Chapter 3: Reconfiguration Issue for Dynamic Traffic in Hierarchical
3.4 A Heuristic Algorithm for Dynamic Traffic in MG-OXC Networks
3.5.1 Performance Analysis
For a traditional OXC network with N nodes, we analyze the time complexities of lightpath addition and lightpath deletion with the algorithm in [13], RBRADT and WBRADT as follows.
Table II
WBRADT
ghtpath addition Lightpath deletion Time Complexity Comparisons between [13], RBRADT and
Li
The algorithm in [13] n1＋N2－N n1＋N2－N RBRADT n1＋n2(N2－N)＋N2－N n1＋N2－N＋n3TCL
WBRADT n1＋n2(N2－N)＋2N n1＋N2－N＋n3TCL
In Table II, n1 is the number of lightpaths, n2 is the number of over-utilized
time to c
3.5.2 S
Ass he number of wavelengths in a fiber is ten and the number of fibers s in a fiber, that is, each st waveband, and the sixth to
To create a simulation traffic pattern for each node pair, a traffic rate function is different patterns. After randomly choosing the rate function, we randomly generate a traffic rate corresponding to the traffic rate function.
r hundred packets with five arrival rates randomly lected in one of the traffic rate functions. Figure 19 shows the five traffic rate func
19(c), a function decreasing first and then increasing in Fig.
lightpaths, n3 is the number of possible lightpaths we want to set up and TCL is the ompute CL, respectively.
imulation Environment
ume t
along a directional link is five. There are two waveband
waveband has five wavelengths, with the first to fifth wavelengths being in the fir the tenth wavelengths being in the second waveband.
randomly selected among five
For each node pair, we generate fou se
tions. These rate functions in Fig. 19 are a monotonic increasing function in Fig.
19(a), a monotonic decreasing function in Fig. 19(b), a function increasing first and then decreasing in Fig.
19(d), and a constant value function in Fig.19 (e), respectively. All values in these five traffic rate functions are between (0, 1].
(a) (b) (c) (d
ig. 19. Ill rate fu
algorithm proposed in [13] for reconfiguration problem with traditional OXCs and compare the maximal lightpath loads and algorithms. In our simulation experiments, let the network run for a period then starting to apply our heuristic approaches to adjust the v
that unne
) (e)
F ustration of five traffic nctions
We divide the simulation experiments into two parts under dynamic traffic pattern. First, we implement our heuristics (i.e. RBRADT and WBRADT) and the period adaptation reconfiguration
adjustment times between these three
irtual topology. We demonstrate the operation of the system by measuring the maximal load of the lightpaths in the network at the end of each observation period.
The observation period is the parameter for observing the change of the maximal lightpath load by using different algorithms. The simulation results show
cessarily addition and deletion operations to the virtual topology cause the network unbalanced.
3.5.3 Simulation Results
Figure 20 plots the maximal loads in network observed at the end of each observation period (400 time units for this experiment). The dot line in Fig. 20 indicates the value of high watermark. Figure 21 shows the frequency of topology
adjustments, where a positive impulse indicates a lightpath addition and a negative impulse indicates a lightpath deletion. The x-axis in both Fig. 20 and Fig. 21 is the umber of observation periods. We fix the time of an adaptation process to 60000 time units, thus, the number of observation periods is 60000/400=150 in Fig. 20 and Fig. 21. The maximal lightpath load with the algorithm proposed in [13] is usually higher than the high watermark in Fig. 20(a) and the adjustment frequency with the
algorithm proposed b) and WBRADT
Fig. 20(c). The unnecessary addition and deletion operations in [13] cause the viole
h watermark is changed to 0.85 and 0.65. When high watermark is higher, the adjustment frequency decreases because fewer lightpaths exist
n
in [13] is higher than with RBRADT in Fig. 20(
in
nt fluctuations on the load of lightpath. However, in RBRADT and WBRADT, we do not make a difference to the virtual topology when no congestion occurs.
Therefore, the performances in our algorithms are better than the algorithm proposed in [13]. The period is 200 time units in Fig. 22 and Fig. 23 and 100 time units in Fig.
