2. A Comparative Cost Analysis of Degradable Location Management Algorithms in Wireless Networks Ing-Ray Chen and Baoshan Gu Presented by: Hongqiang Yang, Jianghui Ying Northern Virginia Center, Virginia Tech

3. Agenda Architecture of Paper: – Introduction – Notion of Degradable Location Management Algorithm – Examples of Degradable Location Management Algorithm – Two-tier Hierarchical Framework – Comparison – Application in the analysis of service handoffs – Summary

4. Introduction Problem  A class of degradable location management algorithms in Personal Communication Service network for tracking mobile user in two-tier HLR-VLR structure  IS-41, FRA, PLA, LAA  Which is better?

5. Introduction Objective – Develop a uniform framework to provide a cost analysis of location update and search operations for a class of degradable location management algorithms in personal communication service (PCS) networks

6. Introduction Method--Two level hierarchical modeling framework  High-level model Calculate the costs incurred to the PCS network:  Location-update operations  Call-delivery operations  Low-level model A stochastic model to estimate the values of high-level model parameters

7. Introduction Location Management Scheme – Aimed to minimize the total cost  Location Update Occurs when a mobile user moves to a new location  Call delivery Occurs when there is a call for mobile user and the network must deliver the call.

8. Introduction Workload condition is indicated by Call-to- Mobility ratio (CMR) – CMR is high: Location Cache Scheme is effective – CMR is low: FRA, PLA, LAA are effective

9. Degradable Location Management No assumption regarding the structure of the PCS network Conceptually, HLR is in high level and VLR is in low level. Maybe some network switches connecting the HLR to VLRs in the mobile network

10. Degradable Location Management IS41: – Service area divided into registration areas each corresponding to a VLR User moves to a new registration area Send the registration information to the new VLR Update information

11. A hierarchical PCS network HLR PSTN RSTP LSTP VLR … … … Home Location Register Public Switched Telephone Network Regional Signaling Transfer Point Local Signaling Transfer Point Visitor Location Register

12. Degradable Location Management The state of a location management algorithm: depends on the extent to which the location information has been degraded since the last location update operation was performed to the HLR – Strong – Weak

13. Degradable Location Management Strong State: – means the HLR store the current information of the mobile user in its own database – HLR can find the mobile user directly Weak State: – means the current information of the mobile user is not in the HLR – HLR must consult location database stored elsewhere to find the mobile user

14. Degradable Location Management The spectrum of degradable location algorithms – encompasses all existing location management algorithm – differ on how fast and in what way the system’s state degrades over time as the user moves across VLR boundaries

15. Degradable Location Management The spectrum of degradable location algorithm IS-41 LAA(2) FRA(2) PLA(2) LAA(3) FRA(4) PLA(3) Paging

16. Degradable Location Management IS-41 User moves across VLR boundary Send information to new VLR Update information in HLR

17. Degradable Location Management FRA(K) User moves across VLR boundary – Length of link of pointers < K: Set up a pointer to the two involved VLRs – Length of link of pointers = K: Update information in HLR Degrades over time as more and more moves

18. Degradable Location Management PLA(n) – HLR records a VLR as the agent – The agent covers all VLRs within a distance n from the agent( local region) – No update at all with local moving – Update when across local region boundary – Paging starts from the agent Degrades over time since the location of the mobile user becomes fuzzier to the HLR as more and more time has elapsed since the last update performed

19. Degradable Location Management LAA(n) – HLR records a VLR as the local anchor(LA) – The LA covers all VLRs within a distance n from the LA – Update in LA with local moving – Update in HLR when across a regional switch boundary Three steps researching: – HLR -> LA -> VLR

20. Degradable Location Management Performance metric: – The network cost due to location update between two successive calls to a mobile user Paper contribution: – Provides method to quantifying the location update cost for a given location management algorithm with respect to the basic scheme – Classify the algorithm

21. The ratio of the average communication cost between two VLRs to the average communication cost between the HLR and a VLR is 0.3

