Gain in prob. of success using FEC over non FEC Fraction of FEC (n k)/k

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1 Optical Packet-Switching using Forward Error Correction Gaurav Agarwal, Jeff Danley and Rahul Shah November 28, 2 Abstract Optical networking technology has experienced remarkable advances in a short time, making it possible to build future Optical Networks that support bursty IP datagrams. This has resulted in numerous efforts to develop optical-burst switching WDM networks for the future Optical Network backbones. However, the optical domain lacks intelligence and cannot process the bursts, leading to increased blocking probabilities. Another option is to use circuit-switched light paths which is inherently management intensive &delay prone and results in poor network utilization. For optical-packet switching, various contention resolution schemes have been suggested which employ wavelength conversion and/or opticalbuffering to reduce the blocking probability. In this report, we presenta pseudo-contention resolution scheme to improve the performance of optical packet-switching for a given blocking probability. We introduce redundancy in the form of forward error correction. Thus, the data can still be recovered in the face of some losses. Simulation results are presented which show the advantages of this scheme.. Introduction The massive explosion of traffic generated by theinternet and the consequent need for bandwidth has shifted the focus of the network engineers towards optical networks. The recent advances in optical technologies, especially wavelengthdivision multiplexed (WDM) transmissions, have increased the available bandwidth by orders of magnitude. Also, all-optical networks are transparent to data-rates and data-formats. A major challenge is to efficiently integrate the optical network to the existing Internet. Since the Internet predominantly uses the TCP/IP protocol suite, IP over WDM has been proposed as the core architecture for the next-generation optical networks. Also, electrical-optical-electrical (E-O-E) conversions can be eliminated inside the optical network by switching in the optical domain rather than the electronic domain.

2 Present daywork on IP over WDM have been derived from IP-over-ATMover-SONET or IP-over-SONET. Many optical networking ideas propose the use of optical pipes for sending data over the optical network. These ideas are usually variants of the circuit-switching paradigm and hence suffer from various shortcomings. Connection setup delay can be large, and the contention for resourses may result in connections being dropped. Hence arises the need for an effective packet-switching method. Also, sophisticated traffic grooming mechanisms are needed at the network edges in order to efficiently utilize the light paths. Another switching paradigm under study is optical burst switching [3],[4]. A control packet for connection setup is sent out on the control-wavelength to reserve resources along the path. A variable length burst is sent without waiting for a confirmation of the connection setup and can be dropped at an intermediate node due to resource contention. A burst consists of many IP datagrams, and a burst-loss results in numerous IP datagram losses. In order to effect statistical multiplexing, better utilize the resourses, and reduce network management, an efficient packet-switching scheme is more desirable. For a survey of packet switching techniques, see [9],[]. Contention occurs whenever more than one packet tries to leave from the same output port of a node. In case of a contention, one or more packets may be dropped unless contention resolution schemes are effected. This can take the form of either space [5],[6], time [7] or wavelength [8] resolution or a combination of the above. Space resolution is implemented in the form of deflection routing where all but one of the contending packets are deflected to randomly chosen available output ports. Implementation of time resolution requires optical buffers which are used to store the contending packets. Wavelength resolution requires the use of wavelength converters to change wavelengths on the fly. In this work, we focus on a pseudo-time contention-resolution scheme. It is a time contention-resolution scheme since it uses forward error correction, which can be viewed as redundancy in the time domain. However, optical buffers/delay lines are not employed which are traditionally associated with time resolution mechanisms. The basic idea is to encode packets just before they enter the optical network with some error-correcting code and then route them using traditional shortest path or deflection routing. No other special contention resolution schemes are needed at the switches, and in case of resource contention, packets can be dropped. However, due to addition of error-correcting codes, loss of a few packets can be tolerated and the data may be recovered from the received subset of packets. We also present simulation results for the AT&T optical backbone network over 2 cities. Using FEC protection, we are able to improve the recovery of data at the destination substantially. The single link case is also presented along with analysis. The rest of the report is as follows. Section 2 gives an overview of Tornado codes. Section 3 presents analysis for a single optical link case. The simulation topology and description is in Section 4. Results are presented in Section 5. We conclude in Section 6. 2

