Cross-Stuck CS Fault Toggle-Stuck TS Fault Verticalr

KNOCKOUT-BASED SWITCHES 170 Ž . stuck-at-zero s-a-0 . Cells passing through the faulty links are always cor- rupted. The link failure can occur at either a vertical or a horizontal link; it is Ž . then called vertical-stuck or horizontal-stuck, respectively. Let SWE i, j represent the switch element located at the ith row and the jth column in Ž . Ž . Ž . Ž . the SWE array. Denote by CS i, j , TS i, j , VS i, j , and HS i, j a cross- Ž . stuck, toggle-stuck, vertical-stuck, and horizontal-stuck fault at SWE i, j , respectively. In the following, we only discuss single-fault failures, since they are much w x more likely to happen than multiple-fault failures in integrated circuits 2 .

6.4.1.1 Cross-Stuck CS Fault

Figure 6.22 shows the cell routing in an Ž . w Ž .x SWE array with across-stuck SWE 4, 3 the shaded one, denoted CS 4, 3 , where a cell from the north is always routed to the south, and a cell from the west to the east. If the CS fault occurs in the last column of the SWE array, as shown in Figure 6.22, cell loss performance is degraded. For instance, cell Ž . Fig. 6.22 An example of cell loss due to a cross-stuck fault at SWE 4, 3 , denoted Ž . Ž . CS 4, 3 . 䊚1994 IEEE. A FAULT-TOLERANT MULTICAST OUTPUT-BUFFERED ATM SWITCH 171 Ž . X4 is discarded because of the cross-stuck SWE 4, 3 . If there are only three cells from the first to the fourth input destined for this output group, one of Ž . these three cells will be discarded at SWE 4, 3 , which contributes to cell loss performance degradation. However, if X4 is not the third cell destined for this group, or there are Ž . more than three the number of output links cells destined for this group, the CS in the last column does not contribute to cell loss performance degradation.

6.4.1.2 Toggle-Stuck TS Fault

Figure 6.23 shows how a toggle-stuck Ž . SWE 4, 2 affects the cell routing in the SWE array. Unlike a cross-stuck fault, a toggle-stuck fault may result in cells being misrouted. If the west input of the toggle-stuck SWE in Figure 6.23 does not have a cell destined for this output, an output link is wasted because the link is mistakenly occupied by this input. Therefore, every input, except this input, may experi- Ž . Fig. 6.23 An example of cell loss due to the toggle-stuck fault at SWE 4, 2 , denoted Ž . Ž . TS 4, 2 . 䊚1994 IEEE. KNOCKOUT-BASED SWITCHES 172 Ž . Fig. 6.24 A cell loss example due to the vertical stuck-at-1 or -0 fault at SWE 4, 2 , Ž . Ž . denoted VS 4, 2 . 䊚1994 IEEE. ence a cell loss performance degradation. For example, in Figure 6.23, cell Ž . X1 is discarded due to the fault of TS 4, 2 .

6.4.1.3 Verticalr

r r r rHorizontal-Stuck VSr r r r rHS Fault Figure 6.24 shows the Ž . cell routing in the SWE array when a fault of stuck-at-one or -zero is found Ž . at the vertical link of SWE 4, 2 . Figure 6.25 shows a fault at the horizontal link. Cells passing through this faulty SWE are always corrupted at either the vertical or the horizontal link. This might cause data retransmission and increase the network load and the congestion probability.

6.4.2 Fault Detection