Waiting Time Distribution Research Articles

Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions.

For renewal-reward processes with a power-law decaying waiting time distribution, anomalously large probabilities are assigned to atypical values of the asymptotic processes. Previous works have revealed that this anomalous scaling causes a singularity in the corresponding large deviation function. In order to further understand this problem, we study in this article the scaling of variance in several renewal-reward processes: counting processes with two different power-law decaying waiting time distributions and a Knudsen gas (a heat conduction model). Through analytical and numerical analyses of these models, we find that the variances show an anomalous scaling when the exponent of the power law is -3. For a counting process with the power-law exponent smaller than -3, this anomalous scaling does not take place: this indicates that if we only consider the standard deviation from the expectation, any anomalous behavior will not be detected. In this case, we argue that anomalous scaling appears in higher order cumulants. Finally, many-body particles interacting through soft-core interactions with the boundary conditions employed in the Knudsen gas are studied using numerical simulations. We observe that the variance scaling becomes normal even though the power-law exponent in the boundary conditions is -3.

Thermodynamic Inference in Partially Accessible Markov Networks: A Unifying Perspective from Transition-Based Waiting Time Distributions

The inference of thermodynamic quantities from the description of an only partially accessible physical system is a central challenge in stochastic thermodynamics. A common approach is coarse-graining, which maps the dynamics of such a system to a reduced effective one. While coarse-graining states of the system into compound ones is a well-studied concept, recent evidence hints at a complementary description by considering observable transitions and waiting times. In this work, we consider waiting time distributions between two consecutive transitions of a partially observable Markov network. We formulate an entropy estimator using their ratios to quantify irreversibility. Depending on the complexity of the underlying network, we formulate criteria to infer whether the entropy estimator recovers the full physical entropy production or whether it just provides a lower bound that improves on established results. This conceptual approach, which is based on the irreversibility of underlying cycles, additionally enables us to derive estimators for the topology of the network, i.e., the presence of a hidden cycle, its number of states, and its driving affinity. Adopting an equivalent semi-Markov description, our results can be condensed into a fluctuation theorem for the corresponding semi-Markov process. This mathematical perspective provides a unifying framework for the entropy estimators considered here and established earlier ones. The crucial role of the correct version of time reversal helps to clarify a recent debate on the meaning of formal versus physical irreversibility. Extensive numerical calculations based on a direct evaluation of waiting time distributions illustrate our exact results and provide an estimate on the quality of the bounds for affinities of hidden cycles.Received 22 March 2022Revised 2 June 2022Accepted 1 July 2022DOI:https://doi.org/10.1103/PhysRevX.12.031025Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFluctuation theoremsNonequilibrium statistical mechanicsStochastic processesStochastic thermodynamicsStatistical Physics

Waiting time distribution and current correlations via a Majorana single-charge transistor

We investigate the electron transport and the waiting time distribution (WTD) in a topological superconducting Coulomb island system weakly coupled to two metallic leads. A pair of Majorana bound states are hosted in the island with a finite charging energy. By employing the Markovian master equation, we study the effect of interplay between Majorana energy splitting and the charging energy on the current correlations and the relevant electron WTDs. It is found that the super-Poissonian shot noise could be induced when the Majorana energy splitting is larger than the charging energy. The reason is that the degeneracy of the ground states in the island could be lifted by a finite Majorana energy splitting, which produces the asymmetry between tunneling channels and leads to the dynamical channel blockade effect. We show that the WTD for electron tunneling through two Majorana bound states is equivalent to the WTD in a single-resonant-level device. For comparison, we also discuss the WTD for electron tunneling through a non-Majorana device. It is found that the WTD sensitively depends on the length of the island and indicates oscillation behaviors in the absence of Majorana bound states. The particular behaviors of the WTDs in a Majorana island device can be useful in identifying the existence of Majorana bound states. Furthermore, we study the randomness parameter of the waiting time to describe the fluctuations of waiting times. It is shown that the randomness parameter indicates behavior similar to that indicated by the noise Fano factor, and both of them reflect the information of tunneling dynamics.

