Schedulability Analysis for Fixed Priority Real-Time Systems with - PowerPoint PPT Presentation

Schedulability Analysis for Fixed Priority Real-Time Systems with Energy- Harvesting ım 1 Younes Chandarli 1 , 2 Rob Davis 3 Damien Masson 1 Yasmina Abdedda¨ ( 1 ) Universit´ e Paris-Est, LIGM UMR CNRS 8049, ESIEE Paris, France ( 2 ) Universit´ e Paris-Est, LIGM UMR CNRS 8049, Universit´ e Paris-Est Marne-La-Vall´ ee, France ( 3 ) Real-Time Systems Research Group, University of York RTNS’14, 10 October 2014 1 / 25

Outline Motivation 1 Model 2 Schedulability Analysis 3 Experiments 4 Conclusion and Future Work 5 2 / 25

Environmental Harvesting Replenishing Consuming Energy Harvester Storage Unit Real-Time system Energy Source Reusable Alkaline Sensing tasks Sun Solar Panel Battery Li-ion polymer Data Processing Wind Turbine Wind Battery Tasks Piezoelectric Vibrations Transmission Supercapacitor Harvester tasks . . . . . . . . . . . . Motivation Energy Harvesting Systems Energy-Harvesting The process by which energy is captured from a system’s environment and converted into usable electric power. 3 / 25

Motivation Energy Harvesting Systems Energy-Harvesting The process by which energy is captured from a system’s environment and converted into usable electric power. Environmental Harvesting Replenishing Consuming Real-Time system Energy Harvester Storage Unit Energy Source Reusable Alkaline Sensing tasks Sun Solar Panel Battery Data Processing Li-ion polymer Wind Turbine Wind Tasks Battery Piezoelectric Vibrations Transmission Supercapacitor Harvester tasks . . . . . . . . . . . . 3 / 25

Model Energy Model Energy Storage Unit E max P r ( t ) Energy Source Harvester E ( t ) E min Energy Source Model Energy Sources: solar, thermal, mechanical, vibration, . . . Harvester: transform the environmental energy into electrical power. Energy Storage Unit Model Energy Unit: battery, super-capacitor, . . . Store the harvested energy: P r ( t ) is the energy replenishment function. Constant rate of replenishment: P r ( t ) = P r The energy stored may vary between two levels E min and E max . 4 / 25

Model Energy Model Energy Storage Unit E max Energy Source P r Harvester E ( t ) E min Energy Source Model Energy Sources: solar, thermal, mechanical, vibration, . . . Harvester: transform the environmental energy into electrical power. Energy Storage Unit Model Energy Unit: battery, super-capacitor, . . . Store the harvested energy: P r ( t ) is the energy replenishment function. Constant rate of replenishment: P r ( t ) = P r The energy stored may vary between two levels E min and E max . 4 / 25

Model Task Model Energy Storage Unit E max Energy Source P r Harvester E ( t ) E min Processor Real−time Tasks A set of sporadic tasks τ i ( C i , P i , E i , T i , D i ) C i : worst-case execution time, P i : worst-case power consumption, E i = P i × C i : worst-case energy consumption, T i : minimal inter arrival time, D i : relative deadline ( D i ≤ T i ). 5 / 25

Model The Model Energy Storage Unit Emax Energy Source Pr Harvester E ( t ) Emin P r = 3 E max = 3 E min = 0 Processor τ 1 : C 1 = 2 P 1 = 6 E 1 = 12 T 1 = D 1 = 4 Real−time Tasks τ 2 : C 2 = 1 P 2 = 1 E 2 = 1 T 2 = D 2 = 5 energy E max 3 2 1 E min 0 1 2 3 4 5 6 time τ 1 τ 2 6 / 25

Model The Model Energy Storage Unit Emax Energy Source Pr Harvester E ( t ) Emin P r = 3 E max = 3 E min = 0 Processor τ 1 : C 1 = 2 P 1 = 6 E 1 = 12 T 1 = D 1 = 4 Real−time Tasks τ 2 : C 2 = 1 P 2 = 1 E 2 = 1 T 2 = D 2 = 5 energy E max 3 2 1 E min 0 1 2 3 4 5 6 time τ 1 τ 2 6 / 25

Model The Model Energy Storage Unit Emax Energy Source Pr Harvester E ( t ) Emin P r = 3 E max = 3 E min = 0 Processor τ 1 : C 1 = 2 P 1 = 6 E 1 = 12 T 1 = D 1 = 4 Real−time Tasks τ 2 : C 2 = 1 P 2 = 1 E 2 = 1 T 2 = D 2 = 5 energy E max 3 2 1 E min 0 1 2 3 4 5 6 time τ 1 τ 2 Consuming Task: P 1 > P r 6 / 25

Model The Model Energy Storage Unit Emax Energy Source Pr Harvester E ( t ) Emin P r = 3 E max = 3 E min = 0 Processor τ 1 : C 1 = 2 P 1 = 6 E 1 = 12 T 1 = D 1 = 4 Real−time Tasks τ 2 : C 2 = 1 P 2 = 1 E 2 = 1 T 2 = D 2 = 5 energy E max 3 2 1 E min 0 1 2 3 4 5 6 time τ 1 τ 2 Consuming Task: P 1 > P r 6 / 25

