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## Utility Maximization for Delay Constrained QoS in Wireless

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**Utility Maximization for Delay Constrained QoS in Wireless**I-Hong Hou P.R. Kumar University of Illinois, Urbana-Champaign**Problem Overview**• Every packet has a hard delay bound • Timely throughput = Throughput of packets delivered within their delay bounds • qn = Timely throughput of client n • Un(qn) = Utility of client n • Channels are unreliable • Goal: Max ∑Un(qn) s.t. [qn] feasible under both channel unreliabilities and delay constraints • Example applications: VoIP, Network control, etc.**Client-Server Model**• A system with N wireless clients and one AP • AP schedules all transmissions • Time is slotted 2 1 AP 3**Traffic Model**• Group time slots into periods with τ time slots • Clients generate packets at the beginning of each period τ 2 1 AP 3**Delay Bounds**• τ = Deadline • Packets are dropped if not delivered by the deadline • Delay of successful delivered packet is at most τ τ 2 1 arrival AP deadline 3**Channel Model**• Each transmission takes one time slot • Links are unreliable • Transmission for client n succeeds with probability pn 2 p2 1 p1 AP p3 3**How the System Works**F F S I S F S I 2 p2 1 p1 AP p3 F S S I 3**Timely Throughput**• Timely throughput (qn) = F F S I S F S I 2 p2 1 p1 AP p3 F S S I 3**Problem Formulation**• Each client has an utility function, • is strictly increasing, strictly concave, and continuously differentiable • AP needs to assign [qn] to maximize total utility, subject to feasibility constraints**Characterization of What is Feasible**• The average number of time slots needed for client n to have timely throughput qn is • Let IS = Expected number of idle time slots when the set of clients is S • Clearly, we need • Theorem: the condition is both necessary and sufficient Average # of packets delivered in a period Average # of transmissions needed for a delivery**Optimization Problem**• SYSTEM: • Decompose SYSTEM into two subproblems • CLIENTn: considers own utility function • ACCESS-POINT: considers feasibility constraints Utility functions may be unknown 2N feasibility constraints**Problem Decomposition**CLIENTn: (Ψn given) Max over ACCESS-POINT: (ρn given) Max s.t. over**A Bidding Game**Step 1. Each client n announces ρn Step 2. Given [ρn], AP finds [qn] to solve ACCESS-POINT Step 3. Client n observes qn, compute Ψn=ρn/qn. Client n finds new ρn to solve CLIENTn Step 4. Go to Step 2.**Solving ACCESS-POINT**• ACCESS-POINT: (ρn given) Max s.t. over By KKT condition:**Solving ACCESS-POINT**• ACCESS-POINT: (ρn given) By KKT condition: Average # of time slots working for client n per period**Solving ACCESS-POINT**• ACCESS-POINT: (ρn given) By KKT condition: The more price paid, the more time slots received**Solving ACCESS-POINT**• ACCESS-POINT: (ρn given) By KKT condition: Depends on prices paid by all clients and feasibility constraints (Difficult to solve)**Scheduling Policy for ACCESS-POINT**• Weighted-Transmission Policy (WT): • 1. Let be the total number of time slots allocated for client n • 2. Sort clients by • 3. Clients with smaller get higher priorities • Theorem: WT solves the ACCESS-POINT problem • Require no knowledge on channel reliabilities**Simulation: Utility Maximization**• Setup: • A set of 30 clients • Utility function: • Parameters: • Setting 1: • Setting 2: • Evaluate the mean and variance of**Evaluated Policies**• WT policies and bidding game (WT-Bid) • WT policies without bidding game (WT-NoBid) • Randomly assign priorities (Rand) • Clients with larger get higher priorities, break ties randomly (P-Rand)**Simulation Results: Mean**WT-Bid has highest total utility**Simulation Results: Variance**WT-Bid has small variance**Conclusion**• Formulate and solve the problem of utility maximization for delay-constrained wireless networks • Propose a scheduling policy to solve ACCESS-POINT τ CLIENTn arrival deadline SYSTEM Ψn ρn p2 1 p1 2 AP ACCESS-POINT**Thank You**Another work on scheduling delay-constrained packets with time-varying channels, different delay bounds, and rate adaptation will be presented in TS60: WIRELESS NETWORK SCHEDULING 3