3 2. FEC - Tornado codes In this section, we giveanoverview of Tornado codes [],[2] which areasetof forward error correction codes. We also present the motivation behind using them in this scheme. Given input parameters k and n, erasure codes are designed to take a set of k packets and produce a set of l redundantpackets for a total of n = k+l encoding packets. If any k of these n packets are received, the original k packets can be decoded. Tornado codes are a type of erasure codes that relax the decoding guarantee as follows: to reconstruct the source data, it is necessary to recover fflk of the n encoding packets, where ffl >. Here, ffl represents the decoding inefficiency. Standard erasure codes, e.g. Reed-Soloman codes, have ffl =. The advantage of using Tornado codes is that they trade off a small increase in decoding inefficiency for a substantial decrease in encoding and decoding times. This makes them more attractive for large values of n and k. Tornado codes have encoding and decoding times proportional to (k + l)ln( )P while that (ffl ) of the Reed-Solomon codes is klp where P is the size of the packets. Usually, ffl ß. The encoding and decoding of the packets will be done at the edges of the optical network. This requires fast FEC computations. Tornado codes provide aconvenient knob to trade off efficiency with time. They can also be used to provide variable degrees of FEC for different paths and/or QoS classes. This feature is used in our simulations and described in detail later. 3. Analysis of a Single Optical link We consider a single optical link across which N users are trying to send data. For ease of analysis, the link is assumed to be time slotted (duration of each slot is ) and the probability ofany user using a particular time slot is p. We assume that all users have the same sending probability. Users select time slots randomly and independent of other users. Each user has to send k packets in time T. We consider two cases: A. Without FEC p = k: T P (user gets through in any time slot P j user sends a packet) =P where P =( p) N N + j=2 j pj ( p) N j P (k packets of a user get through in time T )=P k B. With FEC Each user sends n =(k + l) packets in time T, and at least k of these should be sent through successfully to recover the data. Here, p = n: T = (k+l) T 3

4 5 Gain in prob. of success using FEC over non FEC Fraction of FEC (n k)/k Figure : Improvement using FEC P (user gets through in any time slot P j user sends a packet) =P where P =( p) N N + j=2 j pj ( p) N j P n P (at least k packets get through successfully in time T )= j=k P j ( P ) n j In Fig., the theoretical improvement obtained in the single link case is plotted. A Gbps link is considered with 4 users, each sending 5 packets of kb. The time slot duration was μs, which means that the total utilization was Λ2%. The x-axis shows the ratio of extra FEC packets to the number of uncoded data packets. The y-axis plots the ratio of the probability of success with FEC to that without FEC. As can be seen from the figure, substantial improvement results from the use of 2% FEC or more. 4. Simulation Topology To demonstrate the improvement obtained by FEC, we simulated a 2 node network with 9 bi-directional links. The network was a subset of the AT&T optical backbone network as shown in Fig. 2. Each link is an OC-92 with the delays between nodes given by the actual measured delays, obtained from the AT&T webpage. The simulations were done in ns. Shortest path routing was used over the network, with link buffer size set to zero. Here we discovered a bug in ns, which does not properly account for the transmission time of a packet. This results in the queue size at the node not being effectively zero at all times and forced us to change certain parts of the ns code and recompile the simulator. At each node, the traffic generated consisted of flows of 5kB data, with 4

