# Characterizing the Query Behavior in Peer-to-Peer File Sharing Systems*

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6 # Queries Max Average Min # Queries Max Average Min # Queries Max Average Min : 6: 2: 8: 24: 4.2 Periods of Peak Load To analyze potential correlations between the various workload measures and the time of day, it is useful to identify periods of time that have high and low query activity for each geographical region. To do this, Figure 3 plots the number of queries received from the one-hop peers from each geographical region in bins of 3 minutes as a function of time of day. The average values of each bin are averaged over the entire measurement period. Except for the Asian peers, the average curves for each region show a similar correlation to time of day as Figure. In particular, we identify the following key periods from Figure 3: 3:-4: (peak in North America, sink for Europe), :-2: (sink for North America, peak for Europe), 3:-4: (sink for North America, peak for Europe, peak for Asia), and 9:-2: (joint peak for North America and Europe). The minimum and maximum curves indicate a high variance for each bin. Plots of the number of queries during each hour during an outlier day i.e., a day with the minimum or maximum total number of queries from the geographical region (omitted to conserve space) shows that the number of queries is not consistently low or high during each 3-minute interval, but instead varies greatly from one interval to the next, due to statistical fluctuations in a relatively small sample size during each interval. That is, statistically, some peer sessions issue larger or smaller number of queries than the average, causing the total number of queries during the interval to differ significantly from the average. 4.3 Fraction of Passive Peers We plot the fraction of passive peers versus time of day in Figure 4. In this figure, we count the number of peer sessions that begin in a -hour interval that issue no queries (during the entire session) and calculate the ratio to all sessions that start in the same hour. The average for each -hour interval is computed over the entire : 6: 2: 8: 24: : 6: 2: 8: 24: (a) North America (b) Europe (c) Asia Figure. 3. Load Measured in Number of Queries vs. Time (3 minute bins) measurement period. We observe that the fraction is almost the same for each geographical region, with about 8% to 85% for North America, 75% to 8% for Europe, and 8% to 9% for Asia. Furthermore, the fraction of passive peers fluctuates only by about 5% over time of day. Comparing similar graphs with averages for each bin calculated over the first and the second half of the measurement period the fraction of passive peers does not change. Due to space limitations, we do not show these figures. We conclude from these results that the fraction of passive peers is approximately independent of time of day and of multiple-day periods. 4.4 Connected Session Duration Passive Peers As a passive peer does not send queries, the connected session duration is given by the time during which the peer maintains at least one connection to another peer. To check the correlation between session duration and geographical region, Figure 5 (a) plots the complementary CDF (CCDF) of session duration broken down to the geographical region. We observe that session duration shows a significant correlation to geographical region. For instance, in Asia 85% of the sessions are shorter than 2 minutes, in North America and in Europe only 75% and 55% are shorter than 2 minutes, respectively. Sessions of an intermediate duration between 2 and 2 minutes constitute 2% in Asia, 2% in North America, and 35% in Europe. Longer sessions make up 3% in Asia, 6% in North America, and % in Europe. Note that session durations between 7 and 5 hours account for % of the sessions in each geographical region, indicating that a considerable fraction of the peers stays online for a very long time without generating queries. Considering the impact of multiple-day periods, we observed in an experiment not shown that the distribution of session duration is nearly identical in the first and the second half of the measurement period. Fraction of Passive Peers Max Average Min : 6: 2: 8: 24: Fraction of Passive Peers Max Average Min : 6: 2: 8: 24: Fraction of Passive Peers Max Average Min : 6: 2: 8: 24: (a) North America (b) Europe (c) Asia Figure 4. Fraction of Connected Peers that are Passive