24 and Fig. 25. The violent fluctuation of maximal lightpath load is clearer when the observation period is shorter. When the period is shorter, the frequency of topology adjustments will be much higher and the algorithm proposed in [13] will delete the underloaded lightpath more frequently. The redundant variations result in the loads of the lightpaths fluctuating violently and trigger more actions of redundant addition or deletion. However, the heuristics we proposed do not cause this fluctuation condition because we delete the underloaded lightpath if and only if it interferes with the virtual links we want to setup.
In Fig. 26 and 27, the hig
with the load higher than the high watermark in the network. On the other hand, when high watermark is lower, the adjustment frequency increases because more lightpaths exist with the load higher than the high watermark in the network.
Secondly, we implement the algorithm proposed in [13], RBRADT and WBRADT for reconfiguration problem with MG-OXC nodes and verify that the tunnel reconfiguration is necessary for MG-OXC networks. The tunnels are randomly generated first and we compare the blocking probability between that the tunnels are updated with different periods by PTRADT and that the tunnels are not updated. No matter the tunnels are updated or not, the lightpaths in the network are still updated with a fixed period by the algorithm in [13], RBRADT and WBRADT. In Fig. 28~30, each fiber has ten wavelengths and the switching types on each link are 1F2B2L, 2F1B2L and 2F2B1L, respectively. In Fig. 31~33, each fiber has twenty wavelengths and the switching types on each link are the same as Fig. 28~30. Figure 28(a)~33(a), Fig. 28(b)~33(b) and Fig. 28(c)~33(c) apply the lightpaths adaptation algorithms in [13], RBRADT and WBRADT, respectively. The x-axis in Fig. 28~33 is the traffic load that means the average number of packets left in the network in a time unit and the y-axis is the blocking probability corresponding to the traffic load. When the observation period is the shortest in these figures, the blocking probability is the lowest. If the observation period is tuned longer, the blocking probability is just a little higher or equal to the lowest value. Until the observation period is tuned much longer, the blocking probability is much higher and closes to the highest value where the tunnels are not updated. Comparing Fig. 28~30 and Fig. 31~33, when the observation period is sufficiently short, the blocking probability will not decrease with it. Fig. 30 and 33 also show that when the number of wavelength-switching fibers is less, the blocking probability occurs with less traffic load. The reason is when the ports of wavelength-switching decrease, the total number of lightpaths and tunnels that we can establish also decrease.
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Maxitpmal Lighath Load
Periods RBRADT
High watermark
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Maxtpimal Lighath Load
Periods WBRADT
High watermark
(a)
Maximghtpathadal Li Lo
Periods PARADT
High watermark[13]
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Maximghtpathadal Li Lo
Periods PARADT
High watermark[13]
Fig. 20. Maximal lightpath load with high watermark=0.75 and period=400 time units, (a) is the algorithm in [13], (b) is RBRADT and (c) is WBRADT.
Fig. 21. Impulse graphic indicating times of lightpath addition or deletion with high watermark=0.75 and period=400
postm
time units, (a) is the algorithm in [13], (b) is RBRADT and (c) is WBRADT.
0 50 100 150 200 250 300
Maximal Lightpath Load
Periods RBRADT
High watermark
0 50 100 150 200 250 300
Maximal Lihtpath Load
Periods WBRADT
High watermark
(a)
Maximal Lightpath Load
Periods [13]
high watermark
Fig. 22. Maximal lightpath load with high watermark=0.75 and period=200 time units, (a) is the algorithm in [13], (b) is RBRADT and (c) is WBRADT.
Fig. 23. Impulse graphic indicating times of lightpath addition or deletion with high watermark=0.75 and period=200 time units, (a) is the algorithm in [13], (b) is
RBRADT and (c) is WBRADT.
0 100 200 300 400 500 600
Maximal Lightpath Load
Periods RBRADT
High watermark
0 100 200 300 400 500 600
Maximal Lightpath Load
Periods WBRADT
High watermark
(a)
Maximal Lightpath Load
Periods [13]
High watermark
Fig. 24. Maximal lightpath load in network with high watermark=0.75 and period=100 time units, (a) is the algorithm in [13], (b) is RBRADT and (c) is
WBRADT.
Fig. 25. Impulse graphic indicating times of lightpath addition or deletion with high watermark=0.75 and period=100 time units, (a) is the algorithm in [13], (b) is
RBRADT and (c) is WBRADT.
