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This is a notion related as to how the cells transmitted by a source are clumped together. Typically, a source is bursty if it transmits for a time and then becomes idle for a time, as shown in Figure 4.1. The longer the idle period, and the higher the arrival rate during the active period, the more bursty the source is.
The burstiness of a source can significantly affect the cell loss in an ATM switch. Let us consider an output buffer of the output buffering non-blocking ATM switch. (The switch is shown in Figure 3.10; the buffer is shown in Figure 4.2.) The buffer has a finite capacity queue and is served by a link (see the circle in Figure 4.2). The arrival stream of ATM cells to the queue can be seen as the superposition of several different arrival streams coming from the input ports of the switch. A cell that arrives at a time when the queue is full is lost.
From queueing theory, we know that as the arrival rate increases, the cell loss increases as well. What is interesting to observe is that a similar behavior can be also seen for the burstiness of a source. The curve in Figure 4.3 shows qualitatively how the cell loss rate increases as the burstiness increases while the arrival rate remains constant.
Let us consider successive inter-arrival times of cells generated by a source (see Figure 4.4). In an ATM environment, it is highly likely that the inter-arrival times are correlated either positively or negatively. Positive correlation means that, if an inter-arrival time is large (or small), then it is highly likely that the next inter-arrival time will also be large (or small). Negative correlation implies the opposite. That is, if an inter-arrival time is large (or small), then it is highly likely that the next inter-arrival time will be small (or large). As in the case
active idle active idle
Figure 4.1 A bursty source.
Arrival of cells
Figure 4.2 A finite capacity buffer.
CONGESTION CONTROL IN ATM NETWORKS
Figure 4.3 Cell loss rate vs burstiness.
cell cell cell cell cell cell
\, ËË .*.
Figure 4.4 Successive inter-arrival times of cells.
of burstiness, the correlation of the inter-arrival time of cells can significantly affect the cell loss probability in an ATM switch.
4.1.2 Standardized Traffic Descriptors
The ATM Forum has standardized the following traffic descriptors: peak cell rate, cell delay variation tolerance, sustained cell rate, and maximum burst size. The ITU-T has only standardized the peak cell rate. The source’s characteristics determine the peak cell rate, sustained cell rate, and maximum burst size.
The cell delay variation tolerance is used in the generic cell rate algorithm (GCRA). (See Section 4.7.1.) It is independent of the characteristics of the source, and is specified by the administrator of the network to which the source is directly attached.
4.1.3 Empirical Models
Several empirical models have been developed to predict the amount of traffic generated by a variable bit rate MPEG video-coding algorithm. These empirical models are statistical models and are based on regression techniques.
MPEG is a standards group in ISO that is concerned with the issue of compression and synchronization of video signals. In MPEG, successive video frames are compressed following a format like: IBBBPBBBPBBBI, where I stands for I-frame, B for B-frame, and P for P-frame. An intra-coded frame (I-frame) is an encoding of a picture based entirely on the information in that frame. A predictive-coded frame (P-frame) is based on motion compensated prediction between that frame and the previous I-frame or P-frame. A bidirectional-coded frame (B-frame) is based on motion compensated prediction between that frame and the previous I- or P-frame or the next I-frame or P-frame.
The encoder also can select the sequence of I, P, and B frames, which form a group of frames known as a group of pictures (GOP). The group of frames repeats for the entire duration of the video transmission.
The size of the resulting frame varies significantly between frame types. I-frames are the largest while B-frames are the smallest. The size of an I-frame varies based on picture content. P-frames and B-frames vary depending on the motion present in the scene as well as picture content.
The number of bits produced by each frame in such a sequence is correlated and it can be predicted using an autoregressive integrated moving average (ARIMA) model. Such a model can be used in a performance evaluation study to generate video traffic. For the group of pictures I B B P B B P B B P B B, the following ARIMA model can be used to predict the number of bits S(i) of the ith frame: S(i) = S(i — 12) + e(i) — 0.69748 e(i — 3), where e(i) is white noise and it follows the distribution N(0, î2), with