22. Degradable Location Management Classify mobile users into priority classes based on their quality of service(QoS) requirements Separate QoS classes are being served by separate location management schemes Simplify the per-user-based location management to the per-class-based location management

23. Modeling Degradable Location Management Algorithm Description of two-level model Examples of Degradable location management algorithm – Description of algorithm – Low-level model

24. Modeling Degradable Location Management Algorithm Two-level model – High-level model: cost model Update cost X update Query cost X search X cost = X update *  / + X search – Low-level model Aimed to provide the parameters for high-level model – Low-level model Parameterize equation in high-level model Define parameters in our model

25. Per-mobile-user parameters  The rate at which the mobile user moves across VLR boundaries The rate at which the mobile user is being called CMR / , the call-to-mobility ratio of the mobile user Mobile network parameters TThe average VLR-HLR round-trip communication cost  The average VLR-VLR round-trip communication cost

26. Basic HLR/VLR A mobile user is permanently registered under a location register(HLR) Mobile user enters a new VLR area Reports to VLR VLR inform HLR HLR update location information Location Update Cost = 1

27. Paging and Location Algorithm(PLA) Agent: the VLR performs the last update operation to the HLR HLR update location information only when the distance between the agent and the current VLR is great than or equal to a predefined distance value n

28. R0 R1 R2 R1 R2 SDF partitioning under the hexagonal model

29. PSTN HLR F A Local Movement: within the 2-Distance region Update Action: None Regional Movement: Outside of 2-Distance Region Action: Update the HLR PLA Algorithm E D C B

30. Paging and Location Algorithm(PLA) Modeling parameters – n: specify the (n-1)-distance region within a user causes no update cost –  i : the mobility rate of the mobile user moving from ring i to ring i + 1 –  i : the mobility rate of the mobile user moving from ring i + 1 to ring i –  r : the execution rate to perform a location update to the HLR –  I : the execution rate to locate the mobile user currently located in ring I – P (i,j) :The probability that the system is in a particular state in equilibrium

31. Paging and Location Algorithm(PLA) Assuming random move The probability of the mobile user moving from ring i to i + 1, i >= 0 (2i + 1) / 6i, if i >= 1, 1, if i = 0. The probability of the mobile user moving from ring i + 1 to i, i >= 0 (2 (i + 1) - 1 )/ (6(i +1)), if i >= 0,

32. Paging and Location Algorithm(PLA) The mobility rate of the mobile user moving from ring i to ring i + 1 (2i + 1)  / 6i, if i >= 1,  i = , if i = 0. The mobility rate of the mobile user moving from ring i + 1 to ring i  i = (2i +1)  /( 6* (i + 1)), i >= 0

33. Paging and Location Algorithm(PLA) The execution rate to perform a location update from a new VLR agent to the HLR  r = 1 / T

34. Paging and Location Algorithm(PLA) The time to locate the mobile user in ring i – From HLR to agent – From the agent to the current VLR(in ring i) – From the current VLR back to the HLR The execution rate to locate the mobile user in ring i  i = 1/(T + 0.5*(3i 2 + 3i) *  ) Query one-half of the VLRs in the i-distance region

35. Paging and Location Algorithm(PLA) Low-level Makov model – State represented by (a, b) a: 0, IDLE 1, CALLED b: the current distance between the mobile user and the local agent

36. Markov Model for PLA 0,00,10,20,n-10,n-1* 1,01,1 1,21,n-1 1,n-1* rr 00 11  n-1 00 11 22 00 22 00 11 22  n-1 00 11 22 11 22  n-1 rr

37. Average cost for location update operation Average cost for location search operation Average total cost: Paging and Location Algorithm(PLA)

38. Forwarding and Resetting Algorithm(FRA) HLR only points to the VLR at the beginning of the forwarding chain User moves across VLR boundary – Length of link of pointers < K: Set up a pointer to the two involved VLRs – Length of link of pointers = K: Update information in HLR

