IEEE Transactions on Computers
The state of the art in locally distributed Web-server systems
ACM Computing Surveys (CSUR)
State space collapse with application to heavy traffic limits for multiclass queueing networks
Queueing Systems: Theory and Applications
Strong approximations for Markovian service networks
Queueing Systems: Theory and Applications
IEEE Transactions on Software Engineering
SRPT Scheduling for Web Servers
JSSPP '01 Revised Papers from the 7th International Workshop on Job Scheduling Strategies for Parallel Processing
Connection scheduling in web servers
USITS'99 Proceedings of the 2nd conference on USENIX Symposium on Internet Technologies and Systems - Volume 2
Steady state approximations of limited processor sharing queues in heavy traffic
Queueing Systems: Theory and Applications
Dynamic thread assignment in web server performance optimization
Performance Evaluation
Rate stability and output rates in queueing networks with shared resources
Performance Evaluation
Law of Large Number Limits of Limited Processor-Sharing Queues
Mathematics of Operations Research
Tail-robust scheduling via limited processor sharing
Performance Evaluation
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We investigate a computer network consisting of two layers occurring in, for example, application servers. The first layer incorporates the arrival of jobs at a network of multi-server nodes, which we model as a many-server Jackson network. At the second layer, active servers at these nodes act now as customers who are served by a common CPU. Our main result shows a separation of time scales in heavy traffic: the main source of randomness occurs at the (aggregate) CPU layer; the interactions between different types of nodes at the other layer is shown to converge to a fixed point at a faster time scale; this also yields a state-space collapse property. Apart from these fundamental insights, we also obtain an explicit approximation for the joint law of the number of jobs in the system, which is provably accurate for heavily loaded systems and performs numerically well for moderately loaded systems. The obtained results for the model under consideration can be applied to thread-pool dimensioning in application servers, while the technique seems applicable to other layered systems too.