Mitigating long queues and waiting times with service resetting

Abstract

What determines the average length of a queue which stretches in front of a service station? The answer to this question clearly depends on the average rate at which jobs arrive at the queue and on the average rate of service. Somewhat less obvious is the fact that stochastic fluctuations in service and arrival times are also important, and that these are a major source of backlogs and delays. Strategies that could mitigate fluctuations induced delays are in high demand as queue structures appear in various natural and man-made systems. Here we demonstrate that a simple service resetting mechanism can reverse the deleterious effects of large fluctuations in service times, thus turning a marked drawback into a favourable advantage. This happens when stochastic fluctuations are intrinsic to the server, and we show that the added feature of service resetting can then dramatically cut down average queue lengths and waiting times. While the analysis presented herein is based on the M/G/1 queueing model where service is general but arrivals are assumed to be Markovian, Kingman's formula asserts that the benefits of service resetting will carry over to queues with general arrivals. We thus expect results coming from this work to find widespread application to queueing systems ranging from telecommunications, via computing, and all the way to molecular queues that emerge in enzymatic and metabolic cycles of living organisms.

References in corpus (16)

• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Diffusion in a potential landscape with stochastic resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Intrinsic noise in stochastic models of gene expression with molecular memory and bursting
• Stochastic Search with Poisson and Deterministic Resetting
• The inspection paradox in stochastic resetting
• On the universality of the scaling of fluctuations in traffic on complex networks
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process
• Extremal statistics for stochastic resetting systems
• Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity
• Applications of Little's Law to stochastic models of gene expression
• Mean-performance of Sharp Restart II: Inequality Roadmap
• Role of dimensions in first passage of a diffusing particle under stochastic resetting and attractive bias
• Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: Experiments, theory and numerical tests

Cited by in corpus (17)

• Stochastic Resetting for Enhanced Sampling
• Universal framework for record ages under restart
• Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting
• Resetting mediated navigation of active Brownian searcher in a homogeneous topography
• First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting
• Diversity of Sharp Restart
• Optimizing Leapover Lengths of Lévy Flights with Resetting
• Search with stochastic home-returns can expedite classical first passage under resetting
• Optimal conditions for first passage of jump processes with resetting
• Queues with resetting: a perspective
• Target Search Optimization by Threshold Resetting
• Random resetting in search problems
• Entropy of Sharp Restart
• Drift-diffusive resetting search process with stochastic returns: speed-up beyond optimal instantaneous return
• Stochastic Resetting Mitigates Latent Gradient Bias of SGD from Label Noise
• Universal criterion for selective outcomes under stochastic resetting
• Stochastic 1D search-and-capture as a G/M/c queueing model