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

2. Presentation Outline 1 Frame Packing problem in Wireless Telecommunications  Definition  Relevant literature Proposed modeling approach  Sequential Rectangular Packing model Sample solution Future work

3. Technology 2 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 3 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 4 Figure 1. A sample OFDMA frame structure in TDD mode (Source: So-In et al., 2009b)

6. OFDMA Physical Layer Features 5 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 6 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 7 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 8 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 9 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 10 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 11 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) 12 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 13 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), d i : Total amount (in slots) of remaining requested data for user i, s i : Minimum data transfer rate (slots/frame) for user i,  i = min{ns i, d i } : Data amount to be packed throughout the frame sequence, 14

16. Indices &Parameters - II λ i : 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), α i =   i /A  :Minimum number of frames to which user i should be assigned, θ i : Latest frame to maintain or to begin the data transfer for user i (≤ λ i for ongoing transfers, equal to n for new users). 15

17. 16 Decision Variables

18. 17 Some Constraints - I

19. 18 Some Constraints - II

20. 19 Not solvable on IBM ILOG CPLEX 12.1 solver Sample instance  m=5 (number of users), n=4 (number of frames);  d i = 105, 70, 60, 80, 35; data demand for users 1..5  s i =30; minimum data transfer rate for each user (per frame)  λ i =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) Initial Solutions

21. 20 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 Difficulties

22. 21 Configuration:  Quad-Core 2.3 GHz CPU with 8 GB Ram Sample Solution

23. 22 Dividing the problem (two subproblems):  Master problem to deal with the so-called partitioning issue, (assigning users to frames) defined by the decision variables z ij.  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 Work in Progress

24. 23 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 Future Work

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 strict QoS requirements in IEEE 802.16e Mobile WiMAX networks, Proceedings of 2 nd Wireless Days (2009 IFIP), Paris, France, pp. 1- 5.