1. Registration-Area-based Location Management

2. Location Management: Context Mobility Management: Enables users to support mobile users, allowing them to move, while simultaneously offering them incoming calls, data packets, and other services. Consists of: 1. Location management: tracking mobiles and locating them prior to establishing incoming calls (deliverying pending messages). 2. Handoff management (a.k.a. automatic link transfer): rerouting connections with minimal degradation of QoS.

3. Location Management in Personal Communication Systems (PCS) Keeps track of the location of each user (location tracking) Used in call delivery and in location-dependent services Cells organized in clusters called Registration Areas (RAs) One Location Register for each RA. One Home Location Register for each user. When current LR  HLR then it is called Visitor Location Register (VLR). MH BS MSS

4. Location Management Problem In static networks, a terminal’s network address serves two purposes: 1. End-node identifier 2. Location (access point) identifier Location management keeps mapping between an end-node identifier and its location identifier Basically a directory problem.

5. Registration Area-Based Location Management Registration area == a group of cells; update only when crossing a registration area boundary

6. Location Management: Basic Operations Two primitive operations: 1. Lookup (a.k.a. search/find/paging/locating) operation: is the procedure by which the network finds the location of the mobile. required when a call (message) to a user is placed (to be delivered) 2. Update (a.k.a tracking/move/registration) operation: is the procedure by which the network elements update information about the location of the mobile. required when a user changes its “location” The information gathered during updating/tracking is used during the locating operation

7. Lookup/Update in PCS Lookup: when a call is placed from cell i to user x, the VLR at cell i is queried first, and only if the user is not found there, is x’s HLR contacted. Update: when user x moves from cell i to j, in addition to updating x’s HLR, the entry of x is deleted from VLR at cell i, and a new entry for x is added to the VLR at cell j.

8. Location Management infrastructure-based mobile networks maintains location information of mobile elements Location information is used to properly route data and calls to mobile elements Two basic operations Location information update (set info) Location information search (acquire info) Cost-based description Cost, as a metric of resource use. Load of Location management L=f s c s + f u c u Location Management execution costs Update operations Search operations fufu fsfs cucu cscs rates

9. Location Management: Schemes Several schemes have been developed which are motivated by fundamental trade-off between search operation cost and update operation cost. Schemes which try to minimize one cost tend to increase the other cost Try to optimize the aggregate cost or normalized cost. Categorization: 1. Update Scheme: Static or Dynamic Static update scheme: registration areas Dynamic update scheme: distance/time/movement based strategy 2. Locating Scheme: Static or Dynamic Static location scheme: page all the cells in the network Dynamic location scheme: expanding ring search centered at last reported location of the the user 3. Database Architecture: Flat or Hierarchical

10. Selection of LM Schemes Cost of location updates and lookups Maximum service capacity of each location database = the maximum rate of updates and lookups that each database can service Space restrictions (size of the location database) Type and relative frequency of call to move operations (call-to-mobility ratio (CMR)).

11. Example basic scheme Never-update Zero update cost Will have to search the entire network based on the last-known location Always-update No search cost Distance-based update Time-based update

12. LM improvements Update/search trade-off optimizations Principle of update/search trade-off The more effort spent in updating the information, the less effort needed to seek the information And vice versa Redistribute rates of updates and searches to overall load reduction L = f s c s + f u c u ↓ L = ↓ f s c s + ↑ f u c u Forwarding Pointers, Location Caching etc. Characteristic: optimal point depends on call to mobility ratio (CMR = f s / f u ) Non-trade-off optimizations Do not conform to the update- search trade-off principle Unilateral reduction of one (or more) load components L = f s c s + f u c u ↓ L = ↓ f s c s + f u c u Predictive registration, predictive paging Characteristic: optimal point depends on knowledge of the terminal mobility and/or call model.

13. RA overlapping as LM improvement Can contain more of a mobile terminal’s mobility a Less registrations a,b,c eliminate registrations of “border movements” b Load balancing a Minimize call loss d a Okasaka and Onoe, Proceedings IEEE VTC’91 b Markoulidakis et al., ACM/Baltzer Wireless Networks 1(1):17-29, 1995 d Bejerano and Cidon, Proceedings ACM MobiCom’98 c Wang and Akyildiz, Proceedings ACM MobiCom’00

14. Intra and Inter-RA Handoffs Let mobile m be in cell c and registered in RA k (c  RA k ). move from cell c to cell d. In any configuration, we define two types of handoffs: Intra-RA handoff: if d  RA k. Inter-RA handoff: if d  RA k. after handoff the mobile is registered in RA l such that d  Core(l).

15. Intra- and Inter-RA Calls An intra-RA call is one in which both the caller mobile and the callee mobile are in the same RA. An inter-RA call is one in which both the caller mobile and the callee mobile are in different RA.

