M/G/1-Type Markov Processes: A Tutorial
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
Analysis on queueing systems with synchronous vacations of partial servers
Performance Evaluation
iBOM: A Platform for Intelligent Business Operation Management
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Analysis of a Multiserver Queue with Setup Times
Queueing Systems: Theory and Applications
Dynamo: amazon's highly available key-value store
Proceedings of twenty-first ACM SIGOPS symposium on Operating systems principles
Multi-mode energy management for multi-tier server clusters
Proceedings of the 17th international conference on Parallel architectures and compilation techniques
PowerNap: eliminating server idle power
Proceedings of the 14th international conference on Architectural support for programming languages and operating systems
NapSAC: design and implementation of a power-proportional web cluster
Proceedings of the first ACM SIGCOMM workshop on Green networking
Performance Evaluation
Optimality analysis of energy-performance trade-off for server farm management
Performance Evaluation
Triangular M/G/1-Type and Tree-Like Quasi-Birth-Death Markov Chains
INFORMS Journal on Computing
A distributional form of Little's Law
Operations Research Letters
Are sleep states effective in data centers?
IGCC '12 Proceedings of the 2012 International Green Computing Conference (IGCC)
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The M/M/k/setup model, where there is a penalty for turning servers on, is common in data centers, call centers and manufacturing systems. Setup costs take the form of a time delay, and sometimes there is additionally a power penalty, as in the case of data centers. While the M/M/1/setup was exactly analyzed in 1964, no exact analysis exists to date for the M/M/k/setup with k1. In this paper we provide the first exact, closed-form analysis for the M/M/k/setup and some of its important variants including systems in which idle servers delay for a period of time before turning off or can be put to sleep. Our analysis is made possible by our development of a new technique, Recursive Renewal Reward (RRR), for solving Markov chains with a repeating structure. RRR uses ideas from renewal reward theory and busy period analysis to obtain closed-form expressions for metrics of interest such as the transform of time in system and the transform of power consumed by the system. The simplicity, intuitiveness, and versatility of RRR makes it useful for analyzing Markov chains far beyond the M/M/k/setup. In general, RRR should be used to reduce the analysis of any 2-dimensional Markov chain which is infinite in at most one dimension and repeating to the problem of solving a system of polynomial equations. In the case where all transitions in the repeating portion of the Markov chain are skip-free and all up/down arrows are unidirectional, the resulting system of equations will yield a closed-form solution.