7 with Duration > x. Europe North America Asia Session Duration, x (min) with Duration > x. Start at :-2: Start at 9:-2: Start at 3:-4: Start at 3:-4: Session Duration, x (min) with Duration > x Start at 3:-4: Start at :-2:. Start at 9:-2: Start at 3:-4: Session Duration, x (min) (a) Each Geographic Region (b) Each Key Period of Day, Peers in North America (c) Each Key Period of Day, Peers in Europe Figure 5. Distribution of Connected Session Duration for Passive Peers To analyze correlations between session duration and time of day, we Figures 5 (b) and (c) plot the CCDF of session duration for sessions starting in each of the important periods. We observe that for European peers session duration shows a significant correlation to time of day. In particular, sessions started in the early morning are notably longer than sessions started in the afternoon or evening. For example, the fraction of sessions with duration below 9 minutes for sessions starting between 3: and 4: is 85%. However, this fraction is 93% for sessions starting between 3: and 4:. A similar trend is observed for sessions started in the evening hours in North America; i.e., : to 2: at the measurement peer. We conclude from Figures 5 (b) and (c) that correlations between session duration and time of day are significant for generating synthetic workload. The session duration for passive peers conditioned on geographical region and time of day can be well modeled by a bimodal distribution composed of two lognormal distributions. Table A. provides the parameters of the fitted distributional model for North American peers. 4.5 Active Peer Session Characteristics The connected session duration for active peers is a measure composed of the number of queries issued in a session, the time between the establishment of the connection and the sending of the first query, the time between the sending of two successive queries and the time after sending the last query until termination of the connection. Thus, in the following we characterize each of these measures separately. Figure 6 (a) plots the CCDF of the number of queries per connected session broken down by geographical region. We observe a significant correlation between the number of queries and the geographical region. For instance, the fraction of peers that issue less than 5 queries is 92% for Asia, 8% for North America, and with #Queries > x. Europe North America Asia (a) Each Geographic Region with #Queries > x. Start at 3:-4: Start at 9:-2: Start at 3:-4: Start at :-2: only 7% for Europe. 5% of the Asian peers issue 5 to queries. In North America and in Europe, these fractions constitute 8% and 3%, respectively. Moreover, we find that sessions with many queries comprise 3% of the session in Asia, % in North America and 3% in Europe. As a consequence, we conclude that European peers issue significantly more queries in a session than peers from the other geographical regions. Again, considering multiple-day time periods by separating the first and the second half of the measurement period yields no significant difference in the corresponding curves. In a further experiment, we analyze the correlation between the number of queries per session and the time of day. In Figure 6 (b) we plot the CCDF of the number of queries per session for sessions of European peers starting in each of the important periods identified above. We find that the number of queries per session is roughly insensitive to session start time for 99% of the sessions from Europe. The same holds for sessions of peers from the other geographical regions. Again, we refer to the Appendix for the models and parameters of the conditional distributions of session length in number of queries. Figure A. (a) shows that the lognormal distribution is a suitable model for the number of queries per session. The matched parameters of the model for the three most important geographical regions are stated in Table A.2. In our measurement setup, we use the filter rules presented in Section 3 to discard all queries, which are automatically generated by the Gnutella client. The matching of rules 4 and 5 indicates that there are user-generated queries, which were issued before the peer connects to the measurement node. Thus, these queries contribute to the overall number of queries a user issues in his session, although we cannot determine the sending time due to the measurement setup. Thus, for completeness we provide the (b) Each Key Period of Day, Peers in Europe with #Queries > x Figure 6. Distribution of Number of Queries per Active Session. Europe North America Asia (c) Each Geographic Region (filter rules 4 & 5 not applied)

