Priority queues with setup times
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On a batch arrival Poisson queue with a random setup time and vacation period
Computers and Operations Research
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Queueing Systems: Theory and Applications
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FAST'08 Proceedings of the 6th USENIX Conference on File and Storage Technologies
Service center trade-offs between customer impatience and power consumption
Performance Evaluation
Modeling and analyzing power management policies in server farms using stochastic Petri nets
Proceedings of the 3rd International Conference on Future Energy Systems: Where Energy, Computing and Communication Meet
Energy-performance trade-off in dense WLANs: A queuing study
Computer Networks: The International Journal of Computer and Telecommunications Networking
Trading power consumption against performance by reserving blocks of servers
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Trading power consumption against performance by reserving blocks of servers
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Exact analysis of the M/M/k/setup class of Markov chains via recursive renewal reward
Proceedings of the ACM SIGMETRICS/international conference on Measurement and modeling of computer systems
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ACM SIGOPS Operating Systems Review
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In this paper we consider server farms with a setup cost. This model is common in manufacturing systems and data centers, where there is a cost to turn servers on. Setup costs always take the form of a time delay, and sometimes there is additionally a power penalty, as in the case of data centers. Any server can be either on, off, or in setup mode. While prior work has analyzed single servers with setup costs, no analytical results are known for multi-server systems. In this paper, we derive the first closed-form solutions and approximations for the mean response time and mean power consumption in server farms with setup costs. We also analyze variants of server farms with setup, such as server farm models with staggered boot up of servers, where at most one server can be in setup mode at a time, or server farms with an infinite number of servers. For some variants, we find that the distribution of response time can be decomposed into the sum of response time for a server farm without setup and the setup time. Finally, we apply our analysis to data centers, where both response time and power consumption are key metrics. Here we analyze policy design questions such as whether it pays to turn servers off when they are idle, whether staggered boot up helps, how to optimally mix policies, and other questions related to the optimal data center size.