### Table 1: Parameter Estimates for the Poisson Arrival Process with a Gamma-Distributed Correlation Factor for Tuesday (The Number of Arrivals is Per Half Hour)

"... In PAGE 4: ... We get a better goodness of fit when we assume that the arrival process is time-of-the-day and day-of-the- week dependent. Table1 shows the estimated param- eters for Tuesdays. We observe the arrival rates that are time-of-the-day dependent.... ..."

### Table 5.5: Summary of error statistics for the partial-hit probability of synthetic workloads with 100% reads, request size of 8 KB, and a Poisson arrival process. workload measured error in request rate (requests/s)

### Table 7: Daily Performance Measures Obtained from the Simulation Where the Arrival Process is Poisson with Deterministic Rates and Exponential Service Times

"... In PAGE 7: ... Note that these distributions have the same means as their corresponding counterparts that we have chosen for our original simulation model. Table7 shows a significant increase in the QoS of the simulation under the new set of distributions compared to the original simulation model. This is not surprising, because assuming deterministic arrival rates reduces the traffic variability.... ..."

### Table 2: Parameters. clari cation, which are as follows. 15We believe it is reasonable for us to consider a Poisson arrival process for purposes of this study, since user requests are essentially considered on a \per session quot; basis here; refer to [13]. 16All values are given in units of minutes, unless otherwise speci ed. 21

1998

"... In PAGE 20: ...g., how large the service capacity of each node is | refer to the two architectures used in this study, as given in Table2 ) and (b) how skewed the data access patterns are. The choice of architecture depends partly on the storage and network technologies available, the intended applications, etc.... In PAGE 21: ...ystem (e.g., a = 1:0 corresponds to the maximum service capacity of the system). There is a multitude of parameters that can be varied in studying performance of dynamic replication policies. Table2 lists the parameters considered in this study along with their default values and alternatives as used in the remainder of this section16. (Refer to Table 1 for the de - nition of the notation used in Table 2.... In PAGE 21: ... Table 2 lists the parameters considered in this study along with their default values and alternatives as used in the remainder of this section16. (Refer to Table 1 for the de - nition of the notation used in Table2 .) Several of the entries in this table require a few words of... In PAGE 22: ...se a \generically quot; highly skewed distribution, i.e., the geometric. Furthermore, applications with relatively little skew in access patterns should not, in a sense, present a performance problem, and thus we do not consider such access patterns here. Moreover, the interactivity entry in Table2 refers to how interactive the users are, with NP:FF:RW:PAUSE referring to the ratio between normal playback (NP) and the various VCR 17This is to illustrate that even under a relatively gradual change, dynamic policies are still useful. Furthermore, we believe this is a reasonable \emulation quot; of change in access patterns for many CM applications.... In PAGE 23: ... The default values are in agreement with the range of values used in [10]. Unless otherwise stated, in the gures below, we use the default values given in Table2 . Recall also that we are using the acceptance rate as our performance metric.... In PAGE 24: ...g., Architecture (1) in Table2 ) and not extremely skewed data access patterns (e.g.... In PAGE 24: ...g., Architecture (2) in Table2 ), the static policy also can not keep up with the dynamic policies; this is depicted in Figures 5(b) and 6(b), where the di erence is anywhere from 20% to 100%. This is due to the fact that, as the capacity of a single node grows, using some fraction of this capacity to perform the replication has a less signi cant e ect on the overall system performance.... In PAGE 27: ... Firstly, in our simulations the distribution of residense times in various user playback modes (NP, FF, RW, PAUSE) is uniform as compared to the exponential assumption made in the analytical model. For all cases where the interactivity model corresponds to NP:FF:RW:PAUSE = 19:1:1:1, the probability of entering the \Trap State quot;, as computed by the simulation, is zero | recall that, in our computation of Tea we chose Trap State(tn) = 0:1 (refer to Table2 ). This is partly due to the fact that our analytical model tends to be conservative (as explained in Section 5).... In PAGE 28: ...e., alternative (2) for interactivity settings in Table2 ) | this may not necessarily correspond to a realistic workload but is useful for purposes of illustration. Figures 8, 9(a), and 9(b) depict simulation results for the probability of a user entering the \Trap State quot;, the mean amount of time a user spent in the \Trap State quot;, given that he/she entered it, and the maximum amount of time a user spent in the \Trap State quot;, given that he/she entered, respectively.... In PAGE 28: ... Sensitivity to workload characteristics Next, we would like to show the lack of sensitivity to the workload characteristics, accomplished through the use of early acceptance. To this end we ran a set of simulations with two di erent modi cation to the workload characteristics (refer to Table2 ), as compared to the default workload... In PAGE 30: ...ddition (to smaller clips) (b) higher levels of interactivity, i.e., NP:FF:RW:PAUSE=4:1:1:1 (i.e., interactivity alternatives (1) and (3) in Table2 ). The performance results for case (a) are illustrated in Figures 11 and 12.... ..."

Cited by 8

### Table 2. Disk and Tape Drive Parameters The number of requested pages per CD-request was chosen ac- cording to an exponential distribution with a mean number of 8 pages. CD-requests were generated according to a Poisson arrival process. For the experiments presented here, we investigated a single workload with a mean arrival rate of 55 CD-requests per sec- ond. This results in an CD load at the disk of 70%, i.e. the CD-re- quests alone lead to a disk utilization of 70%. Further experimental results based on additional workloads can be found in [Kra99].

### Table 2. The values for C-requests reflect typical data characteristics of MPEG-2 data with a mean bandwidth of 6.1Mbit/s. The sizes of D-requests are typically smaller and obey a normal distribution. The arrival of D-requests is driven by a Poisson process with arrival rate C0108, and it is assumed that the arriving D-requests are distributed uniformly over the disks.

"... In PAGE 6: ... Table2 : Data Characteristics 4.2 Results We compared the three scheduling policies that we identified as the most promising ones in Section 3: (a)... ..."

### Table 3. Simulation results for different cache sizes (Trace 1, Poisson, LFU Policy) Before Cache Size (MB) Statistics

2002

"... In PAGE 5: ... There is some evidence that the Poisson arrival process character- izes some aspects of Internet user behaviour [3, 21], though it does not provide an adequate characterization of aggre- gate Web traffic [3, 13]. Table3 summarizes the statistical characteristics of the filtered request arrival process, for an LFU replacement pol- icy, and cache sizes ranging from 1 MB to 1 GB. The cache hit ratios are also shown in Table 3.... ..."

Cited by 2

### Table 6. Significant results for flexible assignment policy

2005

"... In PAGE 12: ... We perform new simulations for the alternatives 3 and 4 with less cases arriving to lower the utilization rate of the resources. Table6 shows the results for an arrival intensity of 120 and an arrival intensity of 150 cases per hour (Poisson arrival process). Table 6.... ..."

Cited by 3

### Table 1. The stream arrival process was modeled as a Poisson process. The results are presented with 95% con dence intervals where the length of each con dence interval is bounded by 0.1%. Figures 6-8 show the performance results for the maximum possible catch-up window Wa = 12 minutes, Wa = 6 minutes, and Wa = 2 minutes respectively 8. Parameter Value

1998

"... In PAGE 24: ... Table1 : Values of parameters used in simulation Because of the extremely long computation time (O((n ? 1)!)) of algorithm Brute- force, the simulation results for this algorithm could not be obtained for high arrival rates, at least not within 480 hours of CPU time when Wes was between 6 minutes and 12 minutes. The online brute-force, equal-split, and greedy algorithms achieve a high I/O demand reduction at high arrival rates.... ..."

Cited by 38