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Utility Optimization for Event-Driven Distributed Infrastructures Cristian Lumezanu University of Maryland, College Park Sumeer BholaMark Astley IBM T.J. Watson Research Center

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 2 Event Driven Infrastructure EVENT DRIVEN INFRASTRUCTURE Producers Consumers

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 3 Event Driven Infrastructure Consumers Producers Flow Publish/subscribe Stream processing overlays Enterprise Service Bus

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 4 Flows and Consumer Classes Consumers MAXIMIZE SYSTEM UTILITY Flow Consumers Producers Flow FLOW 1 Rate: r 1 FLOW 2 Rate: r 2 CONSUMER CLASS 1 Number of consumers: n 1 Utility: U 1 (r 1 ) CONSUMER CLASS 2 Number of consumers: n 2 Utility: U 2 (r 2 )

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 5 Model Summary Network of nodes interconnected by links Flows and classes of consumers Control variables: Flow rates (for rate control) Number of consumers (for admission control) Utility function Associated with each consumer Depends on the rate of the flow that serves the consumer Assumed to be strictly concave

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 6 Optimization Problem Consumers Producers Flow LINK CONSTRAINT NODE CONSTRAINT Find the rate allocation and the number of consumers such that the total utility of the system is maximized and the constraints are satisfied OBJECTIVE

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 7 Optimization Problems LINK CONSTRAINT NODE CONSTRAINT Find the rate allocation and the number of consumers such that the total utility of the system is maximized and the constraints are satisfied SYSTEM UTILITY Optimization depends on both rate allocation and consumer allocation System utility not concave Constraint set not convex

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 8 LRGP LAGRANGIAN RATES, GREEDY POPULATIONS Finds the optimal rates for each flow at a certain moment given a constant number of consumers Finds the optimal number of consumers for each class at a certain moment given constant flow rates OPTIMIZATION PROBLEM RATE ALLOCATION CONSUMER ALLOCATION PRICE COMPUTATION Makes trade-offs between rate control and admission control

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 9 Consumer Allocation Increasing the number of consumers has a local effect on the system 1. Sort classes in decreasing order of their benefit/cost ratio 2. Allocate consumers for each class in the order established above until the node constraint is violated

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 10 Rate Allocation Increasing the flow rates has a global effect on the system

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 11 Prices associated with each resource (node, link) reflect how congested the resource is provide a way to control the rate Node Price implements a trade-off between increasing the number of consumers and increasing the rate reflects the maximum benefit/cost ratio of the node Link Price adjusted using a gradient projection algorithm (Low et al.)

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 12 LRGP 1. Each node resource performs local consumer allocation2. Each resource computes a new price… 3. …and sends it to the sources of the flows that go through the resource 4. Each source computes a new rate for its flow…5. …and sends the rate to all nodes and links in the path of the flow 1. Each node resource performs local consumer allocation 2. Each resource computes a new price… 3. …and sends it to the sources of the flows that go through the resource 4. Each source computes a new rate for its flow…

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 13 Results Several workloads Several utility functions CONVERGENCE How fast does it reach the result? LRGP converges in less than 50 iterations OPTIMALITY How good is the result? LRGP achieves better utility than a centralized simulated annealing algorithm

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 14 Convergence

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 15 Convergence Adaptive : Incremental increase, multiplicative decrease

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 16 Optimality ITERATIONS UNTIL CONVERGENCE the number of iterations until convergence does not vary with an increase in the number of flows or consumers ROBUSTNESS recovers quickly when flows or consumers are removed UTILITY comparison with a centralized simulated annealing (SA) algorithm 6 different workloads LRGP finds a utility between 6.47% and 18.75% higher than SA

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 17 Conclusions and Future Work CONCLUSIONS distributed algorithm for optimizing utility in an event-driven infrastructure greedy approach to control the consumers + Lagrangian approach to control the rates prices make trade-offs between admission control and rate control simulation results show good convergence and scalability FUTURE WORK other utility functions asynchronous algorithm other types of resources implementation

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 18 Questions

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 19 Dual Problem

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 20 Dual Problem the r that maximizes the system utility, also maximizes L L concave, thus it has only one maximum, given by: Find the rate allocation and the prices such that D(p e,p l ) is minimized

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Utility Optimization for Event-Driven Distributed Infrastructures ICDCS 2006 21 Recovery / Different utility Recovery from system changesClass utility is

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