Amr Rizk TU Darmstadt

Saving Resources on Wireless Uplinks: Models of Queue-aware Scheduling 1 Amr Rizk TU Darmstadt - joint work with Markus Fidler 6. April 2016 KOM TUD Amr Rizk 1

Cellular Uplink Scheduling freq. time 6. April 2016 KOM TUD Amr Rizk 2

Cellular Uplink Scheduling freq. time 6. April 2016 KOM TUD Amr Rizk 2

Adaptive Resource Allocation in Cellular Uplink Direction Input metrics (LTE) Buffer status reports (BSR) Channel quality indicators (CQI) Goal Statistical QoS guarantee freq. time... 6. April 2016 KOM TUD Amr Rizk 3

Adaptive Resource Allocation in Cellular Uplink Direction Input metrics (LTE) Buffer status reports (BSR) Channel quality indicators (CQI) Goal Statistical QoS guarantee A B time S freq. D Arrival traffic A Buffer filling B... Service S Scheduling epoch 6. April 2016 KOM TUD Amr Rizk 3

Methods Exact analysis for Poisson traffic Analytical framework for general arrival and service processes 6. April 2016 KOM TUD Amr Rizk 4

Exact Analysis for Poisson Traffic freq. time... 6. April 2016 KOM TUD Amr Rizk 5

Exact Analysis for Poisson Traffic l m(t) Model Single M/M/1 queue: fixed λ, variable µ(t) Given λ and the queue length at epoch start Epoch based resource allocation Find µ(t) that provides a probabilistic bound on the queue length at the end of the epoch 6. April 2016 KOM TUD Amr Rizk 5

Exact Analysis for Poisson Traffic 0 1... k k+1... qmax q max+1... 1. Queue initially in state k 2. Fix µ(t) during such that 3. Probability that the queue at time is longer than q max is less than ε Based on the transient behavior of the M/M/1 queue [Kleinrock]. Model parameters: λ, q max, ε, 6. April 2016 KOM TUD Amr Rizk 6

Exact Analysis for Poisson Traffic Required µ for various parameters 50 40 required μ 30 20 10 decreasing q max 0 0 5 10 15 20 state k (a) q max {5, 10, 15, 20} Parameters: λ = 10, ε = 10 2, = 1 and 10 4 epochs for (b). 6. April 2016 KOM TUD Amr Rizk 7

Exact Analysis for Poisson Traffic Required µ for various parameters Improvement w.r.t. the static system with equivalent µ required μ 50 40 30 20 10 decreasing q max 0 0 5 10 15 20 state k (a) q max {5, 10, 15, 20} CCDF 10 0 10 1 10 2 10 3 q max =5 q max =10 q max =15 adaptive static 0 5 10 15 20 25 queue length at Δ (b) Static system parameterized with µ. Parameters: λ = 10, ε = 10 2, = 1 and 10 4 epochs for (b). 6. April 2016 KOM TUD Amr Rizk 7

Exact Analysis for Poisson Traffic Utilization comparison: 1 0.9 adaptive static 0.8 λ/μ 0.7 0.6 0.5 0.4 6 8 10 12 14 16 18 q max Key relation of λ to q max for a given ε Initial queue length is less helpful if the unknown traffic amount in during the epoch, i.e., λ, predominates q max Operation of queue-aware scheduling is non-trivial Resource savings in the adaptive case Proof of concept 6. April 2016 KOM TUD Amr Rizk 8

Beyond the Poisson Model Generalization w.r.t. service and arrival traffic models: B A time S freq. D... Framework: Stochastic Network Calculus Cumulative arrivals A(τ) resp. departures D(τ) up to time τ Backlog at τ: B(τ) = A(τ) D(τ) Service in (τ, t] as random process S(τ, t) Assume strict service resp. adaptive service curve [Burchard et. al 06] 6. April 2016 KOM TUD Amr Rizk 9