8 Europe. North America Asia Time Until First Query, x (sec) (a) Each Geographic Region > 3 Queries. = 3 Queries < 3 Queries Time Until First Query, x (sec) (b) Conditioned on Session Length, Peers in North America Start at 3:-4: Start at :-2:. Start at 3:-4: Start at 9:-2: Time Until First Query, x (sec) (c) Each Key Period, Peers in Europe Figure 7. Distribution of Time Until First Query for Active Sessions distribution of the number of queries per session for each geographical region in Figure 6 (c). We observe that the number of queries without applying filter rules 4 and 5 most significantly changes for Asian peers. For Asian peers there is a large fraction of about 4% of sessions with more than queries. In future work we will further analyze if the queries in these sessions are truly user generated. The analysis in the remainder of this paper is based on the number of queries with filter rules 4 and 5 applied. We plot in Figure 7 (a) the CCDF for the time until the first query after the connection establishment of a session broken down by geographical region. While the curves look very similar for North American and European peers, there is a significant difference for Asian peers. The first query within a session from Asian peers is issued within seconds for % of the peers, whereas this fraction constitutes 2% for North America and Europe. The fraction of peers that issue a query within 3 seconds stays with 4% almost equal for all regions. Another 5% of the Asian peers issue the first query within 3 and 9 seconds. The same fraction of peers issues the first query within 3 and, seconds for Europe, indicating a significant correlation to geographical region. Furthermore, a fraction of % of the sessions started in North America and Europe issue the first query after 8, seconds, i.e., after more than 2 hours. To analyze correlations between the time until first query and the number of queries issued in a session, Figure 7 (b) plots the CCDF for sessions with less than 3 queries, exactly 3 queries and more than 3 queries for North American peers. This figure shows that the conditional distributions are equal for 5% of the sessions with an early first query, while there is a significant difference for the 5% of the session with late first query. In particular, in 9% of the sessions with less than 3 queries the first query is issued before 2 seconds, in the sessions with exactly 3 queries before, seconds and in sessions with more than 3 queries before 2, seconds. We conclude from Figure 7 (b) that for North America the time until first query is correlated with the session length in number of queries. In an experiment not shown, we found the same result for European peers. Figure 7 (c) plots the CCDF of time until first query for the important daily time periods of European peers identified above. We find that in sessions started in the non-peak hours in a significant fraction of the sessions the first query is sent, seconds and more after session start. These fractions constitute % for Europe. The same trend can be observed for the other geographical regions. We conclude from Figure 7 (c) that there is a significant correlation between time of day and the time until first query. To capture this correlation, the workload model distinguishes between sessions starting in peak and in non-peakhours. The time until the first query conditioned on geographical region, time of day and number of queries per session can be modeled by a bimodal distribution composed of a Weibull distribution for the body and a lognormal distribution for the tail as shown in Figure A. (b) of the Appendix. The parameters for the conditional distributions for North American peers are presented in Table A.3. We denote the time between issuing two subsequent queries as query interarrival time. Figure 8 (a) plots the CCDF of query interarrival time broken down by geographical region. This figure shows that queries generated by European peers have shorter interarrival times than the peers from the other two regions. For instance, the fraction of interarrival times below seconds constitutes 9% for Europe, while it is 8% for Asia and 7% for North America. We conclude from Figure 8 (a) that query interarrival time shows a significant correlation to geographical Fraction of Queries with Interarrival Time > x. North America Asia Europe Interarrival Time, x (sec) (a) Each Geographic Region Fraction of Queries Fraction of Queries with Interarrival Time > x = 2 Queries Start at 9:-2:. 3-7 Queries Start at 3:-4: > 7 Queries. Start at :-2: Interarrival Time, x (sec) Interarrival Time, x (sec) (b) Conditioned on Session Length, Peers in Europe Start at 3:-4: (c) Each Key Period, Peers in Europe Figure 8. Distribution of Time Between Queries for Active Sessions

9 Europe. North America Asia Time After Last Query, x (sec) (a) Each Geographic Region. 8 Queries >8 Queries 2 Queries 3-7 Queries Query Time After Last Query, x (sec) (b) Conditioned on Session Length, Peers in North America. Last Query at :-2: Last Query at 3:-4: Last Query at 9:-2: Last Query at 3:-4: Time After Last Query, x (sec) (c) Each Key Period, Peers in Europe Figure 9. Distribution of Time After Last Query for Active Sessions region. The analysis of the correlation between query interarrival time and number of queries per session reveals some interesting results. Whereas there is no significant correlation between these two measures for North American peers, sessions of European peers with many queries have smaller interarrival times than sessions with few queries as can be seen in Figure 8 (b). This indicates that there