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

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Page 1: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Saving Resources on Wireless Uplinks:Models of Queue-aware Scheduling

Amr RizkTU Darmstadt

1

- joint work with Markus Fidler6. April 2016 | KOM TUD | Amr Rizk | 1

Page 2: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Cellular Uplink Scheduling

freq.

tim

e

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Page 3: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Cellular Uplink Scheduling

freq.

tim

e

6. April 2016 | KOM TUD | Amr Rizk | 2

Page 4: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Adaptive Resource Allocation in Cellular UplinkDirection

Input metrics (LTE)I Buffer status reports (BSR)I Channel quality indicators (CQI)

GoalI Statistical QoS guarantee

...freq.

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Page 5: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Adaptive Resource Allocation in Cellular UplinkDirection

Input metrics (LTE)I Buffer status reports (BSR)I Channel quality indicators (CQI)

GoalI Statistical QoS guarantee

BA

S...freq.

tim

e D

I Arrival traffic AI Buffer filling B

I Service SI Scheduling epoch ∆

6. April 2016 | KOM TUD | Amr Rizk | 3

Page 6: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Methods

I Exact analysis for Poisson traffic

I Analytical framework for general arrival and service processes

6. April 2016 | KOM TUD | Amr Rizk | 4

Page 7: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Exact Analysis for Poisson Traffic

...

freq.

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6. April 2016 | KOM TUD | Amr Rizk | 5

Page 8: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Exact Analysis for Poisson Traffic

m(t)l

ModelI Single M/M/1 queue: fixed λ, variable µ(t)I Given λ and the queue length at epoch startI Epoch based resource allocation⇒ Find µ(t) that provides a probabilistic bound on the queue length at the end ofthe epoch

6. April 2016 | KOM TUD | Amr Rizk | 5

Page 9: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Exact Analysis for Poisson Traffic

0 1 k... k+1 maxq

maxq +1 ......

1. Queue initially in state k

2. Fix µ(t) during ∆ such that3. Probability that the queue at time ∆ is longer than qmax is less than ε

I Based on the transient behavior of the M/M/1 queue [Kleinrock].Model parameters: λ, qmax , ε , ∆

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Page 10: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Exact Analysis for Poisson Traffic

I Required µ for various parameters

I Improvement w.r.t. the static system with equivalent µ̄

0 5 10 15 200

10

20

30

40

50

state k

requ

ired

μ

decreasing qmax

(a) qmax ∈ {5, 10, 15, 20}

0 5 10 15 20 2510

−3

10−2

10−1

100

queue length at Δ

CC

DF

adaptivestatic

qmax

=5

qmax

=15

qmax

=10

(b) Static system parameterized with µ̄.

Parameters: λ = 10, ε = 10−2, ∆ = 1 and 104 epochs for (b).

6. April 2016 | KOM TUD | Amr Rizk | 7

Page 11: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Exact Analysis for Poisson Traffic

I Required µ for various parametersI Improvement w.r.t. the static system with equivalent µ̄

0 5 10 15 200

10

20

30

40

50

state k

requ

ired

μ

decreasing qmax

(a) qmax ∈ {5, 10, 15, 20}

0 5 10 15 20 2510

−3

10−2

10−1

100

queue length at Δ

CC

DF

adaptivestatic

qmax

=5

qmax

=15

qmax

=10

(b) Static system parameterized with µ̄.

Parameters: λ = 10, ε = 10−2, ∆ = 1 and 104 epochs for (b).

6. April 2016 | KOM TUD | Amr Rizk | 7

Page 12: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Exact Analysis for Poisson Traffic

Utilization comparison:

6 8 10 12 14 16 180.4

0.5

0.6

0.7

0.8

0.9

1

qmax

λ/μ

adaptivestatic

I Key relation of λ∆ to qmax for a given εI Initial queue length is less helpful if the unknown traffic amount in during the

epoch, i.e., λ∆, predominates qmax→ Operation of queue-aware scheduling is non-trivial

I Resource savings in the adaptive case → Proof of concept

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Page 13: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Beyond the Poisson Model

Generalization w.r.t. service and arrival traffic models:

BA

S

...

freq.

tim

e D

Framework: Stochastic Network CalculusI Cumulative arrivals A(τ) resp. departures D(τ) up to time τI Backlog at τ : B(τ) = A(τ)− D(τ)I Service in (τ , t ] as random process S(τ , t)I Assume strict service resp. adaptive service curve [Burchard et. al’06]