39. PSTN HLR F A Local Movement: length of the forwarding chain is less than 5 Update Action: update the Forwarding Pointer between Two involved VLRs Regional Movement: Chain Length = 5 Action: Update the HLR FRA Algorithm: K=5 E D C B

40. Forwarding and Resetting Algorithm(FRA) Two additional behaviors in modified Markov Model under FRA – The forwarding chain will be reset after a location query operation is performed – When the mobile user moves back to the previously visited VLR in the chain, the length of the forwarding chain is reduced by 1 and no pointer deletion operation is required between Obsolete pointers will be purged automatically after a period of time much greater than the average reset period

41. Forwarding and Resetting Algorithm(FRA) Looping behavior is accounted in Markov model Assume : when the mobile user moves across a VLR, the forwarding pointer information will be updated before it crosses another VLR – Imply that the dwell time of mobile user in a VLR is much greater than the forwarding pointer update operation time

42. Forwarding and Resetting Algorithm(FRA) Model Parameters – k : the length of the forwarding chain at which a reset operation is performed –  n : the mobility rate of the mobile user moving to a new VLR. –  b : the mobility rate of the mobile user moving to the previous VLR –  r : the execution rate to reset a forwarding chain, i.e. to update the HLR –  f : the execution rate to set-up or travel a pointer between two VLRs –  i : 0<= i <=k-1, the execution rate to locate the mobile when the length of forwarding pointer is i.

43. Forwarding and Resetting Algorithm(FRA) The mobility rate of the mobile user moving to a new VLR  n = (5/6) *  The mobility rate of the mobile user moving to the previous VLR  b = (1/6) * 

44. Forwarding and Resetting Algorithm(FRA) The execution rate to reset a forwarding chain, i.e. to update the HLR  r = 1/T The execution rate to set-up a forwarding chain, i.e. to update the HLR  f = 1/  The execution rate to locate the mobile when the length of forwarding pointer is i( 0<= i <= k-1)  i = 1/(T + i *  )

45. Forwarding and Resetting Algorithm(FRA) Low-level Markov Model – States represented by (s 1, s 2 ) s 1 = 0, standing for IDLE 1, standing for Called s 2 indicates the current length of the forwarding chain – States followed by symbol ‘*’ means the mobile user just enters a new VLR but the forwarding pointer operation is not yet performed

46. Markov model for the PCS network under FRA 0,00,1*0,10,2*0,k-10,k-1* 1,01,1*1,11,2*1,k-11,k-1* 00 11  k-1 bb bb bb bb  ff nn ff  ff nn ff nn rr nn rr

47. Forwarding and Resetting Algorithm(FRA) P (i, j) : represent the probability that the system is in state (i, j) fra update : average cost to perform a location update operation

48. Forwarding and Resetting Algorithm(FRA) fra search : average cost to perform a location search operation fra cost : the average total cost

49. Local Anchor Algorithm(LAA) Basic idea  Location Registration operations should be as localized as possible so as to reduce the number of registration messages to the HLR. Local Anchor(LA)  The VLR which performs the last registration operation with the HLR is called the LA of the mobile user.

50. Local Anchor Algorithm(LAA) LA’s Coverage NM (VLR in ring) Coverage 111 267 31219 ……… n6(n-1)3n 2 – 3n + 1

51. Local Anchor Algorithm(LAA) Algorithm  Movement: Cross a VLR boundary but within the local region Operation: New VLR informs the LA without informing the HLR  Movement: regional move Operation: New VLR informs the HLR and also becomes the new LA of the mobile user.

