store-and-forward policies, in both cases, especially at high loads. In all cases, the recirculation bypass policy for blocked frames is shown to reduce the average delay experienced by packets and its variance since these do not suffer OEO conversion. Addi-tionally we can note the following conclusions:

The first node does not experience a big difference in

terms of delay mean and variance in all cases. This is because the closest nodes perceive a high-priority

treat-ment with respect to last nodes, thus experiencing only aboutR+Roe+Reoin most cases.

At low loads, there is no big difference between the

aver-age delay experienced by packets in the two policies, but there is when it comes to variance (jitter).

When the recirculation bypass technique is used, there

is no big difference in terms of average delay between a 60- km ring with 8 or 32 nodes, but there is in terms of variance. This is an important conclusion to keep in mind when upgrading a fixed-length ring with more interme-diate nodes.

The opposite conclusion occurs in the recirculation

store-and-forward technique since it is shown that there is not a big difference in terms of variance when upgrading from 8 to 32 nodes, but there is some difference in terms of average delay.

4.3 Delay analysis when one node offers a peak of traffic

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0 0.02 0.04 0.06 0.08 0.1 0.12

0 0.005 0.01 0.015 0.02 0.025 0.03 0

0 0.005 0.01 0.015 0.02 0.025 0.03 0

Last node Half−distant node First node

Fig. 4 Delay mean and variance experienced by packets in the two policies for variable number of nodesN+1

0 1 2 3 4 5 6 7

thus increasing very significantly their delay mean and espe-cially their variance. This is particularly harmful in the recir-culation store-and-forward case, where the nodes before the misbehaving one experience a significant increase in their

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5 Conclusions

This work has proposed a novel MAC protocol to avoid chan-nel collisions in TT-FR-based WDM rings. The novelty intro-duced by this MAC protocol is that blocked traffic is recir-culated back to upstream nodes, where they can be directly forwarded to the next node (Recirculation bypass) or stored in queue and be forwarded next (Recirculation store-and-forward). In both cases, the delay mean and variance experi-enced by the packets are analysed to show the difference in terms of performance in both cases. The experiments reveal that the recirculation store-and-forward introduces more de-lay to packets than recirculation bypass, especially at high traffic loads and, more significantly, a tremendous delay var-iance, which is very harmful for real-time traffic. Such a model can be used to further study the impact of both poli-cies on traffic demanding strict QoS requirements.

Acknowledgments The work described in this paper was carried out with the support of the BONE project (“Building the Future Optical Network in Europe”), a Network of Excellence funded by the European Commission through the 7th ICT-Framework Programme. Addition-ally, the authors would like to thank the support of the T2C2 Spanish project (under code TIN2008-06739-C04-01) to the development of this work.

References

[1] Chlamtac, I., Fumagalli, A., Kazovsky, L.G., Poggiolini, P.: A multi-Gbit/s WDM optical packet network with physical ring topology and multi sub-carrier header encoding. In: Proceedings of European Conference and Exhibition on Optical Communica-tion, Sept 1993

[2] Marsan, M.A., Fumagalli, A., Leonardi, E., Neri, F.: R-daisy: an all-optical packet network. In: Proceedings of European Symposium on Advanced Networks and Services, March 1995

[3] Marsan, M.A., Bianco, A., Leonardi, E., Meo, M., Neri, F.: MAC protocols and fairness control in WDM multirings with tunable transmitters and fixed receivers. IEEE/OSA J. Lightwave Tech-nol.14(6), 1230–1244 (1996)

[4] Marsan, M.A., Bianco, A., Leonardi, E., Morabito, A., Neri, F.: All-optical WDM multi-rings with differentiated QoS. IEEE Commu. Mag.37(2), 58–66 (1999)

[5] Carena, A., de Feo, V., Finochietto, J.M., Gaudino, R., Neri, F., Piglione, C., Poggiolini, P.: RingO: an experimental WDM optical packet network for metro applications. IEEE J. Sel. Areas Com-mun.22(8), 1561–1571 (2004)

[6] White, I.M., Rogge, M.S., Shrikhande, K., Kazovsky, L.G.: A sum-mary of the HORNET projetc: a next-generation metropolitan area network. IEEE J. Sel. Areas Commun.21(9), 1478–1494 (2003) [7] Kim, K.S., Okagawa, H., Shrikhande, K., Kazovsky, L.G.:

Unslot-ted optical CSMA/CA MAC protocol with fairness control in metro WDM ring networks. In: Proceedings of IEEE Globecom, vol. 3, pp. 2370–2374, Nov 2002

