Throughput Maximization in Mobile WSN Scheduling with Power Control and Rate Selection Yosef Alayev1 , Fangfei Chen2 , Yun Hou3 , Matthew P. Johnson2 , Amotz Bar-Noy1 , Tom La Porta2 , Kin K. Leung4 1 Department
of Computer Science, The Graduate Center, CUNY, NY, USA of Computer Science and Engineering, PSU, PA, USA 3 ASTRI, Hong Kong, China 4 EEE Department, Imperial College, UK
2 Department
May 16, 2012
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Outline
1
Introduction
2
Model
3
Algorithms
4
Simulations
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Outline
1
Introduction
2
Model
3
Algorithms
4
Simulations
Yosef Alayev et. al (CUNY)
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Outline
1
Introduction
2
Model
3
Algorithms
4
Simulations
Yosef Alayev et. al (CUNY)
scheduling with adaptive rate/power control
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Outline
1
Introduction
2
Model
3
Algorithms
4
Simulations
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Scheduling Problem for Data Delivery in WSN
Problem: m APs (machines), K transmission rate levels on each machine, q transmission power levels on each machine, n mobile users (jobs), each job j has a weight wj Goal: Assign timeslots on APs to jobs with adaptive transmission rate and power control so as to maximize total profit of all assigned jobs and prevent interference.
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Scheduling Problem for Data Delivery in WSN
Problem: m APs (machines), K transmission rate levels on each machine, q transmission power levels on each machine, n mobile users (jobs), each job j has a weight wj Goal: Assign timeslots on APs to jobs with adaptive transmission rate and power control so as to maximize total profit of all assigned jobs and prevent interference.
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Scheduling Problem Assumptions
Each job is associated with a single data item that needs to be transmitted Schedule transmission at discrete timeslots Data items are transmitted in contiguous timeslots (no preemption) Channel is dedicated to a single transmission (mutual exclusion)
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Scheduling Problem Assumptions
Each job is associated with a single data item that needs to be transmitted Schedule transmission at discrete timeslots Data items are transmitted in contiguous timeslots (no preemption) Channel is dedicated to a single transmission (mutual exclusion)
Yosef Alayev et. al (CUNY)
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Scheduling Problem Assumptions
Each job is associated with a single data item that needs to be transmitted Schedule transmission at discrete timeslots Data items are transmitted in contiguous timeslots (no preemption) Channel is dedicated to a single transmission (mutual exclusion)
Yosef Alayev et. al (CUNY)
scheduling with adaptive rate/power control
May 16, 2012
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Scheduling Problem Assumptions
Each job is associated with a single data item that needs to be transmitted Schedule transmission at discrete timeslots Data items are transmitted in contiguous timeslots (no preemption) Channel is dedicated to a single transmission (mutual exclusion)
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Scenario
Figure: Clients encountering DAPs
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Transmission Range and Contact Window
Figure: Different Transmission Ranges
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Contact Window and Transmission time C = B log
P N
+1 d2
C - Channel capacity, R-Transmission Rate, where R ≤ C, P - Transmission Power, d - Transmission Range. P/N constant, R ↑, d ↓ contact-window for each job on each machine depends on transmission-rate tT = s/R tT - Transmit Time s - Data-Item Size R ↑, tT ↓ transmit-time (process-time) depends on transmission rate R increases/decreases, both contact-window and process-time decrease/increase Yosef Alayev et. al (CUNY)
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Contact Window and Transmission time (cont.)