Cost–benefit of a state-road charging system: The case of Denmark

We examine the welfare economic performance of fast charging infrastructure investments in Denmark by comparing the monetary value of waiting-time savings from increasing capacity with the cost of investment. Waiting-time calculations are based on interactions between a generalised queuing system and a microscopic space–time model of charging demand. The model allows calculating waiting-time distributions for a given capacity of chargers, leading us to determine the capacity required to fulfil different waiting-time guarantees and their welfare economic performance. The waiting-time distribution is a function of many key variables such as the speed of penetration, future charging speeds, and battery range of EVs. Since such inputs are highly uncertain, 24 scenarios for charging demand in 2030 are considered. These are based on different assumptions concerning technology and behaviour. We find that an efficient waiting-time guarantee, based on maximum waiting times, is approximately 10 min for a baseline scenario. • Planning of a fast-charging infrastructure for EVs for an entire country. • Micro-simulation framework with information-sharing. • Optimisation of sizing and placement accounting for cost of investment. • Investigation of cost–benefit performance of different service guarantees. • Optimal expected utilisation levels of chargers are between 20%–35%.

Report on lung cancer surgery during COVID-19 pandemic at a high volume US institution.

BackgroundThe impact of COVID-19 has been felt in every field of medicine. We sought to understand how lung cancer surgery was affected at a high volume institution. We hypothesized that patients would wait longer for surgery, have more advanced tumors, and experience more complications during the COVID-19 crisis.MethodsA retrospective review was conducted, comparing pathologically confirmed non-small cell lung cancer (NSCLC) surgical cases performed in 2019 to cases performed from March to May 2020, during the height of the COVID-19 crisis. Clinical and pathologic stage, tumor size, time to surgery, follow up time, and complications were evaluated.ResultsA total of 375 cases were performed in 2019 vs. 58 cases in March to May 2020. Overall, there were no differences in the distribution of clinical stages or in the distribution of median wait times to surgery between groups (COVID-19 16.5 days vs. pre-COVID-19 17 days, P=0.54), nor were there differences when subdivided into Stage I-II and Stage III-IV. Case volume was lowest in April 2020 with 6 cases vs. 37 in April 2019, P<0.01. Tumor size was clinically larger in the COVID-19 group (median 2.1 vs. 1.9 cm, P=0.05) but not at final pathology. No differences in complications were observed between groups (COVID-19 31.0% vs. pre-COVID-19 30.9%, P=1.00). No patients from the COVID-19 group tested positive for the disease during their hospital stay or by the median 15 days to first follow-up.ConclusionsSurgical wait time, pathologic tumor size, and complications were not different among patients undergoing surgery before vs. during the pandemic. Importantly, no patients became infected as a result of their hospital stay. The significant decrease in surgical cases is concerning for untreated cancers that may progress without proper treatment.

Changing temporal volatility of precipitation extremes due to global warming

AbstractIt is of utmost importance to understand how precipitation extremes change due to global warming. Here, we examine the volatility of precipitation extremes by analysing the waiting time distribution between events and the clustering of precipitation extremes. For this we use the ERA5 reanalysis data and high‐resolution simulations with the Community Earth System Model (CESM). We find significant evidence for a power‐law distribution of waiting times between precipitation extremes and of serial clustering of precipitation extremes. This suggests that precipitation extremes do not occur independently from each other. This is in contrast with previous studies which typically assume that precipitation extreme events occur independently from each other. CESM reproduces these properties well. The climate change simulations show that the waiting times between precipitation extremes become shorter and that at the same time the clustering of precipitation extremes increases. Hence, global warming affects the temporal characteristics of precipitation extremes and, thus, precipitation extremes will become more volatile.

