A Novel Optimization Problem in Telecommunications

1. A Novel Optimization Problem in Telecommunications UĞUR ELİİYİ, PhDCandidate Department of Statistics, DOKUZ EYLÜL UNIVERSITY Advisor: Prof.Dr. EFENDİ NASİBOV, DOKUZ EYLÜL UNIVERSITY ANADOLU ÜNİVERSİTESİ Endüstri Mühendisliği Seminerleri, 12 October, 2012, ESKİŞEHİR

2. Presentation Outline • Frame Packing problem in Wireless Telecommunications • Definition • Relevant literature • Proposed modeling approach • Sequential Rectangular Packing model • Sample solution • Future work

3. Technology • IEEE 802.16-2009 (2009): Standard for Local and metropolitan area networks, Part 16: Air Interface for Broadband Wireless Access Systems WiMAX (Worldwide Interoperability for Microwave Access) standard, • 4G wireless telecommunications

4. WiMAX - Basics • Highlights: Ranges, 50 km. for fixed, 5-15 km. for mobile; Data rate, 1 Gbps-100 Mbps. • Appropriate for rural areas or metropolitan areas with complex network infrastructure • Important features: • Orthogonal Frequency Division Multiple Access (OFDMA), • Multiple Quality of Service (QoS) classes, • Media Access Control (MAC) scheduler of the base station (BS).

5. WiMAX Features - OFDMA Frame structure Figure 1. A sample OFDMA frame structure in TDD mode (Source: So-In et al., 2009b)

6. OFDMA Physical Layer Features • Two dimensions: frequency and time, • Time axis: Usually covers a 5 ms period, • Bidirectional data transfer, from BS to mobile stations (downlink, DL) & vice versa (uplink, UL): • time division duplexing (TDD) • same frequency bands, but DL precedes UL in time

7. OFDMA DL Subframe Packing • Mapping mobile stations to rectangular (IEEE 802.16 standard) areas (bursts) • The unit of burst allocation : “slot”, • More than one burst per mobile station or more than one connection in one burst (burst compaction) are allowed.

8. Multiple QoS classes • Classification of the mobile stations according to parameters like • throughput (data transmission rate) • delay requirements • priorities with respect to data or subscription types • Nature of wireless network connections • highly variable and unpredictable • time and location

9. MAC Scheduler • Allocation of time and frequency ranges for mobile stations / user terminals: • determining service order and quantity : when (frames) and amount of scheduled data, • assignment of time and frequency resources to every connection (frame packing). • No specific admission control or resource allocation mechanisms for the scheduler • “scheduling”  significant topic for all WiMAX equipment makers and network service providers.

10. Recent Developments • IEEE Std 802.16m™-2011 Amendment 3: Advanced Air Interface (6 May 2011) to IEEE 802.16-2009 • Frame structure: Super and subframes • 1 superframe= 20 ms = 4 frames, • 1 frame = 5 ms = 8 subframes for specific channel bandwiths, • The ratio of DL : UL shall be selected from one of the following values: 6:2, 5:3, 4:4, or 3:5.

11. Relevant Literature - I • Ben-Shimol et al. (2006): OFDMA frame packing (row by row) algorithms with and without QoS constraints, evaluation by extensive simulations • Ohseki et al. (2007): Burst construction and frame packing method for DL subframe aiming to minimize the control data (higher throughput) by defining deadlines (QoS) for each connection • So-In et al. (2009a): Detailed survey of key issues in WiMAX scheduling and review of related work

12. Relevant Literature - II • So-In et al. (2009b): Right-to-left and from-bottom-to-top DL frame packing algorithm for minimizing energy consumption of mobile stations • Lodi et al. (2011): Development of two efficient heuristics considering the trade-off between signaling and data, assigning a profit to every data packet to select the maximum-profit packet set (if not all of them fit into the frame). Attained a 1 ms processing time budget for scheduling in the base station to practically handle the system

13. Sequential Rectangular Packing (SRP) • Allocation of a sequence of 2D identical frames to user data demands due to service constraints like minimum data transfer rate and maximum delay limits. • Model: A representative nonlinear IP model which simultaneously partitions user demand, and packs these demand parts (areas) with unknown sizes.