Figure: contact window and transmission time for different rates
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Power and Contact Window
R constant, P/N ↑, d ↑ contact-window for each job on each machine depends on transmission-power P increases/decreases, contact-window increases/decreases
Problem: Interference
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Model and Notations M = {M1 , . . . , Mm } APs (indices k, ` ∈ {1, . . . , m}) J = {J1 , . . . , Jn } mobile users (indices i, j ∈ {1, . . . , n}) R = {R1 , . . . , RK } (index ρ, ρ1 , ρ2 ∈ {1, . . . , K}) P = {P1 , . . . , Pq } (index π, π1 , π2 ∈ {1, . . . , q}) rjkρπ – release time djkρπ – deadline time (djkρπ − rjkρπ ) – contact window pjkρπ – processing-time of a job wj – weight of a job I(Mk ,M` ) [P × P × R × R] – 0/1 interference matrix s, u – timeslot indices xjkρπs = 1, job j is scheduled at timeslot s, on machine k, with Rρ and Pπ 0, otherwise. Yosef Alayev et. al (CUNY)
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Model and Notations M = {M1 , . . . , Mm } APs (indices k, ` ∈ {1, . . . , m}) J = {J1 , . . . , Jn } mobile users (indices i, j ∈ {1, . . . , n}) R = {R1 , . . . , RK } (index ρ, ρ1 , ρ2 ∈ {1, . . . , K}) P = {P1 , . . . , Pq } (index π, π1 , π2 ∈ {1, . . . , q}) rjkρπ – release time djkρπ – deadline time (djkρπ − rjkρπ ) – contact window pjkρπ – processing-time of a job wj – weight of a job I(Mk ,M` ) [P × P × R × R] – 0/1 interference matrix s, u – timeslot indices xjkρπs = 1, job j is scheduled at timeslot s, on machine k, with Rρ and Pπ 0, otherwise. Yosef Alayev et. al (CUNY)
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Model and Notations M = {M1 , . . . , Mm } APs (indices k, ` ∈ {1, . . . , m}) J = {J1 , . . . , Jn } mobile users (indices i, j ∈ {1, . . . , n}) R = {R1 , . . . , RK } (index ρ, ρ1 , ρ2 ∈ {1, . . . , K}) P = {P1 , . . . , Pq } (index π, π1 , π2 ∈ {1, . . . , q}) rjkρπ – release time djkρπ – deadline time (djkρπ − rjkρπ ) – contact window pjkρπ – processing-time of a job wj – weight of a job I(Mk ,M` ) [P × P × R × R] – 0/1 interference matrix s, u – timeslot indices xjkρπs = 1, job j is scheduled at timeslot s, on machine k, with Rρ and Pπ 0, otherwise. Yosef Alayev et. al (CUNY)
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Model and Notations M = {M1 , . . . , Mm } APs (indices k, ` ∈ {1, . . . , m}) J = {J1 , . . . , Jn } mobile users (indices i, j ∈ {1, . . . , n}) R = {R1 , . . . , RK } (index ρ, ρ1 , ρ2 ∈ {1, . . . , K}) P = {P1 , . . . , Pq } (index π, π1 , π2 ∈ {1, . . . , q}) rjkρπ – release time djkρπ – deadline time (djkρπ − rjkρπ ) – contact window pjkρπ – processing-time of a job wj – weight of a job I(Mk ,M` ) [P × P × R × R] – 0/1 interference matrix s, u – timeslot indices xjkρπs = 1, job j is scheduled at timeslot s, on machine k, with Rρ and Pπ 0, otherwise. Yosef Alayev et. al (CUNY)
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Model and Notations M = {M1 , . . . , Mm } APs (indices k, ` ∈ {1, . . . , m}) J = {J1 , . . . , Jn } mobile users (indices i, j ∈ {1, . . . , n}) R = {R1 , . . . , RK } (index ρ, ρ1 , ρ2 ∈ {1, . . . , K}) P = {P1 , . . . , Pq } (index π, π1 , π2 ∈ {1, . . . , q}) rjkρπ – release time djkρπ – deadline time (djkρπ − rjkρπ ) – contact window pjkρπ – processing-time of a job wj – weight of a job I(Mk ,M` ) [P × P × R × R] – 0/1 interference matrix s, u – timeslot indices xjkρπs = 1, job j is scheduled at timeslot s, on machine k, with Rρ and Pπ 0, otherwise. Yosef Alayev et. al (CUNY)