[8] Bouandallah, N., Beylot, A.L., Dotaro, E., Pujolle, G.: Resolving the fairness issues in bus-based optical access networks. IEEE J. Sel. Areas Commun.23(8), 1444–1457 (2005)

[9] Bouabdallah, N., Perros, H.: Cost-effective single-hub WDM ring networks: a proposal and analysis. Comput. Netw.51(13), 3878– 3901 (2007)

Author Biographies

Isaac Seoanereceived the Telecommunica-tions Engineering degree in 2004 and the M.Sc. in Telematics Engineering in 2007 at Universidad Carlos III de Madrid (Spain). He is an assistant lecturer and researcher at the Department of Telematic Engineering at Universidad Carlos III de Madrid (Spain) since 2006 where he has participated in sev-eral national and European researching pro-jects, such as IMPROVISA, T2C2, and the EU-funded e-Photon/ONe+, BONE and Indect. He is currently working on his Ph.D. Thesis about optical ring networks and also doing research in some other network-ing-related topics such as emergency networks, multipath and multiple description for multimedia content.

Gerson Rodríguez de los Santosreceived his Telecommunications Engineering degree in April 2008 and is pursuing the M.Sc. in Telematics Engineering at Universidad Carlos III de Madrid (Spain). He is cur-rently working at Universidad Carlos III as a research assistant, providing technical sup-port for a number of both national and euro-pean research projects (INDECT, BONE, PASITO, T2C2, etc). His research interests cover the fields of Optical Transparent Networks, Network Hardware development and Switching in general. He is also pursuing the Ph.D. degree in Telematic Engineer-ing at the aforementioned University.

José Alberto Hernández completed the five-year degree in Telecommunications Engineering at Universidad Carlos III de Madrid (Madrid, Spain) in 2002, and the Ph.D. degree in Computer Science at Lough-borough University (Leics, United Kingdom) in 2005. From 2005 to 2009, he was a post-doctoral research and teaching assistant at Universidad Autónoma de Madrid, where he participated in a number of both national and european research projects concerning the modeling and performance evaluation of communica-tion networks, and particularly the optical burst switching technology. In 2009, he moved to Universidad Carlos III de Madrid, where he cur-rently works as a visiting lecturer and senior researcher, with more than 40 articles published in both journals and conference in-proceedings. His research interests include the areas at which mathematical model-ing and computer networks overlap.

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Ricardo Romeralobtained his M.Sc. de-gree in Telecommunications Engineering and his Ph.D. in Telemeatics Engineering from Universidad Carlos III de Madrid (Spain) in 2001 and 2007 respectively. Dr. Romeral is an assistant professor at Universidad Carlos III de Madrid since then, where he combines lecturing and research in the fields of network measuring and monitoring, GMPLS and opti-cal networks, among many others. He has collaborated in several Euro-pean and Spanish projects related to traffic monitoring and analysis in optical backbone networks, and programmable networking.

Ángel Cuevasreceived his M.Sc. in Tele-communication Engineering and M.Sc. in Telematic Engineering at Universidad Carlos III de Madrid in 2006 and 2007, respectively. He was awarded with an Erasmus Schol-arship and complete his Master Thesis at The University of Reading. Currently he is Ph.D. Candidate at the Department of Telem-atic Engineering at University Carlos III de Madrid. Also, he held a research Internship at SAP Labs France. His research interests include Wireless Sensor Networks, Overlay and P2P Networks and Optical Networks.

Gambar

Fig. 2 Recirculation bypass(left) and store and forward(right). a Recirculation Bypassb Recirculationstore-and-forward
Figure 3for such a ring, assuming both policies upon blocked traf-fic: Recirculation store-and-forward (top) and recirculationbypass (bottom)
Fig. 3 Analysis validation with Matlab’s Simulink for a network with N = 8 nodes. Analytical results (on the left) and Simulation results (on theright) are obtained assuming recirculation Store-and-Forward (top) and recirculation bypass (bottom)
Fig. 4 Delay mean and variance experienced by packets in the two policies for variable number of nodes N + 1

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In this context, the study advances the Self-Care Ethic philosophy and a Covering Law theory as the departure of self­help and housing consolidation policies in urban

Kami umumkan bahwa Pemenang Lelang untuk Paket Pekerjaan Pengadaan Belanja Bahan Makanan Ikan di BAT BPTKP adalah

DAFTAR NEGARA TERTENTU BEBAS VISA

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monosakarida, misalnya glukosa, galaktosa, dan fruktosa. Banyak karbohidrat merupakan polimer

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infiltration, structural properties and water repellency of top soils were investigated in a semi-arid rangeland in SE Spain. The soil surfaces had a low vegetative cover and bare