UĞUR ELİİYİ , PhD CandidateDepartment o f Stat i s t ics , DOKUZ EYLÜL UNIVERSITY

Adv i sor : Pro f.Dr. EFENDİ NASİBOV, DOKUZ EYLÜL UNI VERSI TY

ANADOLU ÜNİVERSİTESİ Endüstr i 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.