Mobility Models. Larissa Marinho Eglem de Oliveira. May 26th CMPE 257 Wireless Networks. (UCSC) May / 50

Transcription

1 Mobility Models Larissa Marinho Eglem de Oliveira CMPE 257 Wireless Networks May 26th 2015 (UCSC) May / 50

2 1 Motivation 2 Mobility Models 3 Extracting a Mobility Model from Real User Traces 4 Self-similar Least Action Walk (SLAW) (UCSC) May / 50

3 Contents 1 Motivation 2 Mobility Models 3 Extracting a Mobility Model from Real User Traces 4 Self-similar Least Action Walk (SLAW) (UCSC) May / 50

4 Motivation Why Mobility Models? Wireless nodes are carried by humans and hence inherit human features in what concerns movement. Wireless Community Networks: park, home, city, campus; Hotspots: areas covered by one or more APs; Roaming: users tend to move from one hotspot to another; Predict Movement Patterns: handover optimization; network planning and dimensioning; location updating and paging; path/route computation. (UCSC) May / 50

5 Motivation Why Traces? Traces are essential to understand node mobility behavior under different conditions and hence are key to benchmark analytical models for movement of nodes, i.e, mobility models. Most mobility models are analised from traces based on Bayesian Models; Best mobility models should be able to capture: social behavior; time and space correlation. (UCSC) May / 50

6 Classification Individual Mobility Models: attempts to mimic the mobility pattern behavior of a specific node and from a temporal timeframe; Group Mobility Models: takes into account the need to access a node s perspective towards its neighbors; Synthetic analytical models: Brownian Motion, Random Walk, Levy Patterns; Trace-based: WLAN and GPS traces. (UCSC) May / 50

7 General Characteristics Position; Speed; Direction; Accelaration; Pause Time; Inter-contact time. (UCSC) May / 50

8 Contents 1 Motivation 2 Mobility Models 3 Extracting a Mobility Model from Real User Traces 4 Self-similar Least Action Walk (SLAW) (UCSC) May / 50

9 Individual Models - Synthetic Random Walk: Chooses direction and speed randomly. No pause time; Probabilistic Random Walk: Uses a probability transition matrix to determine a node s next position. Speed is variable. Node stays in a position according to transition matrix; Random Waypoint (RWP): Extension of random walk, however adds pause time between changes of direction and speed. Pause time, direction and speed are randomly chosen from a Uniform distribution; (UCSC) May / 50

10 Individual Models - Trace-based Model-T: based on traces of user s AP registration patterns on a campus. User registration is asymmetric in space distributions, which are hierarchical; A Simple Human Mobility Model: first attempt on trying to identify social behavior; based on traces of a campus indoor. Mobile nodes travel only in straight lines with pre-configured speed. Groups of mobiles nodes are divided according to their common interest. (UCSC) May / 50

11 Summary Most of individual models based on the notion that movement is random; Mobility traces show that nodes on wireless networks do not exhibit random behavior; (UCSC) May / 50

12 Group Models - Synthetic Reference Point Group Model (RPGM): Every group has a Reference Point (RP) and each individual node has a personal space where it behaves randomly. The movement of the RP characterizes the group movement: uses RWP for RP and nodes mobility; military applications; RPs are usually mobile nodes, but could be considered as APs. Nomadic Mobility Model: captures mobility of nomadic groups that move from time to time. Based on RPGM; military operations, as well as robotics applied to agriculture. (UCSC) May / 50

13 Group Models - Hybrid Community Based Mobility Model (CMM): nodes are grouped into communities and move towards another nodes or communities according to the strengh of social associations between nodes: Social associations defined based on likelihood of geographic co-location; People that share strong social ties tend to move to similar places; Communities are defined by using a clustering algorithm; Next direction chosen proportional to the attractiveness of each community Home Cell Community Mobility Model (HCMM): based on CMM, but considers not only attraction torwards other nodes, but also attraction torwards locations. A second work furthers the model taking into account traces. Self-similar Least Action Walk (SLAW): uses fractal waypoints behavior to model attraction by popular places. (UCSC) May / 50

14 Summary Trend: evolution towards social mobility models; Node movement in wireless networks is not random, instead, it exhibits specific characteristics; CMM takes into account social behavior, however does not address pause time, or accelaration. Target of movement is always a node in a cluster, never a location; HCMM adds attraction torwards a location, but does no model pause time; SLAW captures essential properties of human behavior, such as pause time, attraction to popular places and preference to walk around their own confined area. (UCSC) May / 50