Solar Chromospheric Network as a Source for Solar Wind Switchbacks

Recent studies suggest that the magnetic switchbacks (SBs) detected by the Parker Solar Probe carry information on the scales of solar supergranulation (large scale) and granulation (medium scale). We test this claim using high-resolution Hα images obtained with the visible spectropolarimeters of the Goode Solar Telescope in Big Bear Solar Observatory. As possible solar sources, we count all the spicule-like features standing along the chromospheric networks near the coronal hole boundary visible in the Hα blue-wing but absent in the red-wing images and measure the geometric parameters of dense sections of individual flux tubes. Intervals between adjacent spicules located along the chromospheric networks are found in the range of 0.4–1.5 Mm (0.°03–0.°12) tending to be smaller than the medium scale of SBs. Interdistances between all pairs of the flux tubes are also counted and they appear in a single peak distribution around 0.7 Mm (0.°06) unlike the waiting-time distribution of SBs in a scale-free single power-law form. The length-to-diameter ratio of the dense section of flux tubes is as high as 6–40, similar to the aspect ratio of SBs. The number of spicules along a network can be as high as 40–100, consistent with numerous SBs within a patch. With these numbers, it is argued that the medium scale of SBs can be understood as an equilibrium distance resulting from a random walk within each diverging magnetic field funnel connected to the chromospheric networks.

Analysis of Stochastic M/M/c/N Inventory System with Queue-Dependent Server Activation, Multi-Threshold Stages and Optional Retrial Facility

The purpose of this article is to examine the server activation policy (SAP) in a multi-server queuing-inventory system (MQIS). The queue has a total of c number of multi-threshold stages as well as c-homogeneous servers. The activation of each server begins one by one if there is an adequate queue length and inventory in the system; otherwise, they remain idle. The server deactivation process continues until the queue length exceeds the manageable level (predetermined stages) or there is insufficient stock. In addition, when we assume the length of the two successive threshold levels is one, the server activation policy model becomes a regular multi-server model. The Neuts matrix geometric approach is used to discuss the stability condition, stationary probability vector. The Laplace–Stieltjes transform (LST) is used to analyse the waiting time distributions of the queue and orbital customers. Additionally, significant system performance metrics and sensitivity analysis are used to investigate the effects of various parameters and cost values. In the comparative result between the server activation model (SAM) and without the server activation model (WSAM) on the expected total cost, we obtain the minimised cost in the SAM. Moreover, the results are obtained by assuming that the length of the intervals between the two successive threshold levels is to be taken into account as the non-uniform length. The expected inventory level, reorder rate, and waiting time of a customer in the waiting hall and orbit were explored numerically by the parameter analysis.

Quantum trajectory theory and simulations of nonlinear spectra and multiphoton effects in waveguide-QED systems with a time-delayed coherent feedback

We study the nonlinear spectra and multi-photon correlation functions for the waveguide output of a two-level system (including realistic dissipation channels) with a time-delayed coherent feedback. We compute these observables by extending a recent quantum trajectory discretized-waveguide (QTDW) approach which exploits quantum trajectory simulations and a collisional model for the waveguide to tractably simulate the dynamics. Following a description of the general technique, we show how to calculate the first and second order quantum correlation functions, in the presence of a coherent pumping field. With a short delay time, we show how feedback can be used to filter out the central peak of the Mollow triplet or switch the output between bunched and anti-bunched photons by proper choice of round trip phase. We further show how the loop length and round trip phase effects the zero-time second order quantum correlation function, an indicator of bunching or anti-bunching. New resonances introduced through the feedback loop are also shown through their appearance in the incoherent output spectrum from the waveguide. We explain these results in the context of the waiting time distributions of the system output and individual trajectories, uniquely stochastic observables that are easily accessible with the QTDW model.

Statistical time-domain characterization of non-periodic optical clocks

Measuring time means counting the occurrence of periodic phenomena. Over the past centuries a major effort was put to make stable and precise oscillators to be used as clock regulators. Here we consider a different class of clocks based on stochastic clicking processes. We provide a rigorous statistical framework to study the performances of such devices and apply our results to a single coherently driven two-level atom under photodetection as an extreme example of non-periodic clock. Quantum Jump MonteCarlo simulations and photon counting waiting time distribution will provide independent checks on the main results.