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Maximal Lightpath Load
Periods RBRADT High watermark
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Maximal Lightpath Load
Periods WBRADT High watermark
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Fig. 26. Maximal lightpath load and adjustments with high watermark=0.85 and period=400 time units. (a) and (c) are RBRADT. (b) and (d) are WBRADT.
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Maximal Lightpath Load
Periods RBRADT
High watermark
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Maximal Lightpath Load
Periods WBRADT High watermark
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Fig. 27. Maximal lightpath load and adjustments with high watermark=0.65 and period=400 time units. (a) and (c) are RBRADT. (b) and (d) are WBRADT.
RBRADT (1F2B2L)
1200 1300 1400 1500
Load
Blocking probability period=500
period=1000 period=5000 period=10000 tunnels are not updated
WBRADT (1F2B2L)
1200 1300 1400 1500
Load
Blocking probability period=500
period=1000 period=5000 period=10000 tunnels are not updated [13] (1F2B2L)
1200 1300 1400 1500
Load
Blocking probability period=500
period=1000 period=5000 period=10000 tunnels are not updated
(a)
(b) (c)
Fig. 28. Blocking probability of 1F2B2L when each fiber has ten wavelengths.
[13] (2F1B2L)
1200 1300 1400 1500
Load
Blocking probability period=500
period=1000 period=5000 period=10000 tunnels are not updated
RBRADT (2F1B2L)
1200 1300 1400 1500
Load
Blocking probability period=500
period=1000 period=5000 period=10000 tunnels are not updated
WBRADT (2F1B2L)
1200 1300 1400 1500
Load
Blocking probability period=500
period=1000 period=5000 period=10000 tunnels are not updated
(a)
(b) (c)
Fig. 29. Blocking probability of 2F1B2L when each fiber has ten wavelengths.
[13] (2F2B1L)
600 700 800 900
Load tunnels are not updated
RBRADT (2F2B1L)
600 700 800 900
Load
Blocking probability period=500
period=1000 period=5000 period=10000 tunnels are not updated
WBRADT (2F2B1L)
600 700 800 900
Load
Blocking probability period=500
period=1000 period=5000 period=10000 tunnels are not updated
(a)
(b) (c)
Fig. 30. Blocking probability of 2F2B1L when each fiber has ten wavelengths.
[13] (1F2B2L)
2400 2500 2600 2700
Load
Blocking probability period = 2000
period = 8000 period = 12000 period = 20000 tunnels are not updated
RBRADT (1F2B2L)
2400 2500 2600 2700
Load
Blocking probability period = 2000
period = 8000 period = 12000 period = 20000 tunnels are not updated
WBRADT (1F2B2L)
2400 2500 2600 2700
Load
Blocking probability period = 2000
period = 8000 period = 12000 period = 20000 tunnels are not updated
(a)
(b) (c)
Fig. 31. Blocking probability of 1F2B2L when each fiber has twenty wavelengths.
[13] (2F1B2L)
2400 2500 2600 2700
Load
Blocking probability period = 2000
period = 8000 period = 12000 period = 20000 tunnels are not updated
RBRADT (2F1B2L)
2400 2500 2600 2700
Load
Blocking probability period = 2000
period = 8000 period = 12000 period = 20000 tunnels are not updated
WBRADT (2F1B2L)
2400 2500 2600 2700
Load
Blocking probability
period = 2000 period = 8000 period = 12000 period = 20000 tunnels are not updated
(a)
(b) (c)
Fig. 32. Blocking probability of 2F1B2L when each fiber has twenty wavelengths.
[13] (2F2B1L)
1200 1300 1400 1500
Load
Blocking probability period = 2000
period = 8000 period = 12000 period = 20000 tunnels are not updated
RBRADT (2F2B1L)
1200 1300 1400 1500
Load
Blocking probability period = 2000
period = 8000 period = 12000 period = 20000 tunnels are not updated
WBRADT (2F2B1L)
1200 1300 1400 1500
Load
Blocking probability period = 2000
period = 8000 period = 12000 period = 20000 tunnels are not updated
(a)
(b) (c)
Fig. 33. Blocking probability of 2F2B1L when each fiber has twenty wavelengths.