is a difference in the environment of North American and European peers like e.g. the prizing model of the Internet service providers. Due to this difference sessions of North American peers with many queries tend to connect for a longer period compared to similar sessions of European peers. We conclude that the query interarrival time has to be conditioned on the number of queries per session for European peers but not for North American peers. To analyze the correlation to time of day, Figures 8 (c) plots the CCDF of query interarrival time of broken down to the important daily time periods for European peers. It show that queries issued in peak hours (all daily periods except 3:-4:) have longer interarrival times than queries issued in non-peak hours. For example, 94% of the queries issued in Europe between 3: and 4: have an interarrival time below seconds, while this fraction is only 85% for sessions starting between : and 2:. Results for the other geographical regions are identical. We conclude that query interarrival time shows a significant correlation to time of day. As before, we provide a ready-to-use model for the conditional distributions of the query interarrival time in the Appendix. Figure A. (c) shows that a bimodal distribution composed of a lognormal body and a Pareto tail matches well to the measured query interarrival times. The parameters for the conditional distributions are summarized in Table A.4. Figure 9 (a) plots the CCDF of the time after the last query broken down by geographical region. The figure shows that only a very small fraction of peers close the connection in less than 2 seconds after the last query. Furthermore, the distributions are very similar for North American and European peers, while Asian peers tend to close sessions much faster. For instance, the fraction of sessions with a time after last query of more than seconds is 2% for Europe and North America, while it is only % for Asia. We conclude that there is a significant correlation between time after last query and geographical region. The correlation between time after last query and the number of queries per session is shown in Figure 9 (b). We observe the smallest and greatest values for the time after the last query for sessions with a single query, and with 8 and more queries, respectively. Furthermore, the conditional distributions for 2 queries and 3 to 7 queries are identical for 99% of the sessions, similar to the curves for exactly 8 and more than 8 queries. Combining both distributions of these pairs, we observe a positive correlation between time after last query and number of queries per session for 9% of the sessions. We conclude from Figure 9 (b) that the distribution of time after last query must be conditioned on number of queries per session. Analyzing the correlation to time of day for European peers in Figure 9 (c), we find that sessions sending the last query in the nonpeak hours have a shorter time after last query than sessions sending the last query in peak hours. This trend is most noticeable in Europe, where the time after the last query for sessions sending the last query between 3: and 4: is below, seconds for more than 99% of the sessions, while it is below 9% of the sessions sending the last query at other times. For North American peers we observe the same trend. We conclude from Figure 9 (c) that time after last query is significantly correlated to time of day. The time after the last query conditioned on geographical region, time of day and number of queries per session is well modeled by a lognormal distribution. As before the parameters for the conditional distributions are provided in Table A Query Popularity Distribution Since users interests will change over time, we expect that the set of queries that are popular will change within the measurement period. To confirm this assumption, we illustrate the drift in the most popular queries, i.e., the hot set drift []. For illustration, we determine the number of the top ten queries on day n that are found among the top N document on the subsequent day, for N=, 2 and. Furthermore, we perform the same experiment for the queries with rank -2 and 2- on day n, respectively. Figure plots the CCDF of the observed distributions for North American peers. The figure shows that for about 8% of the days the number of top queries that is found in the top on the subsequent day is not larger than 4, indicating a significant hot set drift. Even the top queries change significantly from day to day, as Figure (c) illustrates. We conclude from Figure that the query popularity distribution cannot be calculated over the entire trace, since the hot set drift must be considered. In addition to temporal influences, we conjecture that the query popularity distribution depends on the geographical location of peers. To confirm this conjecture, we determine the set of distinct queries issued by North American, European and Asian peers, subsequently, for periods of length N=,2, and 4 days. Furthermore, we determine the pair-wise intersection between the query sets and

