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

Area of Science:

• Operations Research
• Stochastic Processes
• Applied Mathematics

Background:

• Resource management under environmental randomness is common in natural and artificial systems.
• Queuing theory models systems with random arrivals and service times.
• Search processes with stochastic resetting introduce dynamic arrival patterns.

Purpose of the Study:

• To analyze the convergence of queuing systems with bounded search processes and stochastic resetting.
• To identify parameter regions ensuring steady-state queue dynamics.
• To investigate the impact of stochastic resetting on queue convergence with varying server numbers.

Main Methods:

• Combining queuing theory with stochastic search processes in a bounded domain.
• Analyzing the parameter space of the search process for convergence criteria.
• Investigating the influence of the resetting rate and number of servers.

Main Results:

• Determined parameter space regions for steady-state convergence in the queuing system.
• Identified a threshold resetting rate where stochastic resetting's effect on convergence shifts.
• Observed that the threshold resetting rate increases exponentially with the number of servers.

Conclusions:

• Stochastic resetting can influence queue convergence, with a critical rate determining its effect.
• The number of servers significantly impacts the efficacy of stochastic resetting in improving queue stability.
• High server counts diminish the benefits of stochastic resetting for queue convergence.