Stochastic Modeling and Approaches for Managing Energy Footprints in Cloud Computing Service Siqian Shen Assistant Professor Industrial and Operations Engineering University of Michigan October 8, 2013 Shen, Wang (UMich) Cloud Computing Service Management 1/30
Emerging Trends of Cloud Computing (CC) Source: www.cloudtweaks.com by David Fletcher Shen, Wang (UMich) Cloud Computing Service Management 2/30
CC Advantages: Reducing Carbon Emission Source: Accenture (2010) “Cloud Computing and Sustainability: Environmental Benefits of Moving to the Cloud” Shen, Wang (UMich) Cloud Computing Service Management 3/30
How CC Works... Source: www.veterangeek.com Shen, Wang (UMich) Cloud Computing Service Management 4/30
How CC Works... Source: www.veterangeek.com Shen, Wang (UMich) Cloud Computing Service Management 4/30
Motivation Server Utilization in Google Moreover, an idle server consumes 60%+ energy at full mode. Shen, Wang (UMich) Cloud Computing Service Management 5/30
Virtual Machine Consolidation Large-scale servers with Consolidate the work to low utilization fewer Cloud servers Source: Google’s official blog - Energy efficiency in the cloud. Our data centers use 50% less energy than typical data centers through server (Virtual Machine) consolidation. — Google. Other benefits: more robust operations schedules more idle servers reacting to demand surges Shen, Wang (UMich) Cloud Computing Service Management 6/30
Our Work Stochastic mixed-integer programming models to optimize energy footprints while ensure various Quality of Service (QoS) guarantees for managing servers in Cloud Computing service. Shen, Wang (UMich) Cloud Computing Service Management 7/30
Our Work Stochastic mixed-integer programming models to optimize energy footprints while ensure various Quality of Service (QoS) guarantees for managing servers in Cloud Computing service. Estimate demand based on distributions of historical data, and dynamically consolidate or distribute jobs on servers through operational scheduling. Shen, Wang (UMich) Cloud Computing Service Management 7/30
Our Work Stochastic mixed-integer programming models to optimize energy footprints while ensure various Quality of Service (QoS) guarantees for managing servers in Cloud Computing service. Estimate demand based on distributions of historical data, and dynamically consolidate or distribute jobs on servers through operational scheduling. Vary QoS levels by using joint/multiple chance constraints, to bound chances of job delay and incompleteness. Shen, Wang (UMich) Cloud Computing Service Management 7/30
Our Work Stochastic mixed-integer programming models to optimize energy footprints while ensure various Quality of Service (QoS) guarantees for managing servers in Cloud Computing service. Estimate demand based on distributions of historical data, and dynamically consolidate or distribute jobs on servers through operational scheduling. Vary QoS levels by using joint/multiple chance constraints, to bound chances of job delay and incompleteness. Shen, Wang (UMich) Cloud Computing Service Management 7/30
Outline of Our Research Formulations: Stochastic & Chance-Constrained Programs Algorithms: the Benders Decomposition and Heuristics Computational Design Result Analyses Conclusions and Future Research Shen, Wang (UMich) Cloud Computing Service Management 8/30
Model 1: No Backlogging Parameter N m set of servers in a data center Shen, Wang (UMich) Cloud Computing Service Management 9/30
Model 1: No Backlogging Parameter N m set of servers in a data center Ω set of finite scenarios for realizing uncertain demand Shen, Wang (UMich) Cloud Computing Service Management 9/30
Model 1: No Backlogging Parameter N m set of servers in a data center Ω set of finite scenarios for realizing uncertain demand T total number of time periods considered ℓ t length of period t (in hours) for all t = 1 , . . . , T Shen, Wang (UMich) Cloud Computing Service Management 9/30
Model 1: No Backlogging Parameter N m set of servers in a data center Ω set of finite scenarios for realizing uncertain demand T total number of time periods considered ℓ t length of period t (in hours) for all t = 1 , . . . , T � d t random job requests (demand) received at period t Shen, Wang (UMich) Cloud Computing Service Management 9/30