10 Fraction of Days with > x in Top N on Day n N= N=2 N= Fraction of Days with > x in Top N on Day n N= N=2 N= Fraction of Days with > x in Top N on Day n N= N=2 N= (a) Top on Day n (b) Rank -2 on Day n (c) Rank 2- on Day n the intersection of all three sets. The cardinalities of the sets for typical periods are shown in Table 3. We note that the cardinality of the intersection between the query sets of North American and European peers is about 2.8% of the cardinality of the North American set and the European set for a single day. Even for a 4- day period, the cardinality of the intersection is not larger than 6%. The relative cardinality of the intersection of the query sets from all three continents is about.% and.2% for all geographical regions and periods. We conclude from Table 3 that peers from different geographical regions issue different queries. Nevertheless, there is a small intersection that should be considered in an accurate workload model. As a consequence of Figure and Table 3, we employ the following methodology for calculation of representative query popularity distributions. To account for geographical correlations, we divide the queries for each day into seven sets, i.e., one set for queries that are issued only from a single geographical region, three sets for queries that are issued by peers from two geographical regions (one for each pair), and one set of queries that are issued by peers from all three regions. We rank the queries by their frequency for each day and each of the seven subsets. To consider the hot set drift, we calculate the average frequency for a query with rank i for all days. Note, that according to Figure the query with rank i on day n in general is different from the query with rank i on day n+. Thus, ranking queries separately for each day preserves the hot-set drift and we obtain an average distribution of query popularity for a single day. Figure plots the pmf of the popularity distributions for the class of queries issued only by North American peers, the class issued only by European peers, and the class of queries issued by both North American and European peers. On a log-log scale, the curves are nearly linear, indicating that the query popularity per day Figure. Drift in Query Popularity (North American Peers) follows a Zipf-like distribution. Note that the skew in the Zipf-like distribution (i.e., the slope of the line) is somewhat different for each region; in fact, the fitted Zipf-like distribution has parameter α NA =.386 for queries issued only in North America, and α E =.223 for queries issued only in Europe. We also note that, similar to [9,2], when we computed the popularity distribution for the aggregate set of queries over multiple (e.g., 4 or ) days from our measurement trace, we observe a flattened head in the distribution (not shown to conserve space), since there are multiple queries in the aggregate set that were accessed with similar frequency but on different days. Similarly, the popularity distribution for the queries that are issued by both North American and European peers (shown in Figure (c)) has a flattened head and is fit by two different Zipf-like distributions, one for queries ranked to 45 with α I,body =.453 and the other for queries ranked 46 to with α I,body =4.67. Furthermore, the values of these Zipf parameters are significantly smaller than those observed in related work [2], due to filtering of automated queries. This fact, again, provides evidence that the filtering of automated client behavior is essential for characterizing user behavior in a peer-to-peer file sharing system. As a consequence of the small Zipf parameters, caching of responses will be more effectively in systems that use aggressive automated re-query features than in systems that only issue queries on the users action. For synthetic workload generation, the results shown in Table 3 and Figure can be used as follows: For North American peers, a query is in the set of North American queries with a probability of.97, and with probability.3 in the intersection set. Thus, for each query the set is chosen with these probabilities. After that, the query is chosen by a Zipf like distribution with the parameter determined by Figure for the according set. We use only two geographical regions, North America and Europe in the example. Table 3. Query Class Sizes Measure 4-Day Period 2-Day Period -Day Period Number of Different Queries from North American Peers Number of Different Queries from European Peers Number of Different Queries from Asian Peers Number of Queries in Intersection Set between North American an European Peers Number of Queries in Intersection Set between North American and Asian Peers Number of Queries in Intersection Set between European and Asian Peers 28 5 Number of Queries in Intersection Set between North American, European, and Asian Peers 7 4 2