5 Figure 2: AT&T Optical Backbone destinations randomly chosen. The total traffic in the network was Λ-5% of the network capacity; however, some of the links were used much moreheavily than others, resulting in more losses on those links. The traffic arrival at each node was Poisson distributed with inter-packet times exponentially distributed. This was achieved by having a Poisson distributed event timer on each node which picked a destination at random. Then another counter sent 5 packets of kb each with the inter-sending times exponentially distributed. Apart from FEC, no other contention resolution mechanisms were used. It can be expected that the results would be even better if FEC was used in conjunction with other methods. When using FEC protection, we tried to reconstruct the data at the destination and if we received 5kB or more data, it was counted as a success. The simulations were run with the data having no FEC as well as different levels of FEC protection. Finally, we ran a few simulations using the number of hop information to the destination to provide varying levels of protection. 5. Simulation Results For the various topologies simulated, two types of graphs were plotted. The first one shows the percentage of packet losses for different hopcounts. For the backbone topology, the number of hops varied from to 4. The other graph again considers flows having different number of hops separately, and for each number of hops, it plots a histogram of the number of packet losses. For the histogram, the frequency is normalized to the number of flows for that hop count. The color of the bars in the graph signify the number of losses; the deepest violet is for zero losses, the next is one loss, and so on through the 5

6 Average losses (%) # of hops Figure 3: Average losses, without FEC, 2% network utilization increasing wavelengths to red. A. Without FEC The first simulation was for the case with no FEC. There were two runs, the first with a network utilization of Λ2% and the second with Λ%. However this description is misleading since some of the links were utilized far more than the others, causing a degradation in performance beyond what is expected for such utilizations. The results of the simulation are presented in Figures 3 through 6 respectively. At this point we must caution against trying to draw parallels with electronic routing which uses large buffers and hence can achieve much higher throughputs for such low utilization. The routing in the simulation had no store-and-forward capabilities, and thus any contention for resources led to the packet being dropped. B. With fixed FEC For the fixed FEC case, four different cases with %, 2%, 3% and 4% FEC were simulated. % FEC corresponds to 5 extra packets being sent for each flowof5packets and so on. If at least 5 packets travel through without loss, it is considered a flow experiencing no loss. We say that a flow experienced a loss of m packets if the destination received (5 m) packets only. As expected, the loss dropped dramatically from no FEC to 4% FEC. The results are presented 6

7 Fraction of flows experiencing losses normalized to the # of flows with n hops # of hops (n) with # of losses in each hop Figure 4: Histogram of losses, without FEC, 2% network utilization 25 2 Average losses (%) 5 5 # of hops Figure 5: Average losses, without FEC, % network utilization 7

8 Fraction of flows experiencing losses normalized to the # of flows with n hops # of hops (n) with # of losses in each hop Figure 6: Histogram of losses, without FEC, % network utilization in Figures 7 through 4. As can be seen in Figures 2 (histogram for 3% FEC) and 4 (histogram for 4%FEC), most of the flows traversed the network without experiencing any losses. The network utilization in all cases was Λ%. C. With variable FEC On observing the results for the case of fixed FEC, it can be seen that beyond a certain point, adding more FEC does not improve the performance much for flows of fewer hops. On the contrary, it just results in too many packets being injected into the network which increases the load on the network! Moreover, this is unfair as it is biased towards shorter flows in the network. This is evident especially in Fig. 3 where the avg. loss for one hop flows is only.% while that for four hop flows is 3.7%! To counteract this, we ran two simulations with different FEC for each flow depending on the number of hops it has to traverse. The first run added 6%, 2%, 24% and 3% FEC for, 2, 3 and 4 hop flows respectively. The second run added %, 2%, 28% and 32% FEC for, 2, 3 and 4 hop flows respectively. Figures 5 through 8 plot the results for these runs. In the second run, the loss rates for all the flows was nearly the same, thus achieving fairness. On comparing it with the fixed 3% FEC case, it is seen that the loss rates for 3 & 4 hop flows decrease, while the it increases for the & 2 hop flows, bringing them nearly equal. In these cases also, the network utilization remained Λ%. The purpose of using variable FEC in the simulations was to demonstrate 8

9 5 Average losses (%) 5 # of hops Figure 7: Average losses, with % FEC, % network utilization Fraction of flows experiencing losses normalized to the # of flows with n hops # of hops (n) with # of losses in each hop Figure 8: Histogram of losses, with % FEC, % network utilization 9

