3.2. Scheduling Problems associated with HNN
3.2.4. Total energy function
Total energy is therefore the sum of each constraint and cost function with a corresponding coefficient:
( ) ( ) Compare to the general formulation expanded from Eq. (3.3):
(3.15)
we can get and by comparing their coefficients.
The details are shown as below
4 Experimental Results
In last chapter we proposed a HNN model to schedule input packets for QOPS. In this chapter we compare its performance with other scheduling algorithms Random Assignment (RA) and Sequential Assignment (SA) through experimenting on computers. RA schedules inputs packets by randomly assigning routing paths and wavelengths; and SA assigns packets one after another. Besides, when a path is assigned to one packet, paths which would collide with it are ruled out and the next packet is assigned a path from the rest unless there is no path can be assigned. The advantages for RA are simple and fast, but packets lost because of collision. On the other hand, SA is more complex and time-consuming but low lost probability. Before showing above comparisons, we set details of our experiment and discuss features of coefficients of HNN energy function.
For the purposes of evaluating the performance of the proposed scheduling formula of QOPS based on HNN model we fix the numbers of input and output fibers N, wavelength channels in each fiber (n), space switches (c) and internal wavelength (F), where we assume N=4, n=6, c=2 and
F=4 in our simulation as Fig.4-1. Although each input fiber takes six
wavelengths, we can regard n=6 as a portion of total wavelengths in each fibers which are aggregated into one of those space switches. There could be still many wavelengths are aggregated into other space switches. However, we can extend simulation result of one portion to remnants since they should have the same behaviors besides the wavelengths they take in input fibers andoutput fibers. For the same reason, we can experiment only on the half part of QOPS that is, n=3 and c=1.
In last chapter we design a HNN model to solve the paths scheduling optimization problem in QOPS. But the feature of preemption for high priority packet mentioned in chapter 1 is not covered in the HNN model we design.
Moreover, the non-externally blocking constrain energy function will keep packets not to be routed to any output port in some specific wavelength which will lead to externally blocking, and therefore it is not necessary for packets to preempt any packet has already in delay line. For this reason the experiment does not include the preemption when the non-externally blocking energy function is considered, and vice versa.
The experiment was executed in Language C. The number of iterations is limited under 80 times, that is, we will stop the updating of neurons no matter the HNN has converged or not. If it has converged, we can transfer the status of neurons to routing paths. What if it hasn’t converged? A set of solution for routing paths is still needed anyway. Thus, some compensation is applied on it to function as a filter that filters out those illegal routing paths transferred from status of neurons. The distribution of iterations for convergence is shown in Fig.4-2. About 60% would converge beneath 80 iterations; about 90% would converge beneath 800 iterations; and about 9% would converge after more than 1000 iterations.
The number of input batches for test is not fastened, but varies with the variation of throughputs for each test input batch. In other word, the execution
stops when the throughput varies no more than 0.5% of its mean value for this test for present. Following we will show the results of experiment in two cases:
non-preemption and preemption. Both them include HNN model with and without QoS issue.
Fig. 4-1 System with fixed size
0%
20%
40%
60%
80%
100%
1 21 41 61 83 106 136 174 216 276 320 386 460 575 746 1000 Updating iterations for convergence
Cumulated percent
Fig. 4-2 Distribution of iterations for convergence
Fig. 4-3 Throughputs when coefficient U grows (S=1)
The coefficients which affect the performance (throughput) most are that of acceptation constraint and buffer utility cost function. In Fig.4-3, both throughputs of HNN methods with and without preemption decrease to be zero when the value of coefficient U increases to twice of coefficient S. Here coefficients of other constraints are fixed as following: P=Q=R=50,
, = Hp = Lp =1
priIi (Hp for a high priority packet and for a low priority packet), X=50 for non-preemption, X=0 for preemption. Apparently, HNN without preemption, which non-externally blocking constraint is considered, provides better performance than HNN with preemption.
Lp
SA scheduling algorithm can provide results approximates those of exhaust algorithm because it assigns paths to packets as possible as it can until there is no illegal paths could be assigned. Fig.4-4(A) shows that for different traffic demands A, B, C, and D, HNN without preemption performs as good as SA does. In this figure, the throughput decreases as the distribution of destination request to four output ports gets wider because of the increasing of externally blocking probability.
Now we enable the QoS functionality in our Hopfield neural system model which is achieved by adjust the coefficient in Eq.(3.10) where
for a high priority packet and for a low priority packet.
Fig.4-4(B) and Fig.4-4 (C) are throughputs of high- and low-priority for HNN, RA ad SA. We can see that HNN without preemption method can provides priority differentiation in the pattern similar to SA.
i
pri
I,Hp
priI,i = priI,i =Lp
(A)
(B)
(C)
Fig. 4-4 Comparisons of HNN, RA and SA for different traffic demands (A)no priority difference (B)high-priority (C) low-priority
Distribution of destination request to four output ports for set A- 1:1:1:1, B- 2:1:1:1, C- 7:1:1:1, D- 91:3:3:3
5 Conclusions and Discussions
In this paper we apply HNN to a switching system called QOPS for metro WDM networks to solve the complex problem of routes assigning. The Hopfield model for this switch we designed also provides QoS differentiation by means of giving diverse weights in energy functions of HNN model to obtain different throughput and buffering. In chapter 4, we simulate the performance through not only Hopfield neural method but also optical packet preemption. Both of them could satisfy low loss probability or low-delayed traffic demands by adjusting coefficients and weights in energy functions. The result shows that the system can provide QoS according to optical packet’s priority.
QOPS has been designed and experimented in our related research. The study in this paper aims at designing an algorithm that scheduling the path routes and internal wavelength assignment for QoS Control module of QOPS.
In future works, the HNN model will be apply to the FPGA-based QoS Control module and Central Switch Controller.
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