Non-Markovian waiting time distribution

Simulation methods based on stochastic realizations of state vector evolutions are commonly used tools to solve open quantum system dynamics, both in the Markovian and non-Markovian regime. Here, we address the question of waiting time distribution (WTD) of quantum jumps for non-Markovian systems. We generalize Markovian quantum trajectory methods in the sense of deriving an exact analytical WTD for non-Markovian quantum dynamics and show explicitly how to construct this distribution for certain commonly used quantum optical systems.Comment: journal versio

Are seismic waiting time distributions universal?

We show that seismic waiting time distributions in California and Iceland have many features in common as, for example, a power-law decay with exponent $\alpha \approx 1.1$ for intermediate and with exponent $\gamma \approx 0.6$ for short waiting times. While the transition point between these two regimes scales proportionally with the size of the considered area, the full distribution is not universal and depends in a non-trivial way on the geological area under consideration and its size. This is due to the spatial distribution of epicenters which does \emph{not} form a simple mono-fractal. Yet, the dependence of the waiting time distributions on the threshold magnitude seems to be universal.Comment: 5 pages, 4 figures, accepted for publication in Geophys. Res. Let

A Lindley-type equation arising from a carousel problem

In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phase-type distribution. The picker alternates between the two carousels, picking one item at a time. Important performance characteristics are the waiting time of the picker and the throughput of the two carousels. The waiting time of the picker satisfies an equation very similar to Lindley's equation for the waiting time in the PH/U/1 queue. Although the latter equation has no simple solution, we show that the one for the waiting time of the picker can be solved explicitly. Furthermore, it is well known that the mean waiting time in the PH/U/1 queue depends on to the complete interarrival time distribution, but numerical results show that, for the carousel system, the mean waiting time and throughput are rather insensitive to the pick-time distribution.Comment: 10 pages, 1 figure, 19 reference

Consumer Perception and Evaluation of Waiting Time

Telephone waiting times for a commercial service were varied in two different experiments. In the first experiment, the telephone rate was either zero or fixed at Dfl.1.- (approx. $0.40) per minute. Consumer perceptions of waiting times could be described best by a psychophysical power function. Furthermore, wait evaluations were mainly influenced by the difference between the consumers' acceptable and perceived waiting times. The negative effect of perceived waiting time on wait evaluations was increased by the monetary costs of waiting.In the second experiment, the waiting times were filled in different ways: music, queue information, and information about expected waiting time. Information about the expected waiting time significantly reduced the consumer's overestimation of waiting time, whereas information about wait duration and queue increased the negative effect of perceived waiting time on wait evaluations.customer satisfaction;experiment;psychophysics;telephone waiting times

Perception of Waiting Time at Signalized Intersections

Perceived waiting time at signalized intersections differs from the real value, and varies with signal design. The onerousness of delay depends on the conditions under which it is experienced. Using weighted travel time time may contribute to optimal signal control if its use can improve upon assuming that all time is weighted equally by users. This research explores the perception of waiting time at signalized intersections based on the results of an online survey, which directly collected the perceived waiting time and the user ratings of the signal designs of each intersection on an arterial including 3 intersections. Statistically analyzing the survey data suggests the perception of waiting time is a function of the real time; and a quadratic model better can describes relationship. The survey also indicates that there exists a tradeoff between the total waiting time and the individual waiting time of each intersection. It turns out that drivers prefer to split the total waiting time at different intersections at the price of a longer total wait if the difference of the total waiting time of two signal designs is within 30 seconds. The survey data shows that the perceived waiting time, instead of the real waiting time, better explains how users will rate the individual signal designs for both intersections and arterials including multiple intersections.Traffic Signal, Stated Preference, Virtual Experience Stated Preference, Signalized Intersection, Value of Time, Perception of Time

A model for phenotype change in a stochastic framework

some species, an inducible secondary phenotype will develop some time after the environmental change that evokes it. Nishimura (2006) [4] showed how an individual organism should optimize the time it takes to respond to an environmental change ("waiting time''). If the optimal waiting time is considered to act over the population, there are implications for the expected value of the mean fitness in that population. A stochastic predator-prey model is proposed in which the prey have a fixed initial energy budget. Fitness is the product of survival probability and the energy remaining for non-defensive purposes. The model is placed in the stochastic domain by assuming that the waiting time in the population is a normally distributed random variable because of biological variance inherent in mounting the response. It is found that the value of the mean waiting time that maximises fitness depends linearly on the variance of the waiting time

Waiting time distribution for electron transport in a molecular junction with electron-vibration interaction

On the elementary level, electronic current consists of individual electron tunnelling events that are separated by random time intervals. The waiting time distribution is a probability to observe the electron transfer in the detector electrode at time $t+\tau$ given that an electron was detected in the same electrode at earlier time $t$. We study waiting time distribution for quantum transport in a vibrating molecular junction. By treating the electron-vibration interaction exactly and molecule-electrode coupling perturbatively, we obtain master equation and compute the distribution of waiting times for electron transport. The details of waiting time distributions are used to elucidate microscopic mechanism of electron transport and the role of electron-vibration interactions. We find that as nonequilibrium develops in molecular junction, the skewness and dispersion of the waiting time distribution experience stepwise drops with the increase of the electric current. These steps are associated with the excitations of vibrational states by tunnelling electrons. In the strong electron-vibration coupling regime, the dispersion decrease dominates over all other changes in the waiting time distribution as the molecular junction departs far away from the equilibrium

Inverse Statistics in the Foreign Exchange Market

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) $\rho$ in the price of an investment. The analysis is performed for the Deutsch mark (DM) against the $US for the full year of 1998, but similar results are obtained for the Japanese Yen against the$US. With high statistical significance, the presence of "resonance peaks" in the waiting time distributions is established. Such peaks are a consequence of the trading habits of the markets participants as they are not present in the corresponding tick (business) waiting time distributions. Furthermore, a new {\em stylized fact}, is observed for the waiting time distribution in the form of a power law Pdf. This result is achieved by rescaling of the physical waiting time by the corresponding tick time thereby partially removing scale dependent features of the market activity.Comment: 8 pages. Accepted Physica