Research Article
The Asymmetric Join the Shortest Orbit Queue: Analysis via a Dimensionality Reduction
@INPROCEEDINGS{10.1007/978-3-031-31234-2_11, author={Ioannis Dimitriou}, title={The Asymmetric Join the Shortest Orbit Queue: Analysis via a Dimensionality Reduction}, proceedings={Performance Evaluation Methodologies and Tools. 15th EAI International Conference, VALUETOOLS 2022, Virtual Event, November 2022, Proceedings}, proceedings_a={VALUETOOLS}, year={2023}, month={5}, keywords={Asymmetric Join the Shortest Orbit Queue Retrials Compensation Method}, doi={10.1007/978-3-031-31234-2_11} }- Ioannis Dimitriou
Year: 2023
The Asymmetric Join the Shortest Orbit Queue: Analysis via a Dimensionality Reduction
VALUETOOLS
Springer
DOI: 10.1007/978-3-031-31234-2_11
Abstract
In this work, we investigate the stationary behaviour of the asymmetric join the shortest queue system with a single server and two infinite capacity orbit queues. Arriving jobs that find the server busy, are forwarded to the least loaded orbit queue, and in case of a tie, they choose an orbit randomly. Orbiting jobs retry to connect with the server at different retrial rates, i.e., heterogeneous orbit queues. Our system is described by a Markov modulated two-dimensional random walk. By exploiting its special structure, its invariant measure is obtained in terms of the invariant measure of a non-modulated two-dimensional random walk by applying the compensation method.
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