Queueing Model bits A(t,t + D) B(t ) B(t + D) A D t t + D Evaluation requires a lower bound on the service process t P [S(u, t) S(t u), u [τ, t]] 1 ε s To derive a lower bound on the departures D(τ + ) 6. April 2016 KOM TUD Amr Rizk 10

Wireless Channel Model Basic block fading model for a wireless transmission [Fidler, Al-Zubaidy] Time slotted model with iid increments c i = β ln(1 + γ i ) Rayleigh fading channel: γ i is exp distributed with parameter η Lower bounding function for the service process S(t) = 1 ( ln(ε p) [ t η + θβ ln(η) + ln (Γ(1 θβ, η)) ]) θ with θ > 0, incompl. Gamma fct. Γ and a violation probability ε s = (t τ)ε p. Derivation using Boole s inequality, Chernoff s bound and the Laplace transform of the increments. 6. April 2016 KOM TUD Amr Rizk 11

Infrequent Adaptation 10 0 10 1 CCDF 10 2 10 3 σ=10 σ=20 σ=30 10 4 0 20 40 60 queue length at Δ ] Bound on backlog at the end of epoch P [B(τ + ) b max 1 ε s Requirements on S(t): Allocate resources β during epoch such that the follwoing holds S( ) B(τ) + A(τ, τ + ) b max, and (1) S(τ + u) A(u, τ + ) b max, u [τ, τ + ] (2) 6. April 2016 KOM TUD Amr Rizk 12

Multi-user Scheduling with Infrequent Adaptation Scenario: M homogeneous, statistically independent MS channels Base station decides on amount of resource blocks β j for MS j [1, M] based on the infrequent adaptation technique Overall amount of resource blocks β s in epoch freq. time 6. April 2016 KOM TUD Amr Rizk 13

Multi-user Scheduling with Infrequent Adaptation Scenario: M homogeneous, statistically independent MS Base station decides on amount of resource blocks β j for MS j [1, M] based on the infrequent adaptation technique Overall amount of resource blocks β s in epoch Three basic resource allocation algorithms: 1. deterministic fair : jth MS receives ˆβ j = min{β j, β s/m} 2. priority : MS in class j receives ˆβ j = min{β j, β s j 1 k=1 ˆβ k} 3. proportional fair emulation : Priority scheduler with priorities reordered every epoch according to a score S j(τ, τ + )/(D j(τ)/τ) similar to [Kelly, et al. 98]. 6. April 2016 KOM TUD Amr Rizk 14

Multi-user Scheduling with Infrequent Adaptation: Simulation 10 0 10 0 10 1 10 1 CCDF 10 2 priority user #1 deterministic priority user #10 proportional fairness 10 3 30 40 50 60 70 queue length at Δ (b) 90% utilization CCDF 10 2 priority user #1 priority user #10 deterministic proportional fairness 10 3 30 40 50 60 70 queue length at Δ (c) 95% utilization Adaptive system retains statistical backlog bound depending on scheduling algorithm Notable difference only at very high utilization Parameters: M = 10, λ = 0.65, ε s = 10 2, = 100 slots, b max = 65, SNR 1/η = 3dB 6. April 2016 KOM TUD Amr Rizk 15

Key Takeaway Points Poisson case: Analytical results to quantify best-case resource savings. Model reveals important relation of λ to q max. Analytical framework identifies two regimes, one where adaptive scheduling is effective and one where it is not. A mathematical treatment of queue-aware scheduling that is applicable to a broad class of arrival and service processes. 6. April 2016 KOM TUD Amr Rizk 16

Related Models 1. Optimization of queueing service policies 2. Optimization of power and rate allocation in cellular systems Difference to 1: online, epoch-based technique for general arrival and service processes Difference to 2: dynamic programming to minimize a cost function of weighted power and rate consumption sample path as input 6. April 2016 KOM TUD Amr Rizk 16