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Base Station Location and Service Assignment in W-CDMA Networks

Base Station Location and Service Assignment in W-CDMA Networks. Joakim Kalvenes 1 Jeffery Kennington 2 Eli Olinick 2 Southern Methodist University 1 Edwin L. Cox School of Business 2 School of Engineering. Wireless Network Design: Inputs. Potential locations for radio towers (cells)

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Base Station Location and Service Assignment in W-CDMA Networks

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  1. Base Station Location and Service Assignment in W-CDMA Networks Joakim Kalvenes1 Jeffery Kennington2 Eli Olinick2 Southern Methodist University 1Edwin L. Cox School of Business 2School of Engineering

  2. Wireless Network Design: Inputs • Potential locations for radio towers (cells) • “Hot spots”: concentration points of users/subscribers (demand) • Potential locations for mobile telephone switching offices (MTSO) • Locations of access point(s) to Public Switched Telephone Network (PSTN) • Costs for linking towers to MTSOs, and MTSOs to PSTN

  3. Wireless Network Design: Problem • Determine which radio towers to build (base station location) • Determine how to assign subscribers to towers (service assignment) • Determine which MTSOs to use • Maximize profit: revenue per subscriber served minus infrastructure costs

  4. Wireless Network Design Tool

  5. Code Division Multiple Access (CDMA)Technology • The basis for 3G cellular systems • Channel (frequency) allocation is not an explicit issue since the full spectrum is available in each cell • New calls cause incremental noise (interference) • New calls admitted as long as the signal-to-noise ratio stays with in system limit • Power transmitted by handset depends on distance to assigned radio tower • Tower location and assignment of customer locations to towers must be determined simultaneously

  6. Tower 3 Power Control Example Received signal strength must be at least the target value Ptar Signal is attenuated by a factor of g13 Subscriber at Location 1 Assigned to Tower 3

  7. Signal-to-Interference Ratio (SIR) Tower 3 Tower 4 Subscriber at Location 1 assigned to Tower 3 Two subscribers at Location 2 assigned to Tower 4

  8. Some Related CDMA Literature: Base Station Location & Service Assignment • Galota, Glasser, Reith, and Vollmer (2001) • Profit maximization • Polynomial-time approximation scheme • Amaldi, Capone, and Malucelli (2001a, 2001b) • Minimize cost to serve all users • Randomized add-drop heuristic • Tabu search to improve solutions • Mathar and Schmeink (2001) • Maximize system capacity for a fixed budget • Simplified interference model

  9. Our New Model for CDMA Base Station Location and Service Assignment • Integer linear program (ILP) • Maximizes profit • Enforces hard constraints on signal-to-interference ratio • Incorporates FCC licensing rules for US providers

  10. Constants and Sets Used in the Model • L isthe set of candidate tower locations. • M isthe set of subscriber locations. • gmℓis the attenuation factor from location m to tower ℓ. • is the set of tower locations that can service customers in location . • is the set of customer locations that can be serviced by tower ℓ.

  11. More Constants and Sets Used in the Model • dmis the demand (channel equivalents) in location • r is the annual revenue generated per channel. • is the FCC mandated minimum service requirement. • is the cost of building and operating a tower at location . • SIRminis the minimum allowable signal-to-interference ratio. • s = 1 + 1/SIRmin.

  12. Decision Variables Used in the Model • yℓ =1 if a tower is constructed at location ℓ; and zero, otherwise. • The integer variable xmℓ denotes the number of customers (channel equivalents) at that are served by the tower at location • The indicator variable qm =1 if and only if location m can be served by at least one of the selected towers.

  13. Integer Programming Model The objective of the model is to maximize profit: subject to the following constraints:

  14. Integer Programming Model

  15. Quality of Service (QoS) Constraints • For known attenuation factors, gml, the total received power at tower location ℓ, PℓTOT , is given by • For a session assigned to tower ℓ • the signal strength is Ptarget • the interference is given by PℓTOT – Ptarget • QoS constraint on minimum signal-to-interference ratio for each session (channel) assigned to tower ℓ:

  16. Quality of Service (QoS) Constraints

  17. Enhancing the Basic ILP Model • Global Valid Inequalities • Optimality Cuts • Post-Processing Procedure • Branching Rule

  18. Global Valid Inequalities

  19. Global Valid Inequalities

  20. Optimality Cuts • If customers at site m are served, then profit is maximized by assigning them to the available tower that has the largest attenuation factor (i.e., the nearest available tower). • We can add the following cuts to formulation

  21. Optimality Cuts: Derivation

  22. Optimality Cuts: Derivation

  23. Post Processing • Values of the attenuation factors (gij) have a large range • Coefficients in QoS constraints (6) may differ in magnitude by as much as 109. • Causes scaling problems so that solutions returned by CPLEX are not always feasible • Post-processing procedure ensures feasibility within a reasonable tolerance

  24. Phase II: Eliminating Infeasibilities

  25. Computational Experiments • Branching on tower-location decisions (y's) before customer assignment (x's) reduces branch-and-bound time. • Number of (8) cuts depends on |Cm|; may actually increase solution time if too large. • Computing resources used • Compaq AlphaServer DS20E with dual EV6.7 (21264A) 667 MHz processors and 4,096 MB of RAM • CPLEX version 6.6.0 • AMPL release 9.10.27

  26. Parameters for Dense Data Set Based on data generation used by Amaldi et al. [2001a,b]

  27. Results for Dense Test Data Set PP gives number of problems (out of 20) requiring post processing.

  28. Parameters for Sparse Data Set 300 problem instances: 100 sets of subscriber locations each with 3 distributions for demand at each location.

  29. Results for Sparse Data Set * Only 10 instances were attempted. ** Only 69 of 100 instances were solved within the limits of 8 hours of CPU time and 1.8 Gb RAM.

  30. Conclusions • Branching rule and cuts enable CPLEX to solve realistically sized problem instances of our model • Dense network structure • Previous work uses randomized local search • Our solutions provably within 5% of optimal on average • Sparse network structure • Solved a set of 300 test problems with |L| = 40 and |M| = 250 • Average optimality gap = 1.2% and average CPU time = 13 minutes • Extensions (suggested by a well-known cellular provider) • Maximize capacity of existing 2G system to provide CDMA • Capacity expansion of an existing 3G system subject to budget constraint

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