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Model and Notations M = {M1 , . . . , Mm } APs (indices k, ` ∈ {1, . . . , m}) J = {J1 , . . . , Jn } mobile users (indices i, j ∈ {1, . . . , n}) R = {R1 , . . . , RK } (index ρ, ρ1 , ρ2 ∈ {1, . . . , K}) P = {P1 , . . . , Pq } (index π, π1 , π2 ∈ {1, . . . , q}) rjkρπ – release time djkρπ – deadline time (djkρπ − rjkρπ ) – contact window pjkρπ – processing-time of a job wj – weight of a job I(Mk ,M` ) [P × P × R × R] – 0/1 interference matrix s, u – timeslot indices xjkρπs = 1, job j is scheduled at timeslot s, on machine k, with Rρ and Pπ 0, otherwise. Yosef Alayev et. al (CUNY)
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Model and Notations M = {M1 , . . . , Mm } APs (indices k, ` ∈ {1, . . . , m}) J = {J1 , . . . , Jn } mobile users (indices i, j ∈ {1, . . . , n}) R = {R1 , . . . , RK } (index ρ, ρ1 , ρ2 ∈ {1, . . . , K}) P = {P1 , . . . , Pq } (index π, π1 , π2 ∈ {1, . . . , q}) rjkρπ – release time djkρπ – deadline time (djkρπ − rjkρπ ) – contact window pjkρπ – processing-time of a job wj – weight of a job I(Mk ,M` ) [P × P × R × R] – 0/1 interference matrix s, u – timeslot indices xjkρπs = 1, job j is scheduled at timeslot s, on machine k, with Rρ and Pπ 0, otherwise. Yosef Alayev et. al (CUNY)
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Model and Notations M = {M1 , . . . , Mm } APs (indices k, ` ∈ {1, . . . , m}) J = {J1 , . . . , Jn } mobile users (indices i, j ∈ {1, . . . , n}) R = {R1 , . . . , RK } (index ρ, ρ1 , ρ2 ∈ {1, . . . , K}) P = {P1 , . . . , Pq } (index π, π1 , π2 ∈ {1, . . . , q}) rjkρπ – release time djkρπ – deadline time (djkρπ − rjkρπ ) – contact window pjkρπ – processing-time of a job wj – weight of a job I(Mk ,M` ) [P × P × R × R] – 0/1 interference matrix s, u – timeslot indices xjkρπs = 1, job j is scheduled at timeslot s, on machine k, with Rρ and Pπ 0, otherwise. Yosef Alayev et. al (CUNY)
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Optimization Problem and IP Formulation
max
−pjkρ q djkρπ n X m X K X X X j=1 k=1 ρ=1 π=1
wj · xjkρπs
s=rjkρπ
s.t.: Pn PK Pq Ps (1) π=1 u=s−pjkρ +1 xjkρπu ≤ 1, ∀k,s ρ=1 Pj=1 P m PK Pq djkρπ −pjkρ (2) xjkρπs ≤ 1, ∀j k=1 ρ=1 Ps π=1 s=rjkρπ (3) xjkρ1 π1 s + u=s−pi`ρ +1 xi`ρ2 π2 u + Ik,` (π1 , π2 , ρ1 , ρ2 ) ≤ 2 2 ∀i,j (i 6= j), ∀π1 ,π2 ,ρ1 ,ρ2 , ∀s (4) xjkρs ∈ {0, 1} Constraints: (1) no multiple jobs are scheduled simultaneously on a single machine (2) prevent any single job from being scheduled more than once (3) prevent interference (4) restrict decision variables to integers Yosef Alayev et. al (CUNY)
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Related Work Approximating throughput of multiple machines in real-time scheduling [Bar-Noy et.al.][2001] job-dependant windows only Multi-phase algorithms for throughput maximization for real-time scheduling [Berman and DasGupta][2000] job-dependant windows only Who, When, Where:Timeslot Assignment to Mobile Clients [Fangfei et.al.][2009] job and machine dependant windows Unrelated Machine Scheduling with time-window and machine downtime constraints: An application to a naval battle-group problem[Lee and Sherali][1994] Yosef Alayev et. al (CUNY)
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Example Machines: M1 and M2 Jobs: J1 and J2 Rates: R1 and R2 end time T = 5 Eight job instances (rjkρ , djkρ , pjkρ , wj ) M1 : J1 – (1, 4, 3, 1) and (2, 4, 2, 1) J2 – (2, 5, 3, 2) and (3, 4, 2, 2)
M2 : J1 – (3, 5, 3, 1) and (3, 4, 2, 1) J2 – (0, 4, 3, 2) and (1, 3, 2, 2) Yosef Alayev et. al (CUNY)
