Stochastic 1D search-and-capture as a G/M/c queueing model
File(s)
Published version
Author(s)
Giral Barajas, José
Bressloff, Paul C
Type
Journal Article
Abstract
We study the accumulation of resources within a target due to the interplay between continual delivery, driven by 1D stochastic search processes, and sequential consumption. The assumption of sequential consumption is key because it changes the commonly used G/M/∞ queue to a G/M/c queue. Combining the theory of G/M/c queues with the theory of first-passage times, we derive general conditions for the search process to ensure that the number of resources within the queue converges to a steady state and compute explicit expressions for the mean and variance of the number of resources within the
queue at steady state. We then compare the performance of the G/M/c queue with that of the G/M/∞ queue for an increasing number of servers. We extend the model to consider two competing targets and show that, under specific scenarios, an additional target is beneficial to the original target. Finally, we study the effects of multiple searchers. Using renewal theory, we numerically compute the inter-arrival time density for M searchers in the Laplace space, which allows us to exploit the explicit expressions for the steady-state statistics of the number of resources within G/M/1 and G/M/∞ queues, and compare their behaviour with different numbers of searchers. Overall, the G/M/c queue shows a tighter dependence on the configuration of the search process than the G/M/∞ queue does.
queue at steady state. We then compare the performance of the G/M/c queue with that of the G/M/∞ queue for an increasing number of servers. We extend the model to consider two competing targets and show that, under specific scenarios, an additional target is beneficial to the original target. Finally, we study the effects of multiple searchers. Using renewal theory, we numerically compute the inter-arrival time density for M searchers in the Laplace space, which allows us to exploit the explicit expressions for the steady-state statistics of the number of resources within G/M/1 and G/M/∞ queues, and compare their behaviour with different numbers of searchers. Overall, the G/M/c queue shows a tighter dependence on the configuration of the search process than the G/M/∞ queue does.
Date Issued
2025-09-01
Date Acceptance
2025-08-14
Citation
Journal of Physics A: Mathematical and Theoretical, 2025, 34 (35)
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A: Mathematical and Theoretical
Volume
34
Issue
35
Copyright Statement
© 2025 The Author(s). Published by IOP Publishing Ltd Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
License URL
Publication Status
Published
Article Number
355001
Date Publish Online
2025-08-26