11 Frequency of Query r.. Measured pmf e-4 Fitted Zipf-like Distribution Query Rank, r (a) Queries by North American Peers Only Frequency of Query r.. Measured pmf e-4 Fitted Zipf-like Distribution Query Rank, r (b) Queries by European Peers Only Frequency of Query r.. Measured pmf Fitted Zipf-like Distribution Body e-4 Fitted Zipf-like Distribution Tail Query Rank, r (c) Queries by Both North America & Europe However, the methodology can be extended in a straight-forward way to more geographical regions. 4.7 Generating Synthetic Workloads In this section we outline how to apply the characteristics derived in Sections 4. to 4.6 to generate P2P file sharing system workloads. Consider a system in steady state with N peers. When a peer finishes a session, it is replaced by a new peer. All peers are modeled according as described in Figure 2. The evaluation is performed for a given time of day, which is selected before workload generation. For simplicity, we spell out conditional distributions for North American peers only. The algorithm can be applied for peers from other geographical regions by using the corresponding conditional distributions identified in Sections 4. to CONCLUSIONS This paper provides a detailed characterization of the query behavior of peers in a peer-to-peer (P2P) file sharing system. The measures include the fraction of connected sessions that are completely passive, the duration of such sessions, and for each active session, the number of queries issued, query interarrival time, time until first query, time after last query, and query popularity. The characterization captures the key correlations in the observed workload measures as well as correlation with geographic region and time of day, such that the measured behavior can be used in constructing realistic synthetic workloads for evaluating new P2P system designs. Figure. Distribution of Per Day Query Popularity Key new observations include: () automated re-queries generated by the client software have a significant impact on most workload measures and thus have to be filtered for characterizing user behavior, (2) the most popular queries changes significantly from one day to the next, (3) 97% of the queries issued from peers in North America are not issued by peers in Europe, and vice versa, (4) the number of queries per session and passive session duration are also sensitive to geographic region, with peers in Europe issuing more queries per session and having longer passive session durations, on average, and (5) the time between the last query in an active session and the end of the session has a much heavier tail than the time between queries. Future work includes characterizing the query hit rate of the peers, including the correlation of hit rate with other measures. For each peer: () Select the geographical region, each with probability conditioned on time of day as given by Figure. (2) Determine whether the peer is passive or active, each with the probability conditioned on geographical region, as given by Figure 4. (3) If the peer is passive: (a) Choose the connected session length conditioned on time of day according to Table A.I (4) If the peer is active: (a) Determine the number of queries per session conditioned on geographical region according to Table A.II (b) Determine the time until first query conditioned on the number of queries and time of day, e.g., according to Table A.III for North American peers. (c) For each query: (i) Determine the query interarrival time conditioned on time of day, e.g., according to Table A.IV for North American peers. (ii) Determine the class of the query according to Table 3. (iii) Determine the rank of the query according to the distribution of rank for the query class, e.g., according to Figure (a) for queries by North American peers only. (d) Determine the time after last query conditioned on time of day according to Table A.V Figure 2. Algorithm for generating a synthetic workload 6. ACKNOWLEDGEMENTS The authors thank Carey Williamson for his comments which substantially improved the presentation of this paper. 7. REFERENCES [] E. Adar and B. Hubermann, Free Riding on Gnutella, Technical Report, Xerox PARC, 2.