Electron Shuttle as an Autonomous Single-Electron Source

The majority of experimental realizations of single-electron sources rely on the periodic manipulation of the tunnel junctions through their gate voltages, and thus require a high level of control over the system. To circumvent the necessity of external driving, we utilize the self-oscillatory behavior of the electron shuttle. By means of waiting time distributions, which had not been applied to this autonomous system before, we extensively assess the performance of the shuttle as a single-electron source. We unveil a smooth transition between three regimes, whereas previous studies at the same mean field level of description only predict a sharp bifurcation based on the time-averaged electron current. Over the parameter range of already existing experimental realizations the electron shuttle can perform as a single-electron source, albeit with moderate precision. We propose an alternative design of the position-dependent tunneling rates, which significantly decreases the relative error of charge transmission, and thus paves the way for the realization of autonomous single-electron sources.

Generalized fluctuation-dissipation theorem for non-Markovian reaction networks.

Intracellular biochemical networks often display large fluctuations in the molecule numbers or the concentrations of reactive species, making molecular approaches necessary for system descriptions. For Markovian reaction networks, the fluctuation-dissipation theorem (FDT) has been well established and extensively used in fast evaluation of fluctuations in reactive species. For non-Markovian reaction networks, however, the similar FDT has not been established so far. Here, we present a generalized FDT (gFDT) for a large class of non-Markovian reaction networks where general intrinsic-event waiting-time distributions account for the effect of intrinsic noise and general stochastic reaction delays represent the impact of extrinsic noise from environmental perturbations. The starting point is a generalized chemical master equation (gCME), which describes the probabilistic behavior of an equivalent Markovian reaction network and identifies the structure of the original non-Markovian reaction network in terms of stoichiometries and effective transition rates (extensions of common reaction propensity functions). From this formulation follows directly the solution of the linear noise approximation of the stationary gCME for all the components in the non-Markovian reaction network. While the gFDT can quickly trace noisy sources in non-Markovian reaction networks, example analysis verifies its effectiveness.

Spin activity correlations in driven disordered systems

We study the spatio-temporal correlations in the spin flipping activities of the disordered systems realized within the frame of the field-driven three-dimensional zero-temperature nonequilibrium random field Ising model. Our results for the spatial activity correlations reveal that the rate-dependent scaling holds in the full range of rate regimes provided that the system parameters satisfy the finite-size and rate-dependent scaling conditions. Temporal activity correlations show high sensitivity to the driving, allowing the collapsing of waiting time distributions only in the limit of slow driving rates. These findings, based on extensive numerical simulations of large systems, reliably demonstrate the observed behavior and could be relevant for studies on various, particularly experimental, nonequilibrium systems driven at finite rates.

Magnetization reversal across multiple serial barriers in a single Fe3O4 nanoparticle

Depinning of nanoscale magnetic textures, such as domain walls, vortices and skyrmions, is of paramount importance for magnetic storage and information processing. We measure time-resolved magnetic switching statistics of an individual, non-single-domain Fe$_3$O$_4$ nanoparticle using a micrometer-scale superconducting quantum interference device. Surprisingly, a strong narrowing of the waiting-time distributions before reaching the final state is observed as compared to the exponential distribution expected for a single barrier. The magnetization reversal across the nanostructure is thus shown to result from multiple serial barriers in the minimum energy pathway.

Mountain formation by repeated, inhomogeneous crustal failure in a neutron star

ABSTRACT The elastic crust of a neutron star fractures repeatedly as it spins down electromagnetically. An idealized, macroscopic model of inhomogeneous crustal failure is presented based on a cellular automaton with nearest-neighbour tectonic interactions involving strain redistribution and thermal dissipation. Predictions are made of the size and waiting-time distributions of failure events, as well as the rate of failure as the star spins down. The last failure event typically occurs when the star spins down to $\approx 1{{\ \rm per\ cent}}$ of its birth frequency with implications for rotational glitch activity. Neutron stars are commonly suggested as sources of continuous gravitational waves. The output of the automaton is converted into predictions of the star’s mass ellipticity and gravitational wave strain as functions of its age, with implications for future observations with instruments such as the Laser Interferometer Gravitational Wave Observatory (LIGO).

