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Combinatorial Approaches to QoS Scheduling in Multichannel Wireless Systems

Combinatorial Approaches to QoS Scheduling in Multichannel Wireless Systems. Rajagopal Iyengar Rensselaer Polytechnic Inst. Troy, NY. http://networks.ecse.rpi.edu/~raj. The Problem.

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Combinatorial Approaches to QoS Scheduling in Multichannel Wireless Systems

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  1. Combinatorial Approaches to QoS Scheduling in Multichannel Wireless Systems Rajagopal Iyengar Rensselaer Polytechnic Inst. Troy, NY. http://networks.ecse.rpi.edu/~raj Rajagopal Iyengar

  2. The Problem.. • How to allocate resources (schedule data) to satisfy demand constraints over a given time horizon for a number of users • Variants on this theme (single cell: outlined portion of figure) Rajagopal Iyengar

  3. Where this is Applicable • Any slot based multichannel system. (MAC/PHY layer, single cell scenarios, more) • Any system for which the above abstraction is accurate enough. • Frame based: control portion which specifies allocations • More specific example: 802.16 over an OFDMA PHY. Comments on Multiple Cell Interference Effects later Rajagopal Iyengar

  4. Resource Model and Example Allocations • M channels • T/d Slots on each channel • A matrix with some measure of ‘channel goodness’ is available ( ij ) • User transmits on multiple channels at the same time Rajagopal Iyengar

  5. Throughput Maximization • ij : Channel goodness number • nij: Allocation for user ‘i’ on channel ‘j’ • : Slot Length • di: Demand associated with user ‘i’ • T : Time horizon over which QoS guarantees are satisfied. Rajagopal Iyengar

  6. Throughput Maximization contd. • The Integer Program can be shown to be NP-Hard. • (special case is like PARTITION) • Focus on the LP relaxation instead. • Note that LP relaxation looks like Mixed Covering-Packing LP • Can find approximately feasible solutions and do a binary search on the objective function. Rajagopal Iyengar

  7. LP Solution technique: Interpret as Concurrent Flow problem • Not a standard concurrent flow problem. • Need to use algorithms for a variant with edge multipliers called ‘generalized concurrent flow’. • Heuristic independent of channel condition numbers. Rajagopal Iyengar

  8. Complete Heuristic • Solve Concurrent Flow • Scale back the solution, if larger than 1 • If not, let it be. • Fill up the remainder of the space in a throughput optimal manner. • Find the best user on each channel. Rajagopal Iyengar

  9. Concurrent flow interpretation: Solution Analysis • Input Independent: Does not depend on the channel quality numbers. • Fails gracefully: when program infeasible, we have max-min fair allocations. • Accuracy of Solution: For fine enough slot granularity (large number of slots), rounding errors should not matter much in the case of feasible programs. • Note that the solution to generalized concurrent flow is  approximate in general Rajagopal Iyengar

  10. Performance: Heuristic output is close to optimal LP solution Rajagopal Iyengar

  11. Variant: Simpler Radios on Clients • User can hop channels dynamically • User cannot use 2 channels at the same time Extra set of Constraints Rajagopal Iyengar

  12. Adding Power Control to the mix makes the problem harder. Power Constraints Rajagopal Iyengar

  13. Rectangularized allocations • As the number of users increase, overhead due to communication of allocation to users also increases • Objective: Reduce the control overhead • Solution: Make the allocations rectangular in shape so that fewer numbers are needed to define an allocation Rajagopal Iyengar

  14. Solution Approach • Ensure the following (inspired by VLSI design/layout ideas): • Isolation of allocations: Rectangles do not overlap • Whats available: Supply constraints are not violated • What needs to be satisfied: Demand constraints are met • Detail of formulation in the paper. • Bad news: • Tougher Problem: MILP formulation results, making a hard problem harder • More Constrained: Problem is more constrained due to rectangular shape constraints. • Bad Tradeoff: Not worth the extra effort to solve a harder problem to make allocations rectangular • Alternatives needed: Explore other techniques to reduce overhead (work in progress) • One simple technique to compare against: label each slot. Rajagopal Iyengar

  15. Related Problems • Solve the same resource allocation problem for multihomed clients which can talk to multiple Base Stations • Multiple Channels and Multiple BSes (3-D resource visualization). • Interference Effects need to be considered. • Find sets of (User <-> BS) transmissions schedulable at the same time on a channel. • Online version of resource allocation problem: Solve the throughput maximization problem for arriving and departing users. • How close is the solution to the offline algorithm? • Better Antennas: Adaptive Beamforming, for example: use models (add constraints) to evaluate impact on maximum throughput. Rajagopal Iyengar

  16. Ongoing Work • Multiple Cells, interference effects, impact of smart antenna abstractions. • Simulation modules for 802.16 MAC/PHY in NS2 • Utilize available code to make PHY layer simulation more realistic (accurate fading models + SINR calculation) • Implement as many MAC features from 802.16 standard as possible. Rajagopal Iyengar

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