Rensselaer Polytechnic Institute Rajagopal Iyengar Combinatorial Approaches to QoS Scheduling in Multichannel Wireless Systems Rajagopal Iyengar Rensselaer Polytechnic Inst. Troy, NY.

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)

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: over an OFDMA PHY. Comments on Multiple Cell Interference Effects later

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

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.

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.

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.

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.

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

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

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

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

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

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.

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.

Rensselaer Polytechnic Institute Rajagopal Iyengar Ongoing Work  Multiple Cells, interference effects, impact of smart antenna abstractions.  Simulation modules for 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 standard as possible.