52. PSTN HLR F Local Movement: within the 3-Layer Area Update Action: Only Update the LA(VLR A) Regional Movement: Outside of a 3-Layer Area Action: Update the HLR LAA Algorithm E D C B A

53. Modeling a PCS network operating under LAA Parameters n: specify the n-layer VLR region which covers 3n 2 – 3n + 1 VLRs P 1 :the probability of the mobile user moving under the same network switch P 1 = 6*(3n 2 – 3n + 2) – (12n - 6)/6*(3n 2 – 3n + 1) = (3n 2 – 5n + 2) /(3n 2 – 3n + 1)

54. Modeling a PCS network operating under LAA Parameters σ 1 :the mobility rate of the mobile user moving under the same network switch i.e. σ 1 = P 1 σ = (3n 2 – 5n + 2) /(3n 2 – 3n + 1)σ σ r :the mobility rate of the mobile user crossing a network switch boundary i.e. σ r = (1- P 1 )σ = (2n - 1) /(3n 2 – 3n + 1)σ

55. Modeling a PCS network operating under LAA Parameters μ q :the search execution rate when the mobile user is located in the agent’s area μ q = 1/T μ a :the search execution rate when the mobile user is not located in the agent’s area μ q = 1/(T + τ)

56. Modeling a PCS network operating under LAA Parameters δ 1 :the execution rate to update the agent, i.e. to set up a pointer between the new VLP and the agent δ 1 = 1/ τ δ:the execution rate to update the HLR δ = 1/ T

57. Modeling a PCS network operating under LAA Markov model  state representation (a, b, c) a: whether the mobile user is in the state of being called 0 ---- idle 1---- busy b: whether the mobile user makes a move 0 ---- not move 1---- local move 2 ---- regional move c: whether the agent currently covers the mobile user 0 ---- yes 1 ---- no

58. 0,0,0 0,1,10,0,10,1,0 1,0,0 1,1,11,0,11,1,0 0,2,1 1,2,1 λ λλλμgμg μaμa σrσr σrσr σrσr σrσr δ δ σ1σ1 σ1σ1 σ1σ1 σ1σ1 δ1δ1 δ1δ1 δ1δ1 δ1δ1 λ  (0, i, j)  (1, i, j) when a call comes, the transition rate is λ  (1, 0, 0)  (0, 0, 0) with the transition rate of μ q (1, 0, 1)  (0, 0, 0) with the transition rate of μ a  Regional move (i, 0, j)  (i, 2, 1) with the transition rate of σ r (i, 2, 1)  (i, 0, 0) with the transition rate δ  Local move (i, 0, j)  (i, 1, j) with the transition rate of σ l (i, 1, j)  (i, 0, 1) with the transition rate δ l

59. Modeling a PCS network operating under LAA Markov model  Laa update

60. Modeling a PCS network operating under LAA Markov model  Laa search  Laa cost

61. Analysis and Comparison Using two two-level hierarchical modeling Compare PLA, FRA, LAA with basic HLR/VLR IS-41 algorithm VLR-to-VLR/VLR-to-HLR = 0.3 T = 1 τ = 0.3  IS-41 where IS-41 update = T IS-41 search = T

62.  Comparison of PLA under different n-distance values  Performance n=3 is better than n=2 when CMR is small  Larger n means local agent can cover larger area, thus a smaller probability to cross a regional boundary. Consequently the number of update operations to HLR is reduced as n increase.  After CMR exceed a threshold, n=2 is better than n=3  As CMR increase, the larger location query cost attributed by the larger cover area starts to dominate the reduced location update cost. threshold

63.  Comparison of FRA under different k values  Performance k=4 is better than k=2 when CMR is small  Location update cost dominates the location query cost, so a longer chain is favored since it reduces the location update cost.  After CMR exceed a threshold, k=2 is better than k=3  As CMR increase, higher cost associated with location update operations which happen frequently starts to offset the benefit of lower update operation cost. threshold

64.  Comparison of LAA under different distance values  Performance n=3 is better than n=2 when CMR is small  Larger n means local agent can cover larger area, thus a smaller probability to cross a regional boundary. Consequently the number of update operations to HLR is reduced as n increase.  After CMR exceed a threshold, n=2 is better than n=3  As CMR increase, the larger location query cost attributed by the larger cover area starts to dominate the reduced location update cost. threshold

