Block-Structured Supermarket Models
Quan-Lin Li, John C.S. Lui

TL;DR
This paper develops a generalized matrix-analytic approach for analyzing supermarket queueing models with non-Poisson arrivals and non-exponential service times, providing new insights into their performance characteristics.
Contribution
It introduces a novel combination of matrix-analytic methods, operator semigroup, and mean-field limit to analyze complex supermarket models with MAPs and PH distributions.
Findings
Derived an infinite-dimensional differential system for expected queue fractions.
Established invariance of environment factors in the model.
Computed fixed points to evaluate system performance.
Abstract
Supermarket models are a class of parallel queueing networks with an adaptive control scheme that play a key role in the study of resource management of, such as, computer networks, manufacturing systems and transportation networks. When the arrival processes are non-Poisson and the service times are non-exponential, analysis of such a supermarket model is always limited, interesting, and challenging. This paper describes a supermarket model with non-Poisson inputs: Markovian Arrival Processes (MAPs) and with non-exponential service times: Phase-type (PH) distributions, and provides a generalized matrix-analytic method which is first combined with the operator semigroup and the mean-field limit. When discussing such a more general supermarket model, this paper makes some new results and advances as follows: (1) Providing a detailed probability analysis for setting up an…
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Taxonomy
TopicsAdvanced Queuing Theory Analysis · Probability and Risk Models · Transportation Planning and Optimization
