Multi-Server Queueing Systems with Multiple Priority Classes
Queueing Systems: Theory and Applications
Closed form solutions for mapping general distributions to quasi-minimal PH distributions
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
How many servers are best in a dual-priority M/PH/k system?
Performance Evaluation
Stochastic analysis of multiserver systems
ACM SIGMETRICS Performance Evaluation Review
The twin measure for queueing system predictability
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
On the twin measure and queueing systems predictability
Performance Evaluation
An advanced queueing model to analyze appointment-driven service systems
Computers and Operations Research
A performance modeling scheme for multistage switch networks with phase-type and bursty traffic
IEEE/ACM Transactions on Networking (TON)
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The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chains (DR). Moment matching algorithms allow us to approximate a general distribution with a phase type (PH) distribution. Our moment matching algorithms improve upon existing ones with respect to the computational efficiency (we provide closed form solutions) as well as the quality and generality of the solution (the first three moments of almost any nonnegative distribution are matched). Approximating job size and interarrival time distributions by PH distributions enables modeling a multiserver system by a Markov chain, so that the performance of the system is given by analyzing the Markov chain. However, when the multiserver system involves resource sharing or prioritization, the Markov chain often has a multidimensionally infinite state space, which makes the analysis computationally hard. DR allows us to closely approximate a multidimensionally infinite Markov chain with a Markov chain on a one-dimensionally infinite state space, which can be analyzed efficiently. We validate the accuracy of DR against simulation. Further, we formally define two classes of multidimensionally infinite Markov chains, called recursive foreground-background processes and generalized foreground-background processes (RFB/GFB processes), and analyze the RFB/GFB process via DR. The definition of the RFB/GFB process enables one to easily identify whether a given multiserver system can be analyzed via DR, and our analysis of the RFB/GFB process enables the immediate analysis of a multiserver system by simply modeling it as an RFB/GFB process. These new analytical tools enable us to analyze the performance of many multiserver systems with resource sharing or prioritization for the first time. For example, we study the benefit and penalty of cycle stealing, the effectiveness of prioritization and threshold-based resource allocation policies for multiserver systems, and the impact of job size variability and irregularity of arrival processes on the response time in multiserver systems. Our analysis results in lessons on the design of good resource allocation policies for multiserver systems.