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Example Machines: M1 and M2 Jobs: J1 and J2 Rates: R1 and R2 end time T = 5 Eight job instances (rjkρ , djkρ , pjkρ , wj ) M1 : J1 – (1, 4, 3, 1) and (2, 4, 2, 1) J2 – (2, 5, 3, 2) and (3, 4, 2, 2)
M2 : J1 – (3, 5, 3, 1) and (3, 4, 2, 1) J2 – (0, 4, 3, 2) and (1, 3, 2, 2) Yosef Alayev et. al (CUNY)
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Solution for an Example
Figure: Solution: (J1 on M1 with either R1 or R2 ) and (J2 on M2 with either R1 or R2 ).Objective: 3
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Algorithms k-Admission (Bar-Noy 2001) Accept jobs machine by machine earliest finish time first Criterion: W – total weight of all scheduled jobs overlapping with the current job j. Accept job j if wj > W · β, for some constant β Can be √ extended to machine+rate dependent time windows 3 + 2 2-approximation guarantee still holds Easily extendable to centralized-online Global-Admission
Two-Phase (Berman 2000) phase-1: evaluation phase (pushes candidate intervals on a stack) phase-2: selection phase (schedules selected intervals) Can be extended to machine+rate dependent time windows 2-approximation guarantee still holds Can be extended to machine+rate+power dependent time windows 2 + I-approximation
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Algorithm I - All-Rates k-Admission
Enumerate all possible job instances with all different combinations of (j, k, ρ, s). Run k-Admission algorithm. Approximation guarantee of 3 + 2
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p (2).
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Algorithm II - Max-Ratio Rate-selection k-Admission
Find one rate for each job-DAP pair based on contact-window to processing-time ratio. d −r ρ∗j,k = argρ max jkρpjkρjkρ Enumerate all job instances with the chosen rate with all different combinations of (j, k, ρ∗j,k , s). Run k-Admission algorithm.
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Algorithm III - All-Rates 2PA
Enumerate all possible job instances with all different combinations of (j, k, ρ, s). Run 2PA. Approximation guarantee of 2.
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Algorithm IV - All-Powers 2PA-PC
Enumerate all possible job instances with all different combinations of (j, k, ρ, π, s). Run 2PA-PC. Approximation guarantee of 2 + I.
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Simulation settings R = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} P = {100, 125, 150, 175, 200} Separation between APs vary Use Random Waypoint model for cars with different speeds contact windows are calculated using Shannon’s formula data sizes are uniformly distributed in [0, 10] weights - Zipf distributed with α = 2 clipped by [1,10] window Bandwidth is 20Mbps Interference matrix is calculated using protocol model
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Experiment 3
Figure: Rate-Controlled throughput with 1 AP Yosef Alayev et. al (CUNY)
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Experiment 4
Figure: Rate-Controlled throughput for convoy Yosef Alayev et. al (CUNY)
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Experiment 6
Figure: Rate-Controlled throughput for a grid Yosef Alayev et. al (CUNY)
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Experiment 8
Figure: Power-Controlled throughput for 1AP Yosef Alayev et. al (CUNY)
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Experiment 9
Figure: Power-Controlled throughput for convoy Yosef Alayev et. al (CUNY)
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Thank You
Questions???
[email protected]
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