UĞUR ELİİYİ , PhD CandidateDepar tment of S tat i s t i cs , DOKUZ EYLÜL UNIVERSITY
Adv i sor : Prof.Dr. EFENDİ NASİBOV, DOKUZ EYLÜL UNI VERSI TY
ANADOLU ÜNİVERSİTESİ Endüstri Mühendisl iği Seminerler i , 12 October , 2012, ESKİŞEHİR
A Novel Optimization Problem in Telecommunications
Presentation Outline2
Frame Packing problem in Wireless Telecommunications Definition Relevant literature
Proposed modeling approach Sequential Rectangular Packing model
Sample solutionFuture work
Technology3
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
WiMAX - Basics4
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).
WiMAX Features - OFDMA Frame structure
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Figure 1. A sample OFDMA frame structure in TDD mode (Source: So-In et al., 2009b)
OFDMA Physical Layer Features6
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
OFDMA DL Subframe Packing 7
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.
Multiple QoS classes8
Classification of the mobile stations according to parameters likethroughput (data transmission rate)delay requirementspriorities with respect to data or
subscription typesNature of wireless network
connectionshighly variable and unpredictable
time and location
MAC Scheduler 9
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.
Recent Developments10
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.
Relevant Literature - I11
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
Relevant Literature - II12
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
Sequential Rectangular Packing (SRP)13
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.
SRP – Aims & Assumptions14
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.
Indices &Parameters - I
• User index iI = {1,...,m}, m= # of users,• Frame index jJ = {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,
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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).
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Decision Variables
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Some Constraints - I
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Some Constraints - II
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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)
Initial Solutions
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Optimization version may not be solved in reasonable times, Both width & height are decision
variablesProblem 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
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Configuration: Quad-Core 2.3 GHz CPU with 8 GB Ram
Sample Solution
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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 objectiveTest problem generationInstance & Solution Visualization
Work in Progress
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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
Thank YouQuestionsCriticismsSuggestions
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 2nd Wireless Days (2009 IFIP), Paris, France, pp. 1-5.