arXiv subjects

José Giral-Barajas

Publications and source records attributed to José Giral-Barajas.

3 recordsLinked to original sources

arXiv2026

Universality in the target arrival statistics of non-conservative search processes

Stochastic search processes in which agents are continuously inserted into and removed from a target search domain are fundamental to a wide class of physical and artificial systems. The theory of such non-conservative search processes is, however, much less developed than for search processes with a fixed number of agents. Recent work on the non-conservative case has characterized the fastest first-passage time (FPT) to a target, after which the search process is terminated. Here we consider the complementary problem of continuous arrival statistics to a target. In particular, we derive the full time-dependent distribution of target arrivals, which we use to show that the inter-arrival time distribution is exactly exponential in steady-state regardless of the underlying search process. Thus, counterintuitively, the arrival statistics of non-conservative search are both universal and much simpler than sequential search-and-capture processes involving a fixed number of agents. Our methods also yield an exact expression for the fastest FPT distribution with time-dependent insertion, thereby generalizing previous work on fixed-rate insertion for non-conservative search. Altogether these results have major implications for target resource accumulation, wherein the delivery of resources is counter-balanced by their downstream consumption.

cond-mat.stat-mech↗

arXiv2026

Resetting-induced instability in queues fed by a search process in an interval

Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival distribution is determined by a search process with stochastic resetting. When the queuing system has a limited number of servers and the search process occurs within a bounded domain, the dynamics of expediting or delaying the search through stochastic resetting interact with the long-term dynamics of the number of resources in the queue. We combine results from queuing theory with those from search processes with stochastic resetting in a bounded domain to obtain regions of the parameter space of the search process that ensure convergence of the number of resources in the queue to a steady state. Furthermore, we find a threshold resetting rate at which the effects of stochastic resetting shift from reducing convergence regions to expanding them. Finally, we demonstrate that this threshold value grows exponentially with the number of servers, making it harder for stochastic resetting to improve the convergence of the queueing system.

cond-mat.stat-mech↗

arXiv2025

Stochastic 1D search-and-capture as a G/M/c queueing model

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 $G/M/\infty$ 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 $G/M/\infty$ 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 $G/M/\infty$ 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 $G/M/\infty$ queue does.

cond-mat.stat-mech↗