1. A Mobility Model for Studying Wireless Communication Raymond Greenlaw Armstrong Atlantic State University Savannah, GA, USA Sanpawat Kantabutra Chiang Mai University Chiang Mai, Thailand

2. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 2 Outline Introduction The Mobility Model Definition of the Model A Sample Instance of the Model Problem Definitions Conclusion Acknowledgments References

3. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 3 Introduction Wireless networking is becoming prevalent because of low-cost, ease of installation, scalability, and convenience to users. We consider a model of a mobile network; a wireless network in which the access points themselves may be moving. Such networks are of great importance in supporting relief efforts for natural disasters or for military field exercises.

4. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 4 Outline Introduction The Mobility Model Definition of the Model A Sample Instance of the Model Problem Definitions Conclusion Acknowledgments References

5. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 5 The Mobility Model Goal is to model actual mobile networks. Model needs to be sophisticated enough to model complex real-life situations. Key features need to be abstracted out so the model is feasible to study and apply. After defining the model, a communication protocol is defined to interpret how the model works.

6. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 6 Outline Introduction The Mobility Model Definition of the Model A Sample Instance of the Model Problem Definitions Conclusion Acknowledgments References

7. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 7 Definition of the Model Model operates on a 2-dimensional grid. Model is an 8-tuple (S, D, U, L, R, V, C, O), where 1.Set S = {s 1, s 2, …, s m } is a finite collection of sources, where m N, m is the number of sources. Corresponding to each source s i, for 1 i m, an initial location (x i, y i ) is specified where x i, y i N. 2.Set D = {000, 001, 010, 101, 110} is called the directions and correspond to no movement, east, west, south, and north, respectively.

8. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 8 Definition of the Model Model Definition (continued) 3.Set U = {u 1, u 2,…, u p } is a finite collection of mobile devices, where p N. The set U is called the set of users. The value p is called the number of users. Corresponding to each user u i, for 1 i p, an initial location (x i, y i ) is specified where x i, y i N.

9. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 9 Definition of the Model Model Definition (continued) 4.Let t N. Set L = {l 1, l 2,…, l p } is a finite collection of bit strings, where l i D t for 1 i t. Each group of three bits in l i beginning with the first three defines a step in the given direction for the user u i s movement or no movement at all if the string is 000. The value t is called the duration of the model.

10. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 10 Definition of the Model Model Definition (continued) 5.Let t(i) N for 1 i m. The set R = {r 1, r 2, …, r m } is a finite collection of bit strings, where r i D t(i) for 1 i m. Each group of three bits in r i beginning with the first three defines a step in a given direction for the source s i s movement or no movement at all if the string is 000. The set R is called the random walks of the mobility model.

11. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 11 Definition of the Model Model Definition (continued) 6.Set V = {v 1, v 2, …, v m } is a finite collection of numbers, where v i N. The value v i is the corresponding number of steps from r i per unit time that s i will take. This set is called the velocities. 7.Set C = {c 1, c 2, …, c m } is a finite collection of numbers, where c i N. The value c i is the corresponding diameter of the circular coverage of source s i. This set is called the coverages.

12. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 12 Definition of the Model Model Definition (continued) 8.The set O = {(x 1, y 1, x 2, y 2 ) | x 1, y 1, x 2, y 2 N, x 2 > x 1, and y 2 > y 1 } is a finite collection of rectangles in the plane. The set is called the obstacles.

13. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 13 Definition of the Model Remarks –Sources in S correspond to wireless access points and are broadcasting and receiving signals. –Set D represents the four possible directions for movement in the grid, plus no movement. –Set U represents users with mobile devices. –Set L contains random walks used to model the movement of users. –Set R contains random walks to model the movement of sources.

14. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 14 Definition of the Model Remarks (continued) –To accommodate for different source velocities, the walks in R have different lengths. –Relative speeds of sources are represented by natural numbers contained in set V. –Different sources will broadcast at different signal strengths depending on a variety of factors, available power being the main one.

15. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 15 Definition of the Model Remarks (continued) –Various signal strengths are represented by specifying the diameter of a circle c i for each source indicating where its signal can be received. –This region is its coverage area. –Since buildings and other obstacles may interfere with signal transmission, the model incorporates a set of obstacles O. –For simplicity, only rectangular obstacles are permitted.

16. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 16 Definition of the Model Communication Protocol –Illustrates how the model is interpreted. –Needed so that the model works as intended. –Source are always on. –Users with mobile devices are moving in and out of the range of each other and various sources. –Devices would like to communicate (send and receive messages) with one another.

17. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 17 Definition of the Model Communication Protocol (continued) –Let k > 2 and k N. –Any two sources with overlapping- coverage areas may communicate with each other in full-duplex fashion as long as the intersection of their overlapping- coverage area is not completely contained inside obstacles. Those two sources are currently in range. –A series s 1, s 2, …, s k of sources are currently in range if s i and s i+1 are currently in range for 1 i k-1.

18. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 18 Definition of the Model Communication Protocol (continued) –Two mobile devices cannot communicate directly with one another. –A mobile device D 1 always communicates with another mobile device D 2 through a source or series of sources as defined on the following slides.

19. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 19 Definition of the Model Communication Protocol (continued) –The mobile devices D 1 at location (x 1, y 1 ) and D 2 at location (x 2, y 2 ) communicate through a single source s located at (x 3, y 3 ) if at a given instance in time the lines between points (x 1, y 1 ) and (x 3, y 3 ), and points (x 2, y 2 ) and (x 3, y 3 ) are within the area of coverage of s, and do not intersect with any obstacle from O.

20. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 20 Definition of the Model Communication Protocol (continued) –The mobile devices D 1 at location (x 1, y 1 ) and D 2 at location (x 2, y 2 ) communicate through a series of sources s 1 at location (a 1, b 1 ), s 2 at location (a 2, b 2 ), …, and s k at location (a k, b k ) that are currently in range if the line between points (x 1, y 1 ) and (a 1, b 1 ) is inside s 1 s coverage area and does not intersect any obstacle from O and the line between points (x 2, y 2 ) and (a k, b k ) is inside s k s coverage area and does not intersect any obstacle from O.

21. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 21 Definition of the Model Communication Protocol (continued) –Mobility of the sources and the users are built into this model. –Reflects the situation in a real mobile network where access points and users are moving around. –For simplicity, we implicitly assumed that all users are moving at the same rate of speed, whereas we explicitly modeled sources moving at different velocities.

22. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 22 Definition of the Model Communication Protocol (continued) –Model can handle users moving at different rates of speed by having some users remain stationary while others are moving at each step.

23. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 23 Outline Introduction The Mobility Model Definition of the Model A Sample Instance of the Model Problem Definitions Conclusion Acknowledgments References

24. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 24 A Sample Instance of the Model Let S = {s 1, s 2, s 3, s 4 } with initial locations (2, 5), (5, 5), (6, 4), and (5, 2) respectively. Let D = {000, 001, 010, 101, 110}. Let U = {u 1, u 2, u 3 } with initial location (3, 4), (2, 1), and (6, 2), respectively. Let t = 3 and L = {l 1, l 2, l 3 }, where l i = (000, 000, 000) for 1 i 3.

25. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 25 A Sample Instance of the Model Let R = {r 1, r 2, r 3, r 4 }. For clarity, the figure only shows r 1 = (101, 001, 101) and omits other r i s, which we assume are all (000, 000, 000) except r 2 which is twice as long. Let V = {1, 2, 1, 1}. Let C = {2, 2, 2, 4}. Let O = {(2, 1, 4, 2)}.

26. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 26 A Sample Instance of the Model Three stationary users. Four sources. One obstacle. s 1-3 have coverage of 2, s 4 has coverage of 4. s 1 moves south, east, and south with a velocity of v 1 = 1, or one step per unit of time.

27. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 27 A Sample Instance of the Model Initially, s 2 and s 3 are currently in range, s 2, s 3, and s 4 are a series of sources currently in range, and sources s 1 and s 2 are not currently in range. Initially, users u 1 and u 3 cannot communicate; after three steps, u 1 can communicate with u 3 through the series of sources s 1 and s 4.

28. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 28 Outline Introduction The Mobility Model Definition of the Model A Sample Instance of the Model Problem Definitions Conclusion Acknowledgments References

29. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 29 Problem Definitions User Communication Problem –Instance: Mobility model (S, D, U, L, R, V, C, O), two designated users u a and u b from U, and a time k. –Question: Can users u a and u b communicate at time k?

30. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 30 Problem Definitions Sources Reachability Problem –Instance: Mobility model (S, D, U, L, R, V, C, O), two designated sources s a and s b from S, and a time k. –Question: Are sources s a and s b in range at time k?

31. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 31 Problem Definitions Access Point Location Problem –Instance: Mobility model (S, D, U, L, R, V, C, O), two designated users u a and u b from U, an access point diameter d, and a natural number k. –Question: Can users u a and u b communicate if k or fewer access points of diameter d are placed appropriately in the grid?

32. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 32 Problem Definitions Access Point Placement Problem –Instance: Two mobility models M = (S, D, U = {u 1, u 2 }, L, R, V, C, O), and M = (S, D, U = {u 1, u 2 }, L, R, V, C, O). –Question: Can u 1 and u 2 communicate for more steps in model M than they can in model M?

33. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 33 Problem Definitions Obstacle Removal Problem –Instance: Mobility model (S, D, U, L, R, V, C, O), two designated users u a and u b from U, and a natural number k. –Question: Can u a and u b communicate throughout the duration of the model if k or fewer obstacles are removed?

34. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 34 Outline Introduction The Mobility Model Definition of the Model A Sample Instance of the Model Problem Definitions Conclusion Acknowledgments References

35. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 35 Conclusion Description of a mobility model and several interesting decision problems related to the model were presented. It would be interesting to examine the complexity of other related problems. Mobility model itself can be studied further, including extending the model to three dimensions.

36. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 36 Outline Introduction The Mobility Model Definition of the Model A Sample Instance of the Model Problem Definitions Conclusion Acknowledgments References

37. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 37 Acknowledgments Ray is very grateful to the Computer Science Department at Chiang Mai University for its generosity and hospitality during his stay there during the spring semester of 2006. Rays research was supported by a Fulbright Lecturing/Research Fellowship. Ray thanks the Fulbright Commissions of Thailand and the United States.

38. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 38 Outline Introduction The Mobility Model Definition of the Model A Sample Instance of the Model Problem Definitions Conclusion Acknowledgments References

39. Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 39 References Paul Goransson and Raymond Greenlaw, Secure Roaming in 802.11 Networks, Chapter 11, Elsevier, 2007.