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Queueing Model

bits

t

B(t )

A

D

t t + D

A(t,t + D)

B(t + D)

I Evaluation requires a lower bound on the service processP [S(u, t) ≥ S(t − u), ∀u ∈ [τ , t]] ≥ 1− εs

I To derive a lower bound on the departures D(τ + ∆)6. April 2016 | KOM TUD | Amr Rizk | 10

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Wireless Channel Model

Basic block fading model for a wireless transmission [Fidler, Al-Zubaidy]

I Time slotted model with iid increments ci = β ln(1 + γi)I Rayleigh fading channel: γi is exp distributed with parameter ηI Lower bounding function for the service process

S(t) = 1θ

(ln(εp)− t

[η + θβ ln(η) + ln (Γ(1− θβ, η))

])with θ > 0, incompl. Gamma fct. Γ and a violation probability εs = (t − τ)εp.

Derivation using Boole’s inequality, Chernoff’s bound and the Laplacetransform of the increments.

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Infrequent Adaptation

0 20 40 6010

−4

10−3

10−2

10−1

100

queue length at Δ

CC

DF

σ=10σ=20σ=30

I Bound on backlog at the end of epoch P[

B(τ + ∆) ≤ bmax

]≥ 1− εs

I Requirements on S(t): Allocate resources β during epoch ∆ such that thefollwoing holds

S(∆) ≥ B(τ) + A(τ , τ + ∆)− bmax, and (1)S(τ +∆−u) ≥ A(u, τ + ∆)− bmax, ∀u∈ [τ , τ + ∆] (2)

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Multi-user Scheduling with InfrequentAdaptation

Scenario:I M homogeneous, statistically independent MS channels

I Base station decides on amount of resource blocks βj for MS j ∈ [1, M] basedon the infrequent adaptation technique

I Overall amount of resource blocks βs in epoch ∆

freq.

tim

e

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Multi-user Scheduling with InfrequentAdaptation

Scenario:I M homogeneous, statistically independent MS

I Base station decides on amount of resource blocks βj for MS j ∈ [1, M] basedon the infrequent adaptation technique

I Overall amount of resource blocks βs in epoch ∆

I Three basic resource allocation algorithms:

1. “deterministic fair”: jth MS receives β̂j = min{βj ,βs/M}

2. “priority”: MS in class j receives β̂j = min{βj ,βs −∑j−1

k=1 β̂k}

3. “proportional fair emulation”: Priority scheduler with priorities reordered everyepoch ∆ according to a score Sj(τ , τ + ∆)/(Dj(τ)/τ) similar to [Kelly, et al.’98].

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Multi-user Scheduling with Infrequent Adapta-tion: Simulation

30 40 50 60 7010

−3

10−2

10−1

100

queue length at Δ

CC

DF

priority user #1deterministicpriority user #10proportional fairness

(b) 90% utilization

30 40 50 60 7010

−3

10−2

10−1

100

queue length at ΔC

CD

F

priority user #1priority user #10deterministicproportional fairness

(c) 95% utilization

I Adaptive system retains statistical backlog bound depending on schedulingalgorithm

I Notable difference only at very high utilizationParameters: M = 10, λ = 0.65, εs = 10−2, ∆ = 100 slots, bmax = 65, SNR 1/η = 3dB

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Key Takeaway Points

I Poisson case: Analytical results to quantify best-case resource savings.

I Model reveals important relation of λ∆ to qmax.

I Analytical framework identifies two regimes, one where adaptive scheduling iseffective and one where it is not.

I A mathematical treatment of queue-aware scheduling that is applicable to abroad class of arrival and service processes.

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Page 21: Amr Rizk - disco.cs.uni-kl.de · SavingResourcesonWirelessUplinks: ModelsofQueue-awareScheduling Amr Rizk TU Darmstadt 1-jointworkwithMarkusFidler 6. April 2016 | KOM TUD | Amr Rizk

Related Models

1. Optimization of queueing service policies

2. Optimization of power and rate allocation in cellular systems

Difference to 1:I online, epoch-based technique for general arrival and service processes

Difference to 2:I dynamic programming to minimize a cost function of weighted power and

rate consumptionI sample path as input

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