Capacity Control in a Single-Server Diagnostic--Treatment Queue with Heterogeneous Treatment Modes
Abstract
This study develops an analytical and decision framework for a pooled single-server diagnostic--treatment service receiving both first-time and referred patients. A first-time patient receives diagnosis followed immediately by one of n treatment modes, whereas a referred patient enters directly into the prescribed treatment mode. For the two-treatment case, closed-form probability generating functions characterize the stationary queue-length distribution; for arbitrary n, a matrix-geometric representation provides a computational solution. The queueing analysis is then directed to capacity control decisions. The effective load is decomposed into mode-specific workload contributions, yielding a minimum service-rate increment for a prescribed utilization target to show that utilization-equivalent interventions need not be delay-equivalent. This motivates a distribution-aware control based on the stationary probability of severe congestion. Finally, the total cost function shown to be strictly convex, providing a global minimum for restricted one-mode interventions. Analytical results are cross-validated against the Pollaczek--Khintchine relations and discrete-event simulation.
Related
- Estimating Treatment Effects with a Single Arm Clinical Trial and Data Summaries from an External Control Group: is it Possible?
- Sinkhorn-Optimized Capacity-Constrained Temporal Heterogeneous Graph Model for Startup–Investor Matching
- On Weighted Orthogonal Learners for Heterogeneous Treatment Effects
- Explaining Heterogeneous Treatment Effects with Causal Forests and the Hoeffding Functional Decomposition
- Difference-in-Differences for Heterogeneous Effects of General Treatment Strategies Accounting for Time-Varying Covariates
BibTeX
@misc{rani2026capacity,
title = {{Capacity Control in a Single-Server Diagnostic--Treatment Queue with Heterogeneous Treatment Modes}},
author = {Shobha Rani and Rohit Dehru and Raghu Nandan Sengupta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.07967},
eprint = {2608.07967},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.07967},
}
RIS
TY - UNPB
TI - Capacity Control in a Single-Server Diagnostic--Treatment Queue with Heterogeneous Treatment Modes
AU - Shobha Rani
AU - Rohit Dehru
AU - Raghu Nandan Sengupta
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2608.07967
UR - https://arxiv.org/abs/2608.07967
AB - This study develops an analytical and decision framework for a pooled single-server diagnostic--treatment service receiving both first-time and referred patients. A first-time patient receives diagnosis followed immediately by one of n treatment modes, whereas a referred patient enters directly into the prescribed treatment mode. For the two-treatment case, closed-form probability generating functions characterize the stationary queue-length distribution; for arbitrary n, a matrix-geometric representation provides a computational solution. The queueing analysis is then directed to capacity control decisions. The effective load is decomposed into mode-specific workload contributions, yielding a minimum service-rate increment for a prescribed utilization target to show that utilization-equivalent interventions need not be delay-equivalent. This motivates a distribution-aware control based on the stationary probability of severe congestion. Finally, the total cost function shown to be strictly convex, providing a global minimum for restricted one-mode interventions. Analytical results are cross-validated against the Pollaczek--Khintchine relations and discrete-event simulation.
ER -