Utility Maximization for Delay Constrained QoS in Wireless I-Hong Hou P.R. Kumar University of Illinois, Urbana-Champaign 1 /23

Problem Overview  Every packet has a hard delay bound  Timely throughput = Throughput of packets delivered within their delay bounds  q n = Timely throughput of client n  U n (q n ) = Utility of client n  Channels are unreliable  Goal: Max ∑U n (q n ) s.t. [q n ] feasible under both channel unreliabilities and delay constraints  Example applications: VoIP, Network control, etc. 2 /23

Client-Server Model  A system with N wireless clients and one AP  AP schedules all transmissions  Time is slotted AP /23

Traffic Model  Group time slots into periods with τ time slots  Clients generate packets at the beginning of each period AP τ 4 /23

Delay Bounds  τ = Deadline  Packets are dropped if not delivered by the deadline  Delay of successful delivered packet is at most τ AP /23 τ arrival deadline

Channel Model  Each transmission takes one time slot  Links are unreliable  Transmission for client n succeeds with probability p n AP p1p1 p2p2 p3p3 6 /23

How the System Works AP SF p1p1 p2p2 p3p3 7 /23 S FF S S S FI I I

Timely Throughput AP SF p1p1 p2p2 p3p3 8 /23 S FF S S S FI I I  Timely throughput (q n ) = Client #Throughput

Problem Formulation  Each client has an utility function, is strictly increasing, strictly concave, and continuously differentiable  AP needs to assign [q n ] to maximize total utility, subject to feasibility constraints 9 /23

Characterization of What is Feasible  The average number of time slots needed for client n to have timely throughput q n is  Let I S = Expected number of idle time slots when the set of clients is S  Clearly, we need  Theorem: the condition is both necessary and sufficient 10 /23 Average # of packets delivered in a period Average # of transmissions needed for a delivery

Optimization Problem  SYSTEM:  Decompose SYSTEM into two subproblems CLIENT n : considers own utility function ACCESS-POINT: considers feasibility constraints 11 /23 Utility functions may be unknown 2 N feasibility constraints

Problem Decomposition CLIENT n : (Ψ n given) Max over ACCESS-POINT: (ρ n given) Max s.t. over 12 /23

A Bidding Game Step 1. Each client n announces ρ n Step 2. Given [ρ n ], AP finds [q n ] to solve ACCESS-POINT Step 3. Client n observes q n, compute Ψ n = ρ n /q n. Client n finds new ρ n to solve CLIENT n Step 4. Go to Step /23

Solving ACCESS-POINT  ACCESS-POINT: (ρ n given) Max s.t. over By KKT condition: 14 /23

Solving ACCESS-POINT  ACCESS-POINT: (ρ n given) By KKT condition: Average # of time slots working for client n per period 15 /23

Solving ACCESS-POINT  ACCESS-POINT: (ρ n given) By KKT condition: The more price paid, the more time slots received 16 /23

Solving ACCESS-POINT  ACCESS-POINT: (ρ n given) By KKT condition: Depends on prices paid by all clients and feasibility constraints (Difficult to solve) 17 /23

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 18 /23

Simulation: Utility Maximization  Setup: A set of 30 clients Utility function: Parameters:  Setting 1:  Setting 2:  Evaluate the mean and variance of 19 /23

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) 20 /23

Simulation Results: Mean WT-Bid has highest total utility 21 /23

Simulation Results: Variance WT-Bid has small variance 22 /23

Conclusion  Formulate and solve the problem of utility maximization for delay-constrained wireless networks  Propose a scheduling policy to solve ACCESS-POINT 23 /23 AP 12 p1p1 p2p2 τ arrival deadline CLIENT n SYSTEM ACCESS-POINT ΨnΨn ρnρn

24 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