10 9 8 7 Average losses (%) # of hops Figure 9: Average losses, with 2% FEC, % network utilization Fraction of flows experiencing losses normalized to the # of flows with n hops # of hops (n) with # of losses in each hop Figure : Histogram of losses, with 2% FEC, % network utilization

11 7 6 5 Average losses (%) # of hops Figure : Average losses, with 3% FEC, % network utilization Fraction of flows experiencing losses normalized to the # of flows with n hops # of hops (n) with # of losses in each hop Figure 2: Histogram of losses, with 3% FEC, % network utilization

12 Average losses (%) # of hops Figure 3: Average losses, with 4% FEC, % network utilization Fraction of flows experiencing losses normalized to the # of flows with n hops # of hops (n) with # of losses in each hop Figure 4: Histogram of losses, with 4% FEC, % network utilization 2

13 7 6 hop 6% FEC 2 hop 2% FEC 3 hop 24% FEC 4 hop 3% FEC 5 Average losses (%) # of hops Figure 5: Average losses, with variable FEC (case ), % network utilization the following: ffl Fairness can be achieved among flows with different round trip times and number of hops ffl Given some maximum loss tolerance, we can reduce the amount of FEC on shorter flows and hence reduce network load ffl Preferential treatment (QoS) can be given to certain flows by increasing the level of FEC protection on those flows 6. Conclusion In this report, we have explored a new pseudo-contention resolution scheme for packet-switched optical networks. The scheme adds redundancy to the optical network in the form of forward error correction, so that the received data can be reconstructed even if some of the packets are dropped. Tornado codes, a form of erasure codes, are proposed for FEC due to their unique property of trading slightly increased decoding inefficiency for decreased encoding/decoding time. This use of Tornado codes is of paramount importance because encoding and decoding is done at the edge of the optical network and must be accomplished at line speeds of several Gbps; hence extremely fast and dedicated hardware processors are required. In such a situation, the saving in encoding/decoding 3

14 Fraction of flows experiencing losses normalized to the # of flows with n hops hop 6% FEC 2 hop 2% FEC 3 hop 24% FEC 4 hop 3% FEC # of hops (n) with # of losses in each hop Figure 6: Histogram of losses, with variable FEC (case ), % network utilization hop % FEC 2 hop 2% FEC 3 hop 28% FEC 4 hop 32% FEC Average losses (%) # of hops Figure 7: Average losses, with variable FEC (case 2), % network utilization 4

15 Fraction of flows experiencing losses normalized to the # of flows with n hops hop % FEC 2 hop 2% FEC 3 hop 28% FEC 4 hop 32% FEC # of hops (n) with # of losses in each hop Figure 8: Histogram of losses, with variable FEC (case 2), % network utilization time of Tornado codes, at the expense of decoding inefficiencies, becomes very useful. Simulation results, obtained from ns simulations, are presented and analysed. We used a subset of the AT&T optical backbone network with 2 nodes and 9 links. Heavy losses were experienced when the network was unprotected by FEC and loaded Λ2%. For comparison with the FEC case, we used a network load of Λ%. The simulations were run for various FEC levels, and increased FEC protection resulted in fewer losses. Fixed FEC for all the flows was biased towards shorter flows. So, simulations with varying levels of FEC for different flows were designed. We observed that the scheme can achieve fairness among flows with different number ofhopsby a judicious choice of protection level for various flows. This notion of fairness can be expanded so that it is based upon round-trip times or differences in volume of traffic flow on separate links. Also, varying levels of protection can be used to create intentional bias, which results in differentiated levels of service. This work is by no means complete. One possible extension is to explore different traffic generation models using Exponential ON-OFF, Pareto ON-OFF, Fractal Gaussian, and other probability models. Self-similar models can also be used. In addition, other space, time, and wavelength contention resolution schemes can be implemented and compared to our scheme. Also, two or more schemes can be combined to explore further implementations. Notably, FEC schemes in conjunction with deflection routing may be implemented. 5

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