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Selective void creation/filling for variable size packets and multiple wavelengths

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  • With ever-increasing demand for bandwidth, both optical packet switching and optical burst switching are proposed as alternatives to increase the capacity of optical networks in the future. In these packet-based switching techniques, Fiber Delay Lines (for delay assignments) and wavelength conversion (for channel assignments) are used to avoid contention between contending packets. The involved scheduling algorithms decide on which Fiber Delay Line and wavelength each packet is scheduled in order to maximize performance. For the setting without wavelength conversion we proposed a scheduling algorithm for assigning delays called void-creating algorithm that outperforms existing void filling algorithms for a variety of packet size distributions. This is achieved by selectively delaying packets longer than strictly necessary based on a numerical procedure that assigns a theoretical value to each void based on how likely the void will eventually be filled and thus prove useful. This contribution extends the concept of void-creation to the important case with multiple wavelengths, where also the channel has to be assigned. Results obtained by Monte Carlo simulation show that with our void-creating algorithm the obtainable improvement in various performance measures highly depends on the number of wavelengths present.

    Mathematics Subject Classification: Primary: 68W01; Secondary: 60H30.

    Citation:

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  • Figure 1.  The modelled output port as part of a $K \times M$ optical switch.

    Figure 2.  An example of a provisional schedule for a single wavelength when the packet size is variable ($B \neq E[B] = D = 1$).

    Figure 3.  Evolution of the provisional schedule for a single wavelength when the packet size is fixed and equal to the granularity ($B = E[B] = D$).

    Figure 4.  Life cycles of the voids created by scheduling on the $ \bullet $ and $ \blacktriangle $ of Fig. 2.

    Figure 5.  An example of a provisional schedule for fixed packet size and multiple wavelengths ($c = 4$). The G-VF algorithm will choose to minimize the gap by scheduling on position $a$.

    Figure 6.  An example of a provisional schedule for fixed packet size and multiple wavelengths ($c = 4$) resulting in a possible void creation on the second wavelength.

    Figure 7.  Maximum gain (i.e., reduction giving rise to performance gain) for different performance measures as a function of the number of wavelengths ($c$).

    Table 1.  Performance measures of D-VF for different packet size distributions and a single wavelength.

    D-VFFixed
    B= E[B]=D
    Exponential
    E[B]=D
    Uniform on
    [0, 2D]
    Uniform on
    [0.5D, 1.5D]
    p=0.6p=0.8p=0.6p=0.8p=0.6p=0.8p=0.6p=0.8
    LP2.1 %14.5 %2.6 %9.1 %1.9 %9.8 %2.2 %12.9 %
    LPlength2.1 %14.5 %3.4 %11.9 %2.3 %11.7 %2.3 %13.4 %
    Packet delay3.06.12.54.12.74.83.05.7
    Packet gap0.360.420.290.300.330.340.370.39
     | Show Table
    DownLoad: CSV

    Table 2.  Optimal thresholds and corresponding performance improvements of the void value threshold algorithm for a single wavelength.

    (A) Optimal thresholds
    optimal
    threshold
    Fixed
    B= E[B]=D
    Exponential E[B]=DUniform on [0, 2D]Uniform on [0.5D, 1.5D]
    p=0.6p=0.8p=0.6p=0.8p=0.6p=0.8p=0.6p=0.8
    LP1.01.21.11.41.41.61.21.5
    LPlength1.01.22.33.01.92.01.31.6
    Packet delay1.01.20.90.91.92.01.31.6
    Packet gap1.21.33.02.31.82.01.51.6
    (B) Corresponding performance improvements
    maximum
    gain
    Fixed B= E[B]=DExponential E[B]=DUniform on [0, 2D]Uniform on [0.5D, 1.5D]
    p=0.6p=0.8p=0.6p=0.8p=0.6p=0.8p=0.6p=0.8
    LP54.1 %36.1 %4.5 %6.4 %5.7 %6.9 %28.7 %19.4 %
    LPlength54.1 %36.1 %0.2 %0.1 %0.6 %1.9 %25.0 %16.5 %
    Packet delay16.3 %16.2 %0.8 %3.4 %1.7 %3.9 %8.2 %8.8 %
    Packet gap11.5 %22.8 %0.0 %0.0 %0.3 %1.3 %4.5 %10.3 %
     | Show Table
    DownLoad: CSV

    Table 3.  Performance measures of G-VF for a fixed packet size distribution and a varying number of wavelength ($c = 1,2,4,6$ and $8$).

    G-VFc=1c=2c=4c=6c=8
    p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9
    LP2.1 %14.5 %22.5 %0.0 %4.5 %13.8 %x0.1 %5.7 %x0.0 %1.7 %xx0.3 %
    LPlength2.1 %14.5 %22.5 %0.0 %4.5 %13.8 %x0.1 %5.7 %x0.0 %1.7 %xx0.3 %
    Packet delay3.06.17.11.04.97.10.41.96.20.21.14.50.10.82.8
    Packet gap0.360.420.420.130.250.280.030.080.160.010.040.090.010.020.05
     | Show Table
    DownLoad: CSV

    Table 4.  Optimal thresholds and corresponding performance improvements of the void value threshold algorithm for a fixed packet size distribution and a varying number of wavelength ($c = 1,2,4,6$ and $8$).

    (A) Optimal thresholds
    optimal
    threshold
    c=1c=2c=4c=6c=8
    p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9
    LP0.91.21.30.71.00.9x0.80.7x2.30.5xx1.4
    LPlength0.91.21.30.71.00.9x0.80.7x2.30.5xx1.4
    Packet delay0.91.21.2to1.00.9toto0.7toto1.0toto2.4
    Packet gap1.21.31.30.80.90.9to0.70.7toto0.5toto0.5
    (B) Corresponding performance improvements
    maximum
    gain
    c=1c=2c=4c=6c=8
    p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9p=0.6p=0.8p=0.9
    LP53.5 %35.9 %26.0 %47.2 %41.3 %25.6 %x26.6 %22.1 %x86.5 %12.8 %xx1.8 %
    LPlength53.5 %35.9 %26.0 %47.2 %41.3 %25.6 %x26.6 %22.1 %x86.5 %12.8 %xx1.8 %
    Packet delay16.1 %16.1 %12.9 %0 %14.0 %11.1 %0 %0 %8.3 %0 %0 %3.2 %0 %0 %1.0 %
    Packet gap11.4 %22.7 %24.8 %3.5 %19.8 %20.9 %0 %5.2 %14.3 %0 %0 %7.4 %0 %0 %2.1 %
     | Show Table
    DownLoad: CSV
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