### Table 2 shows some important simulation parameters and their corresponding values. The ra- tionale behind the choices is explained below. (These values are very similar to the corresponding ones in [16, 17], and represent a realistic asymmetric communication environment.) The time unit in our simulator is the time needed to broadcast a single data page (along the downlink). Thus, it is not necessary to specify the downlink channel capacity, because in a real situation this parameter would only a ect the time needed to broadcast a single page, and we are taking this amount as our time unit.

"... In PAGE 16: ... Table2 : Simulation parameters Two di erent access frequency distributions are modeled: Two-level Uniform, combining two di erent access frequencies in the same distribution. The rst 20 items are accessed with 90% probability, the rest of the items only with 10% probability.... ..."

### Table 2 shows some important simulation parameters and their corresponding values. The rationale behind the choices is explained below. (These values are very similar to the corresponding ones in [16, 17], and represent a realistic asymmetric communication environment.) The time unit in our simulator is the time needed to broadcast a single data page (along the downlink). Thus, it is not necessary to specify the downlink channel capacity, because in a real situation this parameter would only a ect the time needed to broadcast a single page, and we are taking this amount as our time unit.

"... In PAGE 14: ... Table2 : Simulation parameters Two di erent access frequency distributions are modeled: Two-level Uniform, combining two di erent access frequencies in the same distribution. The rst 20 items are accessed with 90% probability, the rest of the items only with 10% probability.... ..."

### Table 1: Time bounds for broadcasting in an ideal fat-tree. The resulting running time ranges from O(log N log log N) (for channel capacity proportional to subtree size) to O(log2 N= log log N) (for constant channel capacity). We observe that pipelining is crucial to achieve optimal performance only for rather small capacities, whereas it plays no signi cant role for larger capacities (say, w(n) log n). A comparison between upper and lower bounds shows that our algorithms are optimal for a wide range of channel capacities. A log log N gap remains for large capacities, in the unrestricted case, pointing at interesting aspects of the problem that require further investigation.

1996

"... In PAGE 6: ... We have: S(N) 2S(m) + 4 log N = 2S(w?1(w1=2(N))) + 4 log N ; (2) where the term 2S(m) accounts for the two calls on subtrees of size m [lines 6 and 10], and the term 4 log N accounts for the time to spread the copies [lines 7-8 and 11-15]. The time T(N) of the full broadcast (Algorithm 1) satis es T(N) = S(N) + T N w(N) : (3) In the full paper, we solve the above equation for some interesting cases of function w(n), with the results reported in Table1 of the Introduction. Broadcast(first; n) fSend copy originally at first to leaves first + 1; : : :; first + n ? 1g 1.... ..."

Cited by 1

### Table 1. Payload Architecture Capacity Summary

"... In PAGE 5: ... The resulting data rates are available for user data and assumes error-control coding added so all architectures have the same availability and BER. We started by generating the Bent Pipe architecture column of Table1 . Then, based on the Bent Pipe column, the bandwidth allocations were transformed by introducing the unique artifacts/features of the other architectures analyzed.... In PAGE 5: ... This process was repeated for each row of the table, and resulted in small deviations from existing Circuit and Cell Switch architectures. The resulting payload architecture capacities are summarized in Table1 . The remainder of this section shows that the actual number of user data bits transmitted and received through the satellite (throughput), is significantly less than the raw capacity for some architectures.... In PAGE 6: ...he Bent Pipe and Circuit Switch architectures (i.e., overhead not incurred). For the Cell Switch analysis, the SubChannelRate in the denominator of the Connections equation is replaced by the AverageRate (see Table A1 in the Appendix) due to statistical multiplexing of the downlink.4 Table 2 illustrates the results of applying these equations to the values in Table1 and Table A1. To provide the highest throughput for the Bent Pipe architecture, an all broadcast video traffic model defined in Appendix A was selected.... In PAGE 13: ... Table B2 classifies four of the most common network services including sample applications, timing requirements, data rate variation, and connection type. The user applications modeled here can be supported by a network that provides one or more of the services described in Table1 . The set of service classes required of a network determine the best network and payload architecture, network performance, and the business implications.... ..."

### Table 1: Simulation Parameters We consider a database consisting of 500 distinct data items with various sizes and periods. The period and size of each data item follow the uniform distribution and are permanently associated with each data item. The access frequency distribution of data items is modeled as Zipf distribution. Moreover, a workload generator generates on-demand requests associated with deadline constraints every time unit. The request arrival rate follows the Poisson distribution. The maximum capacity of the uplink channel is 8 requests per time unit. Unlike the traditional broadcast scheduling algorithms that try to minimize the average access time, the metric to evaluate the performance of our scheduling algorithms is the percentage of deadlines of the requests that are missed.

in Abstract Scheduling Real-Time Data Items In Multiple Channels And Multiple Receivers Environments

### Table 2 Untraceable broadcast

1992

"... In PAGE 4: ... Table 1 summarizes general fault-tolerant multi-party protocols because they can be used to implement untraceable broadcast and secret ballot election. Table2 summarizes untraceable broadcast protocols, Table 3 secret ballot election protocols. The assumptions for untraceability and fault tolerance are independent.... ..."