16. Non-overlapping & Overlapping RAs Inter-RA hand-off: a user changes cells and RAs Intra-RA hand-off: a user changes cells within an RA. Inter-RA hand-off doesn’t happen as long as the hand- off can be intra-RA. A non-overlapping cell is serviced by one LR. A overlapping cell is serviced by multiple LRs. Reduction of inter-RA hand- offs. No overlapping With overlapping A B C C B A 1 2 3 1 2 3

17. Registration Area Overlapping Advantages: Each RA can provide service to more mobiles within their covered area. Reduces the number of inter-RA handoffs Reduce the load to update mobile’s HLR. Disadvantages: the communication overhead for call-delivery and intra-RA handoff is increased. the increase in overhead depends upon the underlying network topology. If this overhead is ignored then the extreme configuration in which each RA has all the cells in the system becomes the “optimal” configuration.

18. Dynamic resizing of registration areas

19. Proposed Scheme Dynamically adapts the registration areas to the aggregate call and mobility pattern such that 1. the expected update overhead on mobiles decreases 2. the expected overall signaling system load does not exceed a predefined limit.

20. Some Notations Core(k): set of cells directly connected to MSS k. RA k : Registration Area of MSS k. a dynamic set of cells. Configuration C = {RA 1, RA 2,..., RA M }. Reconfiguration: changing of configuration The MSSs periodically reconfigure the system in a distributed manner at fixed interval of time T.

21. Permissible Configurations Property 1: An RA has at least one cell.  no RA is empty i.e. all MSSs are used. G = (V,E): cell adjacency graph V: set of all cells in the system E: (v 1,v 2 )  E iff cells v 1 and v 2 are neighbors. Property 2: The subgraph of G induced by any RA is connected.  no RA has any group of cells disconnected from the remaining cells. Property 3: RA k  Core(k) = Core(k). Initially, RA k = Core(k).

22. Effect on Intra-Handoff and Call Delivery Costs Even though mobiles a and b belong to the same RA, any calls between them would need to go through two MSSs.

23. Dynamically Resizing RAs We need to find optimal configuration (allowing overlapping RAs) i.e. configuration which minimizes load on MSSs. When move and call patterns periodically change, a static scheme may not provide a good solution. Our Approach: Allow RAs to be dynamically adapted. Periodically resize RAs to minimize MSS load: Resizing criterion: load reduction due to lesser number of inter-RA handoffs > increase in load due to more expensive call delivery and intra-RA handoffs. If resizing criterion is ignored then each RA will grow to maximum size.

24. Inclusion and Exclusion Boundary In order to facilitate orderly growth and shrinking of RAs, an MSS only includes and excludes cells from its RAs current boundary. Two types of boundary: 1. Internal Boundary 2. External Boundary MH BS MSS

25. Problem Formulation Assume an initial non-overlapping topology and configuration Assumption for greater applicability Still applicable to topologies that inherently support overlapping Find the inherent impact of a cell inclusion Keep track of cell-to-cell hand-off and call rates, with respect to users of one registration area: – n c ( r, i, s, j ), n u ( r, i, s, j ) Use those rates with the inherent impact of cell inclusion to see if it is beneficial to include a cell Restrictions Cannot exclude cells that initially belonged to the RA Core of RA

26. Inclusion/Exclusion Decision The decision to include or exclude a candidate cell is based on whether the resulting configuration will have a lower expected load on MSS. For a given system configuration A, mobility pattern M, and call C, SystemLoad(A,M,C) is the combined signaling load (in terms of message time complexity) as a result of all the handoffs due to M and call- deliveries due to C: SystemLoad(A,M,C) =  Load(k,M,C). In case of inter_RA handoffs and call-deliveries we spilt the signaling overhead equally between the two MSSs involved.

27. What changes when a cell x is included to an RA r mobility to the cell x from cells of the RA r is now intra-RA mobility mobility from the cell x to the rest of the RA r performed by users already registered in r is now intra-RA mobility. calls to x from cells of r are now intra- RA calls. calls from users of r that are in x to rest of r are now intra-RA calls. Mobility of users in r that move out of cell x into a new RA is now inter-RA mobility. Inter-RA calls of users in r that call from cell x is inter-RA call loading to r. Call the decreasing part of the load Cost inc and the increasing part Cost dec. Now intra-RA hand-offs Here inter-RA hand-offs Now retaining previous RA New inter-RA hand-offs RA border Here Inter-RA calls Now Intra-RA calls New Inter-RA calls Mobile terminals registered in RA Mobile terminals not registered in the RA

28. Finding the signaling costs There are three cases of signaling costs in a quadruplet ( r, i, s, j ) 1. Cells i, j are both core cells 2. One cell is core cell, the other is non-core cell (included) 3. Both cells i, j are non- core Assuming a typical signaling protocol derive the costs for each operation avav acac  vc  vv

29. Algorithm Outline 1. Calculate the cells along the RA periphery – Both inside and outside the periphery 2. Send data requests to those cells 3. Receive data responses from cells – Those values n c ( r, i, s, j ), n u ( r, i, s, j ) 4. For each cell, calculate if it should be included or excluded – Make sure that there are no holes created in the geographical continuity of RA 5. Send inclusion or exclusion cells Calculate border cells Query border cells for statistics Calculate what to include and what to exclude Notify cells of their inclusion or exclusion LR cell s

30. Simulation Discrete Event Simulation using SES Workbench Mobility Models: 1. Highway 2. Urban 1. 1-Dimensional Random Walk 400 cells divided in nine RAs 10,000 MHs call frequency: 1 call per hr to 1 call per 15 min move frequency: 1 handoff per hr to 1 call per 15 min 2. 2-Dimensional Random Walk 50x50 cells organized as 5x5 RA.

