Modelling Skill-Based Queueing Systems using Pass-and-Swap Queues and Whittle Networks
Abstract
This paper establishes a unified framework for analyzing skill-based queueing systems (SBQSs) by connecting pass-and-swap (P&S) queues and Whittle networks, two key classes of product-form queueing models. We demonstrate their equivalence under specific conditions, enabling the analysis of complex systems through simpler, well-understood components. More precisely, our contributions are threefold: (i) Following Comte and Dorsman (2021), we propose a closed tandem network representation of SBQSs, where P&S queues and Whittle networks serve as building blocks, allowing us to derive product-form stationary distributions for a wide range of systems. Furthermore, we prove a form of equivalence between P&S queues and Whittle networks. (ii) We provide explicit results for load-balancing policies, including (a) a proof of equivalence between assign-to-the-longest-idle-server (ALIS) and randomly-assign-to-idle-server (RAIS), and between FCFS-ALIS and FCFS-RAIS, and (b) the first closed-form expression for RAIS routing probabilities. (iii) Lastly, we highlight generalizations to state-dependent arrival rates, multi-stage waiting mechanisms, and priority-based scheduling, showcasing the framework's broad applicability. This work provides a general, flexible, and computationally tractable approach to analyzing SBQSs, with implications for performance evaluation in computer systems, telecommunications, and service operations.
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BibTeX
@misc{comte2026modelling,
title = {{Modelling Skill-Based Queueing Systems using Pass-and-Swap Queues and Whittle Networks}},
author = {Céline Comte and Jan-Pieter Dorsman and Kristen Gardner},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05830288v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Modelling Skill-Based Queueing Systems using Pass-and-Swap Queues and Whittle Networks
AU - Céline Comte
AU - Jan-Pieter Dorsman
AU - Kristen Gardner
PY - 2026
DA - 2026/10/21
PB - HAL
UR - https://hal.science/hal-05830288v1
AB - This paper establishes a unified framework for analyzing skill-based queueing systems (SBQSs) by connecting pass-and-swap (P&S) queues and Whittle networks, two key classes of product-form queueing models. We demonstrate their equivalence under specific conditions, enabling the analysis of complex systems through simpler, well-understood components. More precisely, our contributions are threefold: (i) Following Comte and Dorsman (2021), we propose a closed tandem network representation of SBQSs, where P&S queues and Whittle networks serve as building blocks, allowing us to derive product-form stationary distributions for a wide range of systems. Furthermore, we prove a form of equivalence between P&S queues and Whittle networks. (ii) We provide explicit results for load-balancing policies, including (a) a proof of equivalence between assign-to-the-longest-idle-server (ALIS) and randomly-assign-to-idle-server (RAIS), and between FCFS-ALIS and FCFS-RAIS, and (b) the first closed-form expression for RAIS routing probabilities. (iii) Lastly, we highlight generalizations to state-dependent arrival rates, multi-stage waiting mechanisms, and priority-based scheduling, showcasing the framework's broad applicability. This work provides a general, flexible, and computationally tractable approach to analyzing SBQSs, with implications for performance evaluation in computer systems, telecommunications, and service operations.
ER -