65. Comparison of PLA, FRA and LAA head to head  Comparison of location update cost only  Provide the basis for classifying existing degradable location management algorithms based on the update cost per move relative to IS-41 for a wide range of CMR.  IS-41 keeps the system in Strong State all the time, LAA(2) is next to it in terms of maintaining the location information in a good state.  PLA(3) incurs the least amount of update overhead, since under PLA(3) the possibility of local movement is high. PLA(3) least LAA(2) highest

66. Comparison of PLA, FRA and LAA head to head  Comparison of the search cost only  PLA(3) incurs the most overhead to deliver a call

67. Comparison of the search cost only Comparison of location update cost only LAA 2 FRA 2 PLA 2 LAA 3 FRA 4 PLA 3 PLA 2 FRA 4 LAA 3 FRA 2 LAA 2

68.  Comparison of total communication cost  PLA(3) is the best when CMR is 0.1  FRA(4) is the best when CMR>0.3  PLA(2) is the worst when CMR is small  PLA(3) is the worst when CMR is large

69.  Comparison of total communication cost for multiple users  All users are served under a single algorithm against the case when individual users are served by their respective per- user best algorithms.  As the number of users increases, the total cost difference increases because of cumulative effect.  Under single algorithm, FRA(4) is the best.  Per-user selective strategy outperform all single- algorithm cases.

70. Service Handoff What is Service Handoff The process of transferring or migrating the service of a client from one server to another in client-server applications Difference between location handoff and service handoff  transfer of context information  Static: user profile, authentication data  Dynamic: files opened, locks, stamps

71. Service Handoff Analysis of Service Handoff  Using LAA scheme  Assumptions  A service area corresponds to a network switch area, when a user moves across a switch boundary a service handoff will be triggered.  Context transfer communication cost C s  Mobile user communicates with the serer by means of operations  The location and service networks are integrated

72. Service Handoff  Cost factors  The communication cost between the server and the LA, the cost is τ  The communication cost between the LA and the VLR in which the mobile user currently resides if the LA is not the current VLR, which is also τ  The communication cost of migrating the service context from the old server to the new server if during the time of access, the mobile user happens to cross a service boundary, the cost of which is C s

73. Service Handoff Recall Markov model of LAA  state representation (a, b, c) a: whether the mobile user is in the state of being called 0 ---- idle 1---- busy b: whether the mobile user makes a move 0 ---- not move 1---- local move 2 ---- regional move c: whether the agent currently covers the mobile user 0 ---- yes 1 ---- no

74. Service Handoff Average cost per service operation  Reward of C s +τ to states in which component b is 2, i.e. (0, 2, 1) and (1, 2, 1)  Reward of τ to states in which c is 0, i.e. (0,0,0) (1,0,0) (0,1,0) and (1,1,0)  Reward of 2τ to states in which c is 1 but b is not equal to 2, i.e. (0,0,1) (1,0,1) (0,1,1) and (1,1,1)

75. Crossover Point Cost per service operation in LAA under different CMR and C s values τ =1  When Cs is relatively low, LAA(2) is better especially at low CMR value.  Since when CMR when CMR is low and the probability of crossing switch boundary is low, so the call ratio must be low, therefore the contribution of context transfer cost is low for both schemes. There are more VLRs covered when n=3, the contribution of the 2rd cost factor is higher in LAA with n=3.  Cross point shift left as CMR increases.  As C s increases, LAA(3) will be favored over LAA(2) for smaller probability of crossing boundary  As CMR increases, the advantage become manifest even in small C s.

76. Summary  Discussed the notion of degradable location management algorithm used in PCS for locating users  Classified existing location management algorithms  Developed methods to obtain the location update cost for location management algorithms  Tested the method by modeling PLA, FRA and LAA and demonstrated the applicability of the modeling method  Showed how the modeling methodology can be applied to support service handoff

77. Conclusion and Future Work Future Work  Introducing a real-time component into the design and deriving conditions under which user location queries can be satisfied in real-time while minimizing the location update cost  Considering users with different priority classes and discovering an optimal way to design location management algorithms so that a global design objective can be best satisfied  Investigating the applicability of the uniform framework developed in this paper to the analysis of tree-based location management algorithms.

78. Thank You!