Many empirical studies of human walks have reported that there exist fundamental statistical features commonly appearing in mobility traces taken in various mobility settings. These include: 1) heavy-tail flight and pause-time distributions; 2) heterogeneously bounded mobility areas of individuals; and 3) truncated power-law intercontact times. This paper reports two additional such features: a) The destinations of people (or we say waypoints) are dispersed in a self-similar manner; and b) people are more likely to choose a destination closer to its current waypoint. These features are known to be influential to the performance of human-assisted mobility networks. The main contribution of this paper is to present a mobility model called Self-similar Least-Action Walk (SLAW) that can produce synthetic mobility traces containing all the five statistical features in various mobility settings including user-created virtual ones for which no empirical information is available. Creating synthetic traces for virtual environments is important for the performance evaluation of mobile networks as network designers test their networks in many diverse network settings. A performance study of mobile routing protocols on top of synthetic traces created by SLAW shows that SLAW brings out the unique performance features of various routing protocols.

We report that human walk patterns contain statistically similar features observed in Levy walks. These features include heavy-tail flight and pause-time distributions and the super-diffusive nature of mobility. Human walks are not random walks, but it is surprising that the patterns of human walks and Levy walks contain some statistical similarity. Our study is based on 226 daily GPS traces collected from 101 volunteers in five different outdoor sites. The heavy-tail flight distribution of human mobility induces the super-diffusivity of travel, but up to 30 min to 1 h due to the boundary effect of people's daily movement, which is caused by the tendency of people to move within a predefined (also confined) area of daily activities. These tendencies are not captured in common mobility models such as random way point (RWP). To evaluate the impact of these tendencies on the performance of mobile networks, we construct a simple truncated Levy walk mobility (TLW) model that emulates the statistical features observed in our analysis and under which we measure the performance of routing protocols in delay-tolerant networks (DTNs) and mobile ad hoc networks (MANETs). The results indicate the following. Higher diffusivity induces shorter intercontact times in DTN and shorter path durations with higher success probability in MANET. The diffusivity of TLW is in between those of RWP and Brownian motion (BM). Therefore, the routing performance under RWP as commonly used in mobile network studies and tends to be overestimated for DTNs and underestimated for MANETs compared to the performance under TLW.

The IEEE 802.11 standard supports multiple PHY rates. However, the IEEE 802.11 DCF in a multiple-rate environment may cause a performance anomaly. There have been many studies about the performance analysis and improvement of single- and multi-rate WLAN systems. However, there were a few studies about a generalized analysis on throughput and channel utilization for successful transmissions in multi-rate WLAN systems with different frame parameters and channel errors. In particular, the performance anomaly problem of the multi-rate WLANs still needs to be solved. We propose a more generalized mathematical model for each station with a different data transmission time and mathematically analyze the throughput and channel utilization for successful transmission in error-prone multi-rate WLANs. Moreover, we propose a contention window size adjustment scheme and a payload adjustment scheme to resolve the well-known performance anomaly problem in multi-rate WLANs by achieving temporal fairness. Numerical results show that the proposed scheme is very effective in achieving temporal fairness.

Simulating human mobility is important in mobile networks because many mobile devices are either attached to or controlled by humans and it is very hard to deploy real mobile networks whose size is controllably scalable for performance evaluation. Lately various measurement studies of human walk traces have discovered several significant statistical patterns of human mobility. Namely these include truncated power-law distributions of flights, pause-times and inter-contact times, fractal way-points, and heterogeneously defined areas of individual mobility. Unfortunately, none of existing mobility models effectively captures all of these features. This paper presents a new mobility model called SLAW (self-similar least action walk) that can produce synthetic walk traces containing all these features. This is by far the first such model. Our performance study using using SLAW generated traces indicates that SLAW is effective in representing social contexts present among people sharing common interests or those in a single community such as university campus, companies and theme parks. The social contexts are typically common gathering places where most people visit during their daily lives such as student unions, dormitory, street malls and restaurants. SLAW expresses the mobility patterns involving these contexts by fractal way points and heavy-tail flights on top of the way points. We verify through simulation that SLAW brings out the unique performance features of various mobile network routing protocols.