## 3 Materials and Methods
### Trace Anonymization
### Temporal Difference

Interactions among players in a multiplayer game can result in increased network traffic, especially from the server to the client, making it essential to understand temporal differences in traffic patterns. In particular, we conjectured the inter-packet arrival time may be influenced by the concurrent number of connected players if the games are concerned about underlying network robustness and bandwidth. We split Game \(B\)'s log data into a 1-hour time frame and compared packet inter-arrival times for off-peak window and peak window. Table 4 summarizes the least busy time frame and the busiest time frame. Figure 5 depicts the distribution of inter-arrival times for the compared time frames given in Table 4. Interestingly, the graphs exhibit similar patterns to those observed in Figure 4. Because the overall inter-packet latency is already noticeably short, as shown in Figure 4, this observation suggests that the mobile game does not employ any special traffic offloading techniques such as message aggregation. This may also indicate that recent mobile games have network performance expectations as high as those in PC MMORPGs. Figure 4: Packet inter-arrivals distribution for Game \(B\). Figure 3: Packet inter-arrivals distribution for Game \(A\). ### Self-Similarity

Previous research on PC MMORPG games has discovered that the distribution of packet arrival times in such game genres exhibits self-similarity; that is, it displays similar burstiness characteristics regardless of the time scale [11]. Therefore, we initially conjectured that mobile games would exhibit the same characteristics because they seem to have similar expectations of network robustness. Burstiness over different time scales can be assessed via a \"variance-time plot\" [28]. We first count the packets observed every 100 milliseconds. Then, we aggregate these 100-millisecond buckets and calculate the variance across the aggregated buckets by increasing the aggregation size. By plotting the aggregation sizes and corresponding variances on a log-log graph, we can check if the traffic exhibits self-similarity. If the graph exhibits a linear line with a slope between \(-1\) and \(0\), it indicates the traffic pattern has a similar burstiness characteristic regardless of the time scale. For comparison between traffic with different numbers of arrivals, we normalized variances by dividing by the square of the mean of 100-millisecond buckets. Figure 6 presents the variance-time plot for Game \(A\). The dashed green line represents a reference line with a slope of \(-1\) on the log-log scale, serving as a benchmark for comparing the self-similarity characteristics of the traffic pattern. The client-to-server traffic does not exhibit strict self-similarity; its variance decreases more steeply at lower time scales than at larger time scales, as shown in Figure 6a. This indicates that the traffic has self-similarity at a larger time scale (i.e., time scale more than 1 s), but its burstiness characteristic is different from that at a lower scale. To understand the traffic pattern, we compared the result to synthesized traffic (i.e., the solid yellow line labeled \"Exp\"). We generated traffic such that the arrival times for each session follow an exponential distribution with a mean rate of 1 packet per second. Then, we multiplexed 400 independent identically distributed (i.i.d.) sessions. The comparison suggests that the trace resembles an aggregated exponential process rather than a self-similar process. Including server-to-client traffic exaggerates the pattern and now clearly shows that the traffic does not have self-similarity because it shows a non-linear curve below the dashed line with a slope of \(-1\) (Figure 6b). The results may be explained by traffic that is not directly initiated by the player (e.g., keep-alive traffic to detect mobile network hiccups or \"auto-hunt\" mode, which is typically adopted by a mobile MMORPG that plays a game on human's behalf), but further research is required to understand this correctly.