31. Highway Model Highway Systems: Overlapping does not help

32. Urban Model Urban systems (localized traffic): Overlapping does help Uses a random walk model transition probability of a MH moving farther from a pre-defined pole of attraction drops progressively with the distance from that pole.

33. Effect of CMR to load with respect to overlapping (1)

34. Effect of CMR to load with respect to overlapping (2)

35. Optimal Registration Sequence Problem

36. Impact of choice on subsequent registrations and impact of knowledge of mobility Without probabilities A mobile terminal can move to either RA 1 or RA 2 Assume that the registration choice is RA 2 However, the mobile terminal moves to the upper end of RA 1, and has to perform one more registration Bad choice, there will be two registrations total With probabilities 0.3 probability of moving to RA 1 0.7 probability of moving to RA 2 Then we always choose the most probable On average: 70% of the times the choice will cause 1 registration 30% of the times the choice will cause 2 registrations 1 x 0.7 + 2 x 0.3 = 1.3 registrations Concept of regions: We will refer to an overlapped portion as “region” Availability of registration areas is the same throughout a region Performing a second registration within the same region has no benefit RA 1 RA 2 0.7 0.3

37. Off-line Formulation We need to find the minimum number of registrations along a mobility path Assume a mobility path p from regions ‘a’ to ‘i’. (a) We can make a graph of region adjacency. (b) At each region we know the availability set A, the set of available RAs in the region Using a sort of inner product of mobility path p and availability sets, we make a new partially ordered directed graph. (c) If an edge goes from a node ( k, R i ) to ( m, R i ), then it has weight 0 If an edge goes from a node ( k, R i ) to ( m, R j ), then it has weight 1 Problem is now defined as shortest path problem Can be solved in linear time M(r, p): minimum number of registrations along path p with initial registration choice r (c)

38. On-line Formulation On-line computational model Need to make a decision at every new region Decision choices include retaining the registration choice so long as it is available. Knowledge of mobility Assumed to be given as a random walk graph With respect to walking across regions Can be extracted from statistical data. Problem formulated as: Find the averaged effect of a registration choice r to all probable subsequent paths p of length k, starting at region g : Expct( r,g,k ) =  all paths p Prob[ p ] × M(r,p) Length k is referred to as look-ahead depth Algorithm Straightforward computation of Expct Finds a registration that minimizes Expct Exponential complexity with respect to look-ahead depth Paths of length 1 Paths of length 2 Paths of length 3 Paths of length 4

39. Analysis of Competitiveness Competitiveness ratio of an on-line algorithm Defined with respect to a measure on a solution The maximum possible ratio of the measure of the algorithm’s solution over the measure of the off-line optimal solution for an arbitrary input Competitiveness is usually proved using an adversary approach Example for 2-competitive: There are three RAs: A, B, C For any move, we can move to an overlapping region not covered by the chosen RA Example on-line: (AB)B(AC)C(AB)A(BC)C(AB)B(AC)A Example off-line (AB)A(AC)(AB)B(BC)(AB)A(AC) Can be expanded to n -competitive for any arbitrary n. Unlimited lower bound However, for any given topology, there is an upper bound to the competitive ratio a (AB) (AC) (BC) B C A a Konjevod et al., ACM DIAL’M 2002

40. Average Case Comparison Determine probability that The Expct-minimizing algorithm matches the performance of off-line optimal The random approach matches the performance of the off-line optimal Analysis shows that there is a certain probability that: Random choice will match the optimal algorithm, P random ORS algorithm will match the optimal algorithm, P expct Comparison of those values shows that – P expct ≥ P random ORS algorithm is more likely to match the optimal algorithm

41. Minimizing Hard registrations Soft registration model Assumption: registrations while not on a hand-off are cheaper (soft registrations) Objective: Minimize hard registrations. Algorithm Pre-emptive application (use before we need) Minimize Expct(1), i.e., look-ahead 1 Converts hard registrations to soft registrations How cheap a soft registration can be to still have a benefit We use the load function to investigate If a is the increase in total number of registrations and b is the average update cost reduction (because hard registrations are converted to soft) Then: Analysis shows linear relation to registrations: The cost ratio between soft and hard registrations has to be at greater than the ratio of increase in total number of registrations.