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Resetting-induced instability in queues fed by a search process in an interval
José Giral-Barajas1, Paul C Bressloff1
1Imperial College London, Department of Mathematics, London SW7 2AZ, United Kingdom.
Physical Review. E
|July 24, 2026
Summary
Managing random resource arrivals in queues is key. Stochastic resetting can help, but its effectiveness decreases with more servers, impacting steady-state convergence.
Area of Science:
- Operations Research
- Stochastic Processes
- Statistical Physics
Background:
- Resource management under environmental randomness is crucial in natural and artificial systems.
- Queuing processes model systems with random arrivals and consumption.
- Search processes with stochastic resetting influence arrival distributions.
Purpose of the Study:
- To determine conditions for queue convergence in systems with limited servers and bounded search domains.
- To analyze the impact of stochastic resetting on queue dynamics.
- To identify the threshold resetting rate for convergence shifts.
Main Methods:
- Combining queuing theory with search processes with stochastic resetting in a bounded domain.
- Analyzing parameter space regions for steady-state convergence.
- Investigating the influence of the number of servers on resetting effectiveness.
Main Results:
- Identified parameter space regions ensuring queue convergence to a steady state.
- Discovered a threshold resetting rate where resetting effects shift from detrimental to beneficial.
- Demonstrated that this threshold increases exponentially with the number of servers.
Conclusions:
- Stochastic resetting's ability to improve queue convergence diminishes as the number of servers increases.
- The interplay between resetting dynamics and bounded search is critical for system stability.
- System design must consider the number of servers when implementing stochastic resetting for resource management.
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