14. SRP – Aims & Assumptions • Feasibility • No specific objectives • Each user can be allocated at most one rectangle in a frame, • Continuous allocation process, • solution of an instance  input for the next instance • QoS parameters  constraints, • Minimum transfer rate, maximum delay. • Capacity of all frames cover total demand for the planning horizon or queueing mechanism, • All parameters positive integers.

15. Indices &Parameters - I • User index iI = {1,...,m}, m= # of users, • Frame index jJ = {1,...,n}, n= number of frames in the sequence (planning horizon),  • di : Total amount (in slots) of remaining requested data for user i, • si : Minimum data transfer rate (slots/frame) for user i, • i = min{nsi, di} : Data amount to be packed throughout the frame sequence,

16. Indices &Parameters - II • λi : Maximum delay period (in frames) for user i causing timeout error, • W : Frame width, H : Frame height, A= WH: Frame area (all frames identical in size), • αi = i/A  :Minimum number of frames to which user i should be assigned, • θi : Latest frame to maintain or to begin the data transfer for user i (≤ λi for ongoing transfers, equal to n for new users).

17. Decision Variables

18. Some Constraints - I

19. Some Constraints - II

20. Initial Solutions • Not solvable on IBM ILOG CPLEX 12.1 solver • Sample instance • m=5 (number of users), n=4 (number of frames); • di= 105, 70, 60, 80, 35; data demand for users 1..5 • si=30; minimum data transfer rate for each user (per frame) • λi =2, 1, 2, 3, 1; maximum delay period for users • W=6 (frame width), H=15 (frame height). • Nonlinear terms  Solved using BARON v. 8.1.5 solver in GAMS (later with AMPL, AIMMS)

21. Difficulties • Optimization version may not be solved in reasonable times, • Both width & height are decision variables • Problem still hard even without any nonlinear terms: • Partition of user demands over frames + • Packing problems with unknown sizes: • Finding widths, heights and positions. • NP-Hard

22. Sample Solution • Configuration: • Quad-Core 2.3 GHz CPU with 8 GB Ram

23. Work in Progress • Dividing the problem (two subproblems): • Master problem to deal with the so-called partitioning issue, (assigning users to frames) defined by the decision variables zij. • Second subproblem to generate the best possible bounds by packing the assigned users for those frames in a cyclic manner until the solution (feasible/optimal) • Including a load balancing objective • Test problem generation • Instance & Solution Visualization

24. Future Work • Incorporating user priorities in the model (profit maximization) • Fuzzy approach for sequential packing • Employing fuzziness in item areas and maximum delay constraints, and using attachment and compatibility relations between and within frames and items • SRP using Constraint Programming(CP), • Partitioning with maximum delays

25. Thank You Questions Criticisms Suggestions

26. References • Ben-Shimol, Y., Kitroser, I., Dinitz, Y. (2006). Two-dimensional mapping for wireless OFDMA systems, IEEE Transactions on Broadcasting, Vol. 52, No. 3, pp. 388-396. • Lodi, A., Martello, S., Monaci, M., Cicconetti, C., Lenzini, L., Mingozzi, E.C., Eklund, C., Moilanen, J. (2011). Efficient Two-Dimensional Packing Algorithms for Mobile WiMAX, Management Science, Articles in Advance, 2011 INFORMS, pp. 1–15. • Ohseki, T., Morita, M., Inoue, T. (2007). Burst Construction and Packet Mapping Scheme for OFDMA Downlinks in IEEE 802.16 Systems, Proceedings of IEEE Global Telecommunications Conference, pp. 4307-4311. • So-In, C., Jain, R., Tamimi, A.K. (2009a). Scheduling in IEEE 802.16e Mobile WiMAX Networks: Key Issues and a Survey, IEEE Journal on Selected Areas in Communications, Vol. 27, No. 2, pp. 156-171. • So-In, C., Jain, R., Tamimi, A.K. (2009b). eOCSA: An algorithm for burst mapping with strictQoS requirements in IEEE 802.16e Mobile WiMAX networks, Proceedings of 2ndWireless Days (2009 IFIP), Paris, France, pp. 1-5.