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Fig. 11. S=8, Antenna, mixed routing, throughput after a burst of packets.

Figure 11 S=8, Antenna, mixed routing, throughput after a burst of packets.

Related Figures (13)

Fig. 1. Generic structure of an all-optical packet router.
Fig. 1. Generic structure of an all-optical packet router.
Fig. 2. Digraph and the numbers defining an Eulerian tour. The major problem is to derive a trade-off between the cost of an ending guarantee on the throughput and the cost of the deflections on the tail of the delay. Let us first illustrate these two problems by using some simulation results.
Fig. 2. Digraph and the numbers defining an Eulerian tour. The major problem is to derive a trade-off between the cost of an ending guarantee on the throughput and the cost of the deflections on the tail of the delay. Let us first illustrate these two problems by using some simulation results.
Fig. 4. Head of the distribution of the packet delays on the mesh with nonuniform traffic. We have analyzed by simulation a 11 x 11 2D mesh. If the traffic is unbalanced, we have shown that the mean number of deflection is quite low but a large number of packets are heavily deflected. In these ex- periments, the source of traffic is uniform on the mesh, but the destinations follow a skewed distribu- tion based on the superposition of a uniform distribu- tion on the whole mesh for 10% of the traffic and the uniform distribution on a small centered mesh of size 5 x5 for the remaining traffic. The link capacity is 1, and the global arrival rate for the whole network is 20 packets per time-slot. In Figs. 4 and 5, we present the distribution of the resulting transport delays (i.e., the length of the paths followed by the packets). Figure 4 indicates that most packets will experience a fast transport inside the mesh. The average delay mea- sured during the simulation is 16.6, much smaller than the diameter (the maximal physical distance), which is only 20 in a 11X11 2D mesh. Thus the aver- age performances sound good. Figure 5 shows the tail of the distribution of delays. For the sake of readabil- ity, we use a logarithmic scale for the probability, and we gather the packet delays in intervals of 50 time slots. Approximately 2 million packets have been de-
Fig. 4. Head of the distribution of the packet delays on the mesh with nonuniform traffic. We have analyzed by simulation a 11 x 11 2D mesh. If the traffic is unbalanced, we have shown that the mean number of deflection is quite low but a large number of packets are heavily deflected. In these ex- periments, the source of traffic is uniform on the mesh, but the destinations follow a skewed distribu- tion based on the superposition of a uniform distribu- tion on the whole mesh for 10% of the traffic and the uniform distribution on a small centered mesh of size 5 x5 for the remaining traffic. The link capacity is 1, and the global arrival rate for the whole network is 20 packets per time-slot. In Figs. 4 and 5, we present the distribution of the resulting transport delays (i.e., the length of the paths followed by the packets). Figure 4 indicates that most packets will experience a fast transport inside the mesh. The average delay mea- sured during the simulation is 16.6, much smaller than the diameter (the maximal physical distance), which is only 20 in a 11X11 2D mesh. Thus the aver- age performances sound good. Figure 5 shows the tail of the distribution of delays. For the sake of readabil- ity, we use a logarithmic scale for the probability, and we gather the packet delays in intervals of 50 time slots. Approximately 2 million packets have been de-
Fig. 3. Directed ring representation of the same network.
Fig. 3. Directed ring representation of the same network.
Fig. 5. Tail of the distribution of the packet delays on the mesh with nonuniform traffic.
Fig. 5. Tail of the distribution of the packet delays on the mesh with nonuniform traffic.
Fig. 7. Comparison of average distance and average shortcut in- tervals in p Xp meshes.
Fig. 7. Comparison of average distance and average shortcut in- tervals in p Xp meshes.
Fig. 6. Antenna Eulerian tour in a 7X7 square mesh.
Fig. 6. Antenna Eulerian tour in a 7X7 square mesh.
Fig. 8. S=20, Antenna, 11X11 mesh, delay versus arrival rate for deflection, mixed (20), sc-mixed (20), and sc-mixed (8) routing algorithms.
Fig. 8. S=20, Antenna, 11X11 mesh, delay versus arrival rate for deflection, mixed (20), sc-mixed (20), and sc-mixed (8) routing algorithms.
Fig. 9. Antenna, 11X11 mesh, mixture traffic, distribution of transport delay for a sc-mixed routing algorithm with threshold 20.
Fig. 9. Antenna, 11X11 mesh, mixture traffic, distribution of transport delay for a sc-mixed routing algorithm with threshold 20.
Fig. 10. S=8, Antenna, mixed routing, phase transition sample path due to a burst of packets.
Fig. 10. S=8, Antenna, mixed routing, phase transition sample path due to a burst of packets.
Fig. 12. S=20, Antenna, mixed routing, effect of a burst of packets. As such an undesirable behavior is probabilistic in nature, it must be clear that this phase transition is always possible, but we can decrease its probability and increase the probability of the reverse transition. We have shown in [18] that increasing S and the av- erage transport delay of Eulerian packets may solve the problem. This is illustrated in Fig. 12, where we have considered the same arrival process with the same burst and the same network as in Fig. 10. But now the threshold value is 20. The population inside the network increases; so does the number of packets in Eulerian mode. But after a delay, the number of packets in Eulerian mode will decrease, and quickly the total number of packets will go back to the initial range (140,200). So we have assumed a large value for the threshold: simulations have shown that choosing S equal to the diameter is sufficient, even if is not a formal proof. But a large value for S does not help to minimize the transport delay guarantee. Again we ex-
Fig. 12. S=20, Antenna, mixed routing, effect of a burst of packets. As such an undesirable behavior is probabilistic in nature, it must be clear that this phase transition is always possible, but we can decrease its probability and increase the probability of the reverse transition. We have shown in [18] that increasing S and the av- erage transport delay of Eulerian packets may solve the problem. This is illustrated in Fig. 12, where we have considered the same arrival process with the same burst and the same network as in Fig. 10. But now the threshold value is 20. The population inside the network increases; so does the number of packets in Eulerian mode. But after a delay, the number of packets in Eulerian mode will decrease, and quickly the total number of packets will go back to the initial range (140,200). So we have assumed a large value for the threshold: simulations have shown that choosing S equal to the diameter is sufficient, even if is not a formal proof. But a large value for S does not help to minimize the transport delay guarantee. Again we ex-
‘ig. 18. S=8, Antenna, sc-mixed routing, effect of a burst of oackets.
‘ig. 18. S=8, Antenna, sc-mixed routing, effect of a burst of oackets.
Fig. 14. S=5, Antenna, sc-mixed routing, effect of a burst of packets.
Fig. 14. S=5, Antenna, sc-mixed routing, effect of a burst of packets.
Related topics:
Computer ScienceRouting algorithmPacket SwitchingRouting AlgorithmsAll optical NetworksOptical SwitchesCore NetworkDeflection routingPacket Routing
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