First results from the ENTOTO neutron monitor: Quantifying the waiting time distribution

We discuss a newly established neutron monitor station installed at the ENTOTO Observatory Research Center outside of Addis Ababa, Ethiopia. This is a version of a mini-neutron monitor, recently upgraded to detect individual neutrons and able to calculate the waiting time distribution between neutron pulses down to ∼1μs. From the waiting time distribution we define and calculate a new quantity, the correlation ratio, as the ratio of correlated to uncorrelated neutrons measured inside the monitor. We propose that this quantity can, in future, be used as a proxy for spectral index of atmospheric particles incident on the monitor and show that this quantity has a weak pressure dependence. We believe that future measurements from the ENTOTO mini-neutron monitor will contribute towards the understanding of cosmic ray acceleration and transport in the heliosphere.

Coarse-grained Stochastic Model of Myosin-Driven Vesicles into Dendritic Spines.

We study the dynamics of membrane vesicle motor transport into dendritic spines, which are bulbous intracellular compartments in neurons that play a key role in transmitting signals between neurons. We consider the stochastic analog of the vesicle transport model in [Park and Fai, The Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors. Bull. Math. Biol. 82, 141 (2020)]. The stochastic version, which may be considered as an agent-based model, relies mostly on the action of individual myosin motors to produce vesicle motion. To aid in our analysis, we coarse-grain this agent-based model using a master equation combined with a partial differential equation describing the probability of local motor positions. We confirm through convergence studies that the coarse-graining captures the essential features of bistability in velocity (observed in experiments) and waiting-time distributions to switch between steady-state velocities. Interestingly, these results allow us to reformulate the translocation problem in terms of conditional mean first passage times for a run-and-tumble particle moving on a finite domain with absorbing boundaries at the two ends. We conclude by presenting numerical and analytical calculations of vesicle translocation.

Nonstandard diffusion under Markovian resetting in bounded domains.

We consider a walker moving in a one-dimensional interval with absorbing boundaries under the effect of Markovian resettings to the initial position. The walker's motion follows a random walk characterized by a general waiting time distribution between consecutive short jumps. We investigate the existence of an optimal reset rate, which minimizes the mean exit passage time, in terms of the statistical properties of the waiting time probability. Generalizing previous results, we find that when the waiting time probability has first and second finite moments, resetting can be either (i) never beneficial, (ii) beneficial depending on the distance of the reset point to the boundary, or (iii) always beneficial. Instead, when the waiting time probability has the first or the two first moments diverging we find that resetting is always beneficial. Finally, we have also found that the optimal strategy to exit the domain depends on the reset rate. For low reset rates, walkers with exponential waiting times are found to be optimal, while for high reset rate, anomalous waiting times optimize the search process.

Asymptotics of waiting time distributions in the accumulating priority queue

Asymptotics of waiting time distributions in the accumulating priority queue

Understanding the Benefit of Being Patient in Payment Channel Networks

Scaling blockchain efficiency is crucial to its widespread usage in which the payment channel is one of the most prominent approaches. With payment channels and the network they construct, two users can move some transactions off-chain to avoid expensive and time-consuming on-chain settlements. Existing works are devoted to designing high-throughput payment channel networks (PCNs) or efficient PCN routing policies to reduce the fee charged by intermediate nodes. In this paper, we investigate the PCN routing from a different perspective by answering whether the routing fee of transactions can be saved through being a bit more patient. The key idea is to reorder the processing sequence of atomic transactions, other than to handle each of them separately and immediately. We present two mechanisms, one is periodic transaction processing and the other is purely strategic waiting. In the former, the incoming transactions in a short time interval are processed collectively. We formulate an optimization model to minimize their total routing fee and derive the optimal permutation of processing transactions as well as the routing policy for each of them. A <i>Shapley value</i> based scheme is presented to redistribute the benefit of reordering among the transactions efficiently and fairly. In the latter, we model the waiting time of a strategic transaction on a single payment channel as the <i>first passage time</i> problem in queuing theory when the transaction value is higher than the channel balance upon its arrival. By capturing the balance dynamics, we are able to calculate the recursive expression of waiting time distribution that is useful to gauge a user&#x0027;s cost of patience. Experimental results manifest that our cost redistribution mechanism can effectively save routing fees for all the transactions, and the waiting time distribution coincides with the model well.