Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications
by Lakhmi C. Jain; N.M. Martin
CRC Press, CRC Press LLC
ISBN: 0849398045   Pub Date: 11/01/98
  

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Our Fuzzy Logic (FL) System contains two subsystems as shown in Figure 4. One of them is to process Si and δTi, then predicting possible cell loss. The second one is to monitor εTi. Its purpose is to adjust the crispy output of the first one, when error in previous estimations is detected.


Figure 4  High-Level Diagram of the Fuzzy System Components

Si and δTi are fed into the first of our fuzzy logic subsystems. This subsystem generates a crispy output μ1 as the possibility of cell discarding in the near future. The bigger the μ1 is, the more cells are likely to be discarded. In order to make our prediction, we use another fuzzy logic subsystem which monitors previous estimation errors and then adjusts the value of μ1. To do this, an error function is defined below as:

The negative sign of εTi indicates that OTi was underestimated, which may have resulted in some cells being discarded. On the other hand, the positive sign represents an overestimation of OTi. The first condition states that a good prediction should not cause any cell loss. Any cell loss must have been caused by a previous low estimation. The second condition states that, if the length of pseudo-queue is still long enough, no reduction of transmission rate should be taken. This error is processed by the second fuzzy logic subsystem. Our scheme considers the propagation delay time of the feedback signal; it makes the prediction more difficult, but it approaches the real world application.

Three fuzzy If-Then rules are used in the first subsystem:

  If Si is HIGH and δTi is Positive SMALL then do shaping LESS
  If Si is HIGH and δTi is Positive MEDIUM then do shaping MEDIUM
  If Si is HIGH and δTi is Positive LARGE then do shaping MORE

Two fuzzy rules are used in our second subsystem:

  If εTi is smaller than 0 then increase output of first system
  If εTi is greater than 0 then decrease output of first system.

The first rule in the second subsystem says that, if any cell is discarded (εTi<0), we should reduce ℜi, which means we have to increase μ1. The more cells are discarded, the more μ1 needs to be incremented. The second rule says that, if overestimation is detected, increment of ℜi or decrement of μ1 must be considered. The amount of adjustment depends on the degree of overestimation in previous predictions.

Assuming the output of the second fuzzy subsystem is μ2, we define OTi+1 = min {1, μ1 x μ2} as the output of our fuzzy system. The membership functions used in our system are shown in Figure 5.


Figure 5  Membership Functions for Fuzzy Rate Regulator

3.2 Traffic Shaping

The Usage Parameter Control (UPC) mechanism discussed above has its intrinsic limitation in the ability to ensure that the negotiated connection parameters are respected, due to the stochastic behavior of the controlled source. An alternative approach is to pre-shape the cell generation process.

In the following subsections, we propose two alternatives which accept our fuzzy system’s crisp output to perform traffic shaping, namely Rate Regulation (RR) and Rate Reduction with Rate Increment (RRRI).

In RR, we neither control the peak bit rate nor the burst length as long as LB still has enough “space” to accept cells. On the other hand, if possible overflow (cell discarding) in the LB is detected, the transmission rate is reduced to ℜi = (1-OTi) Ri. The transmission rate is updated every ΔT seconds. Its objective is to avoid cell discarding by LB. So when traffic is regulated, some delay time is usually needed to complete the requested transmission. For example, assume an unshaped traffic is to generate data at a constant rate Rc cells/second for Tc seconds. The source generates data at a constant rate of Rc cells/per second for nΔT seconds at first, n<m. It is then regulated to a generation rate of ℜi cells/second for the rest of the transmission (ℜi < Rc). It then takes (m-nT(Rc/ℜi-1) seconds of delay to complete the transmission.

In RRRI, we assume that there is infinite buffer space for the source. The buffer is similar to the one discussed above and is able to serve at a rate equal to or lower than the declared peak bit rate [2]. All cells generated by the source pass through the buffer in FIFO sequence. The shaper is now located at the output of the buffer. So, even if ℜi is equal to 0, the source can still generate cells that enter the buffer at a rate Ri. The main difference between RR and RRRI is that the latter allows the transmission rate to increase to Bp when OTi-1 and OTi are both equal to 0 and there are cells in the buffer. That is to say, if there are cells delayed in the buffer and no cell will be discarded in the near future (judging from the trend of OTi-1 and OTi), we allow those cells to be transmitted as soon as possible at the declared peak bit rate. So in this case, ℜi may be greater than Ri. This mechanism may still have extra delay time if the transmission rates of the last few time units are high compared to the depletion rate.


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