15 Design Goals Time and Spatial correlation: capable of determining nodes movement with a relation in time and space; Node pattern: type of movement a node has in its individual space; Obstacle modeling: capable of capturing collisions between nodes; Social behavior: attraction areas, communities, hotspots. (UCSC) May / 50

16 Applicability Handover optimization; Resource management; Network optimization: routing, context-aware applications, opportunistic networks; Simulation. (UCSC) May / 50

17 Contents 1 Motivation 2 Mobility Models 3 Extracting a Mobility Model from Real User Traces 4 Self-similar Least Action Walk (SLAW) (UCSC) May / 50

18 Collecting User Traces Traces extracted from always-on WiFi devices from a 13-month data set (VoIP traces); Direction of movement closely reflects the direction of roads and walkways; Focus on movement among hotspots; Speed and pause time follow a log-normal distribution; Synthetic traces derived from the mobility model match real traces with a median relative error of 17%; Syslog traces parsed to obtain mobility traces: list locations of APs with which each device associated; for each user, the events were extracted for each day; working days from 8am to 6pm; workday traces divided into mobile and stationary; if the distance between any two APs that a user visits in a workday is greater or equal to 100m, the trace is considered mobile if user off for more than 30min: multiple walks mobile traces generate 3838 walks and 3876 stationary traces generates 4006 walks; (UCSC) May / 50

19 Processing Trace Algorithm From the mobility traces, extract users location or user tracks; Estimate pause duration; Users generally do not stay close to an AP; Mobile devices do not necessarily associate with the closest AP; Different mobile devices have different policies to changing associations (UCSC) May / 50

20 Estimating User Location Triangle Centroid: uses location of past three AP associations as the vertice of the triangle; location estimate at every association message Time-based centroid: every p seconds, update the user s location with associations that happened during the past q seconds. n is the number of associations within the past p seconds. (UCSC) May / 50

21 Kalman Filter: is a recursive data processing algorithm that produces optimal estimates. Infers parametes of interest from indirect, innacurate and uncertain observations. If all noise is Gaussian, the Kalman filter minimizes the mean square error of the estimated parameters: where x k is the system model, z k is the measumerent (UCSC) May / 50

22 Validation 4 walks with GPS tracker, Voicera VoIP communicators and Cisco VoIP phones; Kalman Parameters: covariance matrix for wk and v k : assume that the variances are independent of each other; values of w k set to 1; assume movement in x and y directions are likely symmetric, therefore errors in directions x and y are the same, so only one variable for v 2. v 2 is empirically chosen as 25; (UCSC) May / 50

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24 Different types of devices have different association patterns. Vocera communicators agressively associated with many APs, whereas CISCO phones tended to stay with a single AP for a longer time. Kalman Filter offers the best common fit for both devices (UCSC) May / 50

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26 Extracting Pause Time Time between two associations divided between travel time and pause time; Pause duration is estimated based on users speed; Assuming users are pedestrians, if s i = [min, 10ms], user did not pause at l i ; where s i is the user s speed, d i is the distance from location l i+1 l i and e i = t i+1 t i (UCSC) May / 50

27 Shorter e i leads to higher speeds, however shorter e i are due to aggressive associations in search for better signal reception. Speed after pause time: (UCSC) May / 50

28 Extracting Hotspots Regions First approach: divide the area into fixed-regions or grid. The question is how to choose the size of the grid. Too small may overlook the hotspots, making it too big may create an oversized hotspot; Chosen approach: a 2-D Gaussian distribution to each pause location, weighted by duration of pause, and then sum up the distribution. At each pause location, the 2-D Gaussian distribution creates a small mountain, uniformly distributed about its vertical axis: to select the appropriate Gaussian distribution, the standard deviation should reflect the confidence of the user s location and the agressiveness in aggregation pauses. σ = 20m. (UCSC) May / 50

29 Mobility Characteristics Mobile Walks: Kalman Filter (pause time estimator) pause time; speed; direction; start and end time. Stationary Walks: Triangle Centroid (location estimator) duration of stay; start and end time. (UCSC) May / 50

30 Mobile Set Pause time and Speed: using MLE estimation, clustered pauses fit a log-normal distribution, so does speed. (UCSC) May / 50

31 Direction of Movement: manual comparison with a map of Darthmouth, shows that direction of larger peaks corresponds to direction of popular roads; symmetry around 180 degrees; people in a road move in both directions. Start/End Times of a workday: exponential distributions; Hotspots: gym, restaurant, engineering building, CS department, office of network administration and library. (UCSC) May / 50

32 Stationary Set Duration of a walk given by the difference between the time when the first and last messages of that walk were recorded. If only one message, duration is zero; (UCSC) May / 50