Model 1: No Backlogging Parameter N m set of servers in a data center Ω set of finite scenarios for realizing uncertain demand T total number of time periods considered ℓ t length of period t (in hours) for all t = 1 , . . . , T � d t random job requests (demand) received at period t Shen, Wang (UMich) Cloud Computing Service Management 9/30
Model 1: No Backlogging Formulation T � � ( g i y t i + v i x t i + f i z t min: i ) (1a) t =1 i ∈N m � i ≥ � e i ℓ t x t d t s.t. ∀ 1 ≤ t ≤ T (1b) i ∈N m ℓ t x t i + s i y t i ≤ ℓ t z t ∀ i ∈ N m , 1 ≤ t ≤ T (1c) i y 1 i ≥ z 1 ∀ i ∈ N m (1d) i i − z t − 1 y t i ≥ z t ∀ i ∈ N m , 2 ≤ t ≤ T (1e) i 0 ≤ x t i ≤ 1 ∀ i ∈ N m , 1 ≤ t ≤ T (1f) y t i , z t i ∈ { 0 , 1 } ∀ i ∈ N m , 1 ≤ t ≤ T (1g) The basic model consolidates demand on severs to minimize the total energy consumed by all servers over t = 1 , . . . , T. Shen, Wang (UMich) Cloud Computing Service Management 10/30
Model 1: No Backlogging Formulation T � � ( g i y t i + v i x t i + f i z t min: i ) (1a) t =1 i ∈N m � i ≥ � e i ℓ t x t d t s.t. ∀ 1 ≤ t ≤ T (1b) i ∈N m ℓ t x t i + s i y t i ≤ ℓ t z t ∀ i ∈ N m , 1 ≤ t ≤ T (1c) i y 1 i ≥ z 1 ∀ i ∈ N m (1d) i i − z t − 1 y t i ≥ z t ∀ i ∈ N m , 2 ≤ t ≤ T (1e) i 0 ≤ x t i ≤ 1 ∀ i ∈ N m , 1 ≤ t ≤ T (1f) y t i , z t i ∈ { 0 , 1 } ∀ i ∈ N m , 1 ≤ t ≤ T (1g) g i y t i : energy used for booting machine i at period t . y t i ∈ { 0 , 1 } : = 1 if server i is switched to “on” at period t . Shen, Wang (UMich) Cloud Computing Service Management 10/30
Model 1: No Backlogging Formulation T � � ( g i y t i + v i x t i + f i z t min: i ) (1a) t =1 i ∈N m � i ≥ � e i ℓ t x t d t s.t. ∀ 1 ≤ t ≤ T (1b) i ∈N m ℓ t x t i + s i y t i ≤ ℓ t z t ∀ i ∈ N m , 1 ≤ t ≤ T (1c) i y 1 i ≥ z 1 ∀ i ∈ N m (1d) i i − z t − 1 y t i ≥ z t ∀ i ∈ N m , 2 ≤ t ≤ T (1e) i 0 ≤ x t i ≤ 1 ∀ i ∈ N m , 1 ≤ t ≤ T (1f) y t i , z t i ∈ { 0 , 1 } ∀ i ∈ N m , 1 ≤ t ≤ T (1g) v i x t i : energy for job processing in machine i at period t . x t i ≥ 0: percentage of server i ’s capacity used at period t . Shen, Wang (UMich) Cloud Computing Service Management 10/30
Model 1: No Backlogging Formulation T � � ( g i y t i + v i x t i + f i z t min: i ) (1a) t =1 i ∈N m � i ≥ � e i ℓ t x t d t s.t. ∀ 1 ≤ t ≤ T (1b) i ∈N m ℓ t x t i + s i y t i ≤ ℓ t z t ∀ i ∈ N m , 1 ≤ t ≤ T (1c) i y 1 i ≥ z 1 ∀ i ∈ N m (1d) i i − z t − 1 y t i ≥ z t ∀ i ∈ N m , 2 ≤ t ≤ T (1e) i 0 ≤ x t i ≤ 1 ∀ i ∈ N m , 1 ≤ t ≤ T (1f) y t i , z t i ∈ { 0 , 1 } ∀ i ∈ N m , 1 ≤ t ≤ T (1g) f i z t i : energy used at “idle” of machine i at period t . z t i ∈ { 0 , 1 } : = 1 if server i is “idle” at period t . Shen, Wang (UMich) Cloud Computing Service Management 10/30
Model 1: No Backlogging Formulation T � � ( g i y t i + v i x t i + f i z t min: i ) (1a) t =1 i ∈N m � i ≥ � e i ℓ t x t d t s.t. ∀ 1 ≤ t ≤ T (1b) i ∈N m ℓ t x t i + s i y t i ≤ ℓ t z t ∀ i ∈ N m , 1 ≤ t ≤ T (1c) i y 1 i ≥ z 1 ∀ i ∈ N m (1d) i i − z t − 1 y t i ≥ z t ∀ i ∈ N m , 2 ≤ t ≤ T (1e) i 0 ≤ x t i ≤ 1 ∀ i ∈ N m , 1 ≤ t ≤ T (1f) y t i , z t i ∈ { 0 , 1 } ∀ i ∈ N m , 1 ≤ t ≤ T (1g) Computational time allocated to each period t is no less than the random demand � d t . Shen, Wang (UMich) Cloud Computing Service Management 10/30
Model 1: No Backlogging Formulation T � � ( g i y t i + v i x t i + f i z t min: i ) (1a) t =1 i ∈N m � i ≥ � e i ℓ t x t d t s.t. ∀ 1 ≤ t ≤ T (1b) i ∈N m ℓ t x t i + s i y t i ≤ ℓ t z t ∀ i ∈ N m , 1 ≤ t ≤ T (1c) i y 1 i ≥ z 1 ∀ i ∈ N m (1d) i i − z t − 1 y t i ≥ z t ∀ i ∈ N m , 2 ≤ t ≤ T (1e) i 0 ≤ x t i ≤ 1 ∀ i ∈ N m , 1 ≤ t ≤ T (1f) y t i , z t i ∈ { 0 , 1 } ∀ i ∈ N m , 1 ≤ t ≤ T (1g) d t is discretely distributed, If � Shen, Wang (UMich) Cloud Computing Service Management 10/30
Model 1: No Backlogging Formulation T � � ( g i y t i + v i x t i + f i z t min: i ) (1a) t =1 i ∈N m � e i ℓ t x t ω ∈ Ω d tω s.t. i ≥ max ∀ 1 ≤ t ≤ T (1b) i ∈N m ℓ t x t i + s i y t i ≤ ℓ t z t ∀ i ∈ N m , 1 ≤ t ≤ T (1c) i y 1 i ≥ z 1 ∀ i ∈ N m (1d) i i − z t − 1 y t i ≥ z t ∀ i ∈ N m , 2 ≤ t ≤ T (1e) i 0 ≤ x t i ≤ 1 ∀ i ∈ N m , 1 ≤ t ≤ T (1f) y t i , z t i ∈ { 0 , 1 } ∀ i ∈ N m , 1 ≤ t ≤ T (1g) d t is discretely distributed, and let d tω represent a realization of � d t in If � scenario ω ∈ Ω, reformulate (1b) as a set of deterministic constraints Shen, Wang (UMich) Cloud Computing Service Management 10/30
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