12 [2] R. Bhagwan, S. Savage, and G. Voelker, Understanding Availability, Proc. 2 nd Int. Workshop on P2P Systems, Berkeley, CA, 22. [3] Y. Chawathe, S. Ratnasamy, L. Breslau, N. Lanham, and S. Shenker, Making Gnutella-like P2P Systems Scalable, Proc. ACM Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication (SIGCOMM 3), Karlsruhe, Germany, 23. [4] J. Chu, K. Labonte, and B.Levine, Availability and Locality Measurements of Peer-to-Peer File Systems, Proc. SPIE ITCom: Scalability and Traffic Control in IP Networks, Boston. MA, 22. [5] E. Cohen and S. Schenker, Replication Strategies in Unstructured Peer-to-Peer Networks, Proc. ACM Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication (SIGCOMM 2), Pittsburgh, PA, 22. [6] Collab.Net and Sun Microsystems, 23. [7] Z. Ge, D. R. Figueiredo, S. Jaiswal, J. Kurose, and D. Towsley, Modeling Peer-Peer File Sharing Systems, Proc. IEEE Conference on Computer Communications (INFOCOM 3), San Francisco, CA, 23. [8] Gnutella Developer Forum, Gnutella A Protocol for a Revolution, 23. [9] K. Gummadi, R. Dunn, S. Saroiu, S. Gribble, H. Levy, and J. Zahorjan, Measurement, Modeling, and Analysis of a Peerto-Peer File-Sharing Workload, Proc. 9 th ACM Symp. on Operating Systems Principles, Bolton Landing, NY, 23. [] MaxMind, LLC, Geotargeting IP Address, [] A. Mahanti, D. Eager, and C. Williamson, Temporal Locality and its Impact on Web Proxy Cache Performance, Performance Evaluation 42, 87-23, 2. [2] Mutella Hompage. [3] Napster Homepage. [4] S. Ratnasamy, P. Francis, M. Handley, R. Karp, and S. Shenker, A Scalable Content-Addressable Network, Proc. ACM Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication (SIGCOMM ), San Diego, CA., 2. [5] S. Saroiu, K. P. Grummadi, R. J. Dunn, S. D. Gribble, and H. M. Levy, An Analysis of Internet Content Delivery Systems, Proc. 5 th Symposium on Operating Systems Design and Implementation (OSDI 2), Boston, MA, 22. [6] S. Saroiu, K. Gummadi, and S. Gribble, A Measurement Study of Peer-to-Peer File Sharing Systems, Proc. Multimedia Computing and Networking (MMCN 2), San Jose, CA, 22. [7] S. Sen and J. Wang, Analyzing P2P Traffic Across Large Networks, Proc. 2 nd Internet Measurement Workshop (IMW 2), Marseilles, France, 22. [8] Sharman Networks Ltd., [9] I. Stoica, R. Morris, D. Karger, F. Kaashoek, and H. Balakrishnan, Chord: A Scalable Peer-to-Peer Lookup Service for Internet Applications, Proc. ACM Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication (SIGCOMM ), San Diego, CA, 2. [2] K. Sripanidkulchai, The Popularity of Gnutella Queries and its Implications on Scalability, Featured on O'Reilly's website, February 2. [2] StreamCast Networks, [22] B. Yang and H. Garcia-Molina, Comparing Hybrid Peer-to- Peer Systems. Proc. 27 th Int. Conf. on Very Large Data Bases (VLDB 2), Rome, Italy, 2. APPENDIX with #Queries > x. Measured Fitted Lognormal (a) Number of Queries Per Active Session Fraction of Queries with Interarrival Time > x Measured Time Measured. Fitted Weibull Body Fitted Lognormal Tail. Fitted Lognormal Body Fitted Pareto Tail Time Until First Query, x (sec) Interarrival Time, x (sec) (b) Time Until First Query, < 3 Queries, Peak Period (c) Time Between Queries, Peak Period Figure A.. Example Fitted Distributions for Workload Measures (North American Peers)

13 Table A.. Connected Session Duration for Passive Peers Period of the Day and Peer Location distribution function parameters Peak for North American peers Body: -2 minutes (75%) Lognormal σ = 2.52 µ = 2.8 Tail: > 2 minutes (25%) Lognormal σ = µ = Non-peak for North American peers Body: -2 minutes (55%) Lognormal σ = µ = 2.2 Tail: > 2 minutes (45%) Lognormal σ = µ = 6.87 Table A.2. Active Session Length (number of queries per session) Geographical region Fitted distribution Matched parameters North America Lognormal σ =.36 µ = Europe Lognormal σ =.36 µ =.52 Asia Lognormal σ =.68 µ = -.29 Time of day period Peak period for North American peers Non-peak period for North American peers Table A.3. Time Until First Query for North American Peers Number of queries Fitted per session distribution Matched parameters < 3 queries Body: -45 seconds Weibull α =.477 λ =.5252 Tail: > 45 seconds Lognormal σ = 2.95 µ = queries Body: -45 seconds Weibull α =.26 λ =.8 Tail: > 45 seconds Lognormal σ = 2.45 µ = 6.33 > 3 queries Body: -45 seconds Weibull α =.982 λ =.2662 Tail: > 45 seconds Lognormal σ = µ = 6.3 < 3 queries Body: 64-2 seconds Weibull α =.59 λ =.779 Tail: > 2 seconds Lognormal σ = µ = 5.44 = 3 queries Body: 64-2 seconds Weibull α =.27 λ =.446 Tail: > 2 seconds Lognormal σ = µ = 6.4 > 3 queries Body: 64-2 seconds Weibull α =.935 λ =.338 Tail: > 2 seconds Lognormal σ = µ = 7.86 Table A.4. Query Interarrival Time of North American Peers Time of day period Fitted distribution Matched parameters Peak for North American peers Body: 3 seconds Lognormal σ =.625 µ = Tail: > 3 seconds Pareto α =.94 β = 3 Non-peak for North American Body: 3 seconds Lognormal σ =.4 µ = peers Tail: > 3 seconds Pareto α =.43 β = 3 Table A.5. Time After Last Query of North American Peers Time of day period Number of queries per session Fitted distribution Matched parameters query Lognormal σ = 2.36 µ = Peak for North American peers 2-7 queries Lognormal σ = µ = > 7 queries Lognormal σ = 2.45 µ = 6.7 query Lognormal σ = 2.62 µ = 4.76 Non-peak for North American peers 2-7 queries Lognormal σ = 2.56 µ = > 7 queries Lognormal σ = µ = 6.36

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