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

2. Rensselaer Polytechnic Institute Rajagopal Iyengar 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)

3. Rensselaer Polytechnic Institute Rajagopal Iyengar 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

4. Rensselaer Polytechnic Institute Rajagopal Iyengar 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

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

6. Rensselaer Polytechnic Institute Rajagopal Iyengar 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.

7. Rensselaer Polytechnic Institute Rajagopal Iyengar 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.

8. Rensselaer Polytechnic Institute Rajagopal Iyengar 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.

9. Rensselaer Polytechnic Institute Rajagopal Iyengar 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

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

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

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

13. Rensselaer Polytechnic Institute Rajagopal Iyengar 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

14. Rensselaer Polytechnic Institute Rajagopal Iyengar 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.

15. Rensselaer Polytechnic Institute Rajagopal Iyengar 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.

16. Rensselaer Polytechnic Institute Rajagopal Iyengar 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.