Concentration Decoding Process Overflow and Call Splitting

BANYAN-BASED SWITCHES 132 consists of two fields: one is the dummy address interval, represented by two Ž . log N-bit binary numbers the minimum and the maximum , and the other 2 contains an index reference, which is equal to the minimum of the address interval. Note that the length of each interval is equal to the corresponding copy number in both addressing schemes. Denoting by S the ith running sum, the sequence of dummy address i intervals will be generated as follows: 0, S y 1 , S , S y 1 , . . . , S , S y 1 , Ž . Ž . Ž . 1 Ny2 Ny1 where the address is allocated beginning with 0. As shown in the previous section, this sequence satisfies the nonblocking condition over the broadcast banyan network.

5.6.3 Concentration

To satisfy the nonblocking condition of the broadcast banyan network, idle inputs between active inputs must be eliminated. This function should be performed before cells enter the broadcast banyan network, e.g., prior to the RAN or right after the DAE in Figure 5.22. A reverse banyan network is thus used to concentrate active inputs into a contiguous list. As illustrated in Figure 5.29, the routing address in the reverse banyan network is determined by the running sums over activity bits to produce a set of continuous monotonic addresses. Fig. 5.29 An input concentrator consists of a running adder network and a reverse banyan network. MULTICAST COPY NETWORKS 133

5.6.4 Decoding Process

When a cell emerges from the broadcast banyan network, the address interval in its header contains only one address, that is, according to the Boolean interval-splitting algorithm, min log N s max log N s output address. Ž . Ž . 2 2 The cell copies belonging to the same broadcast channel should be distin- guished by the CI, which is determined at the output of the broadcast banyan Ž . network see Fig. 5.30 by, CI s output address y index reference. Recall that the index reference is initially set equal to the minimum of the address interval. A TNT is used to assign the actual address to each cell copy so that it will be routed to its final destination in the succeeding point-to-point switch. TN assignment can be accomplished by a simple table lookup in which the Ž . identifier searching key consists of the BCN and the CI associated with each cell. When a TNT receives a cell copy, it first converts the output address and IR into the CI, and then replaces the BCN and CI with the corresponding TN in the translation table. The translation process is illus- trated in Figure 5.31.

5.6.5 Overflow and Call Splitting

Overflow will occur in the RAN of the copy network when the total number of copy requests exceeds the capacity of the copy network. If partial service Ž . also called call splitting is not allowed in cell replication and a cell must Fig. 5.30 Computation of copy indexes. BANYAN-BASED SWITCHES 134 Fig. 5.31 Trunk number translation by table lookup. Fig. 5.32 An 8 = 8 nonblocking copy network without call splitting: Only five instead of eight cell copies are allowed in this time slot. generate all its copies in a time slot, then the throughput may be degraded when overflow occurs. As illustrated in Figure 5.32, overflow occurs at port 3, and only five cell copies are allowed, although more than eight requests are available.

5.6.6 Overflow and Input Fairness