33 User s location computed using the triangle centroid. Gaussian distribution for each stationary location * gym and restaurant not popular Start/End Times follow a Uniform distribution. (UCSC) May / 50

34 Characterizing Hotspots hotspots defined using a Gaussian distribution: the area outside hotspots become the cold region; threshold defined to determine individual hotspots: (UCSC) May / 50

35 Hotspots and its pause time distributions: Movement between regions: nxn transition matrix where n 2 is the number of hotspots. The remaining two columns are the cold region and the off state; cold regions are treated as waypoints (l i ). the waypoint matrix is a (n 1)x(n 1) matrix that consists of the average number of waypoints when users moved between two regions. (UCSC) May / 50

36 Modeling Mobility Stationary set: a stationary user enters the network at a time from the start time distribution at the location from the initial location map. It then stays at the location for the duration chosen from the duration-of-stay distribution; Mobile set: a mobile user enters the network at a time selected from the start time distribution at a region selected from the initial region distribution. The user s next destination is then chosen based on the probabilities in the region transition matrix. The number of waypoints visited on the way to the destination is based on the waypoint matrix; Gaussian distribution with the mean based on this matrix to choose the number of waypoints, k, for each move. The speed of movement is chosen from the overall speed distribution. Once a user has reached the destination, it pauses for a period chosen from the pause time distribution for that particular region. When the pause time elapses, the next destination is chosen using the region transition matrix. (UCSC) May / 50

37 Validation Number of visitors within a given region in each hour of a workday (UCSC) May / 50

38 Distribution matches for most of the hotspots, but the first; Model does not capture the large peek during lunch time; Proposed model only takes into account variations that occur within the start and end times, but does not consider variations throughout the day; To consider variations within the day, it would be necessary to have previous knowledge of hotspots. (UCSC) May / 50

39 Contents 1 Motivation 2 Mobility Models 3 Extracting a Mobility Model from Real User Traces 4 Self-similar Least Action Walk (SLAW) (UCSC) May / 50

40 Concepts Least Action Principal: all objects (nodes) move in the direction of minimizing their discomfort, in this case, traveled distance; Self-similarity Property: the features of a given set of points hold independently of the spatial or time scale of the observation. Human destinations tend to form hotspots in the region of movement, and hotspots can clearly be observed independent of the spatial granularity of the observation. (UCSC) May / 50

41 Properties F1 - Truncated power-law flights and pause times: humans flights are straight line trips without change of direction or pause; F2 - Heterogeneously bounded mobility areas: people move mostly within their confined areas of mobility and different people may have widely different mobility areas; F3 - Truncated power-law inter-contact times (ICTs): time elapsed between two sucessive contacts of the same two persons; F4 - Fractal waypoints: people are always more attracted to more popular places. fractal: a natural phenomenon or mathematical set that exhibis a repeating pattern that displays at every scale. (UCSC) May / 50

42 SLAW produces Synthetic traces containing all the previous properties; Uses GPS traces of human walks from students in a University campus and turists in a park; Simple as RWP: only need as parameters the size of the walk area, number of walkers and the Hurst value to generate fractal waypoints; Does not depend on real traces. (UCSC) May / 50

43 Overview 1 Generates fractal waypoints (F4) using a Brownian Motion Generator over a 2-D image; 2 Generates power-law flights (F1) on top of fractal waypoints: proves analytically that fractal points induce power-law gaps (inter-spacing among neighboring fractal points) 3 Least Action Trip Planning Algorithm (LATP): people plan their trips over known destinations in a gap-preserving manner, where they visit nearby destinations first before visiting farther destinations. LATP satisfies (F4) and (F1) 4 Individual Walker Model satisfies (F2) and (F3) (UCSC) May / 50

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45 LAPT Next waypoint is selected based on a weight function of 1 d α, where d is the distance between the current waypoint to an unvisited waypoint and α is the constant deciding the distance weight. If α = 0, randomly chooses next waypoint, if α =, chooses the closest waypoint. (UCSC) May / 50

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47 Individual Walk Model 1 Restricts the mobility of each walker to a predicted sub-section of the total area; 2 Selects a subset of fractal waypoint clusters and restrict the movement of each walker to its own designated set of clusters; 3 To add randomness, it allows walkers to move out of their predefined walkabout areas occasionally with some controlled probability; 4 The walker model ensures (F2) and combined with LAPT and fractal waypoints it generates truncated power-law ICTs (F3). (UCSC) May / 50

48 Performance Analysis (UCSC) May / 50

49 Performance Analysis (UCSC) May / 50

50 Performance Analysis - DTN Routing (UCSC) May / 50