Model The Model Energy Storage Unit Emax Energy Source Pr Harvester E ( t ) Emin P r = 3 E max = 3 E min = 0 Processor τ 1 : C 1 = 2 P 1 = 6 E 1 = 12 T 1 = D 1 = 4 Real−time Tasks τ 2 : C 2 = 1 P 2 = 1 E 2 = 1 T 2 = D 2 = 5 energy E max 3 2 1 E min 0 1 2 3 4 5 6 time τ 1 τ 2 Consuming Task: P 1 > P r 6 / 25

Model The Model Energy Storage Unit Emax Energy Source Pr Harvester E ( t ) Emin P r = 3 E max = 3 E min = 0 Processor τ 1 : C 1 = 2 P 1 = 6 E 1 = 12 T 1 = D 1 = 4 Real−time Tasks τ 2 : C 2 = 1 P 2 = 1 E 2 = 1 T 2 = D 2 = 5 energy E max 3 2 1 E min 0 1 2 3 4 5 6 time τ 1 τ 2 Consuming Task: P 1 > P r Gaining Task: P 2 ≤ P r 6 / 25

Model The Scheduling Problem The Model Storage Unit: Constant rate replenishment P r and E max , E min the maximal and minimal level of energy. A set Γ = Γ c ∪ Γ g of sporadic tasks τ i = ( C i , P i , E i , T i , D i ) in priority order with D i ≤ T i : Consuming Tasks: Γ c = { τ i ∈ Γ , P i > P r } Gaining Tasks: Γ g = { τ i ∈ Γ , 0 ≤ P i ≤ P r } Feasibility A task set is feasible if all the tasks meet their deadlines: timing constraints and ∀ t ≥ 0 the energy level is between E min and E max : energy constraints . 7 / 25

Model Related Work An algorithm for Frame-Based Model, A. Allavena and D. Moss´ e, “Scheduling of Frame-based Embedded Systems with Rechargeable Batteries”, Workshop in conjunction with RTAS, 2001. LSA Algorithm assumes variable execution time, C. Moser, D. Brunelli, L. Thiele and L. Benini, “Real-time scheduling with regenerative energy”, ECRTS, 2006. EDeg Algorithm based on EDF priority assignment. H. EL Ghor, M. Chetto and R. Chehade, “A real-time scheduling framework for embedded systems with environmental energy harvesting”, Computers & Electrical Engineering journal, 2011. PFP ASAP Algorithm 8 / 25

Model Related Work An algorithm for Frame-Based Model, A. Allavena and D. Moss´ e, “Scheduling of Frame-based Embedded Systems with Rechargeable Batteries”, Workshop in conjunction with RTAS, 2001. LSA Algorithm assumes variable execution time, C. Moser, D. Brunelli, L. Thiele and L. Benini, “Real-time scheduling with regenerative energy”, ECRTS, 2006. EDeg Algorithm based on EDF priority assignment. H. EL Ghor, M. Chetto and R. Chehade, “A real-time scheduling framework for embedded systems with environmental energy harvesting”, Computers & Electrical Engineering journal, 2011. PFP ASAP Algorithm Y. Abdedda¨ ım, Y. Chandarli and D. Masson, “The Optimality of PFP ASAP Algorithm for Fixed-Priority Energy-Harvesting Real-Time Systems”, ECRTS, 2013. 8 / 25

Model The PFP ASAP Algorithm Execute tasks whenever there is enough energy available in the battery. Replenish as long as needed to execute one time unit of the highest priority active task. PFP ASAP is an Energy Work-Conserving FPPS Algorithm The processor is idle only if there is insufficient energy to schedule at least one time unit of the highest priority active task. Optimality PFP ASAP is optimal in the class of energy work conserving fixed priority pre-emptive scheduling algorithms in the case where all the task consume energy ( Γ = Γ c ). Our Goal Provide a schedulability test for PFP ASAP when the set of tasks is composed of both consuming and gaining tasks. 9 / 25

Model The PFP ASAP Algorithm Execute tasks whenever there is enough energy available in the battery. Replenish as long as needed to execute one time unit of the highest priority active task. PFP ASAP is an Energy Work-Conserving FPPS Algorithm The processor is idle only if there is insufficient energy to schedule at least one time unit of the highest priority active task. Optimality PFP ASAP is optimal in the class of energy work conserving fixed priority pre-emptive scheduling algorithms in the case where all the task consume energy ( Γ = Γ c ). Our Goal Provide a schedulability test for PFP ASAP when the set of tasks is composed of both consuming and gaining tasks. 9 / 25

Schedulability Analysis Classical Response Time Analysis Method Find the wost-case scenario: scenario where τ i is subject to the 1 maximum possible delay, Compute R i the longest response time of task τ i : is the response time of 2 τ i in the worst-case scenario, Exact schedulability test: If ∀ τ i , R i ≤ D i the task set is schedulable. 3 Work-Conserving FPPS with D i ≤ T i Worst-case scenario for task τ i : Synchronous release of all the tasks, 1 R i is given by the smallest t > 0 that satisfies t = F ( i , t ) with: 2 F ( i , t ) = C i + Maximum interference from higher priority tasks in [ 0 , t ) � t � � F ( i , t ) = × C h T h h ≤ i 10 / 25