Related papers: $1/f^{3/2}$ noise in heavy traffic M/M/1 queue
Within the lowest-order Born approximation, we calculate the exact dynamics of a single qubit in the presence of 1/f noise, without making any Markov approximation. We show that the non-Markovian qubit time-evolution exhibits asymmetries…
Noise power spectra in spatially extended dynamical systems are investigated, using as a model the Complex Ginzburg-Landau equation with a stochastic term. Analytical and numerical investigations show that the temporal noise spectra are of…
We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/f^b noise, power-law autocorrelations and second order structural (height-height correlation)…
We present a simple model reproducing the long-range autocorrelations and the power spectrum of the web traffic. The model assumes the traffic as Poisson flow of files with size distributed according to the power-law. In this model the…
Phantom traffic jams may emerge ``out of nowhere'' from small fluctuations rather than being triggered by large, exceptional events. We show how phantom jams arise in a model of single lane highway traffic, which mimics human driving…
Finite-capacity single-server queues with general service-time distributions form the backbone of numerous real-world systems, yet classical simulation of performance metrics such as blocking probabilities and delay becomes computationally…
We present a simple point process model of $1/f^{\beta}$ noise, covering different values of the exponent $\beta$. The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence or waiting times…
Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly accurate approximations of the workload distribution of…
The quantum indeterminacy caused by non-commutativity of observables at different times sets a lower bound on the voltage noise power spectrum in any conducting material. This bound is calculated explicitly in the case of semiconductors…
We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semi-Markov service times is the most prominent example in this class and…
We analyze an M/M/1 queue with a service discipline in which customers, upon arriving when the server is busy, search a sequence of stations for a vacant station at which to wait, and in which the server, upon becoming free when one or more…
This paper studies the heavy-traffic (HT) behaviour of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves…
This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…
The slow-to-start mechanism is known to play an important role in the particular shape of the Fundamental diagram of traffic and to be associated to hysteresis effects of traffic flow.We study this question in the context of exclusion and…
In this paper, we consider five models of heavy-tailed queues involving Mittag-Leffler distributions that generalize the classical $M/M/1$ queues. These models are suitable modifications of previously defined models in such a way that the…
We study the accumulation of resources within a target due to the interplay between continual delivery, driven by 1D stochastic search processes, and sequential consumption. The assumption of sequential consumption is key because it changes…
We propose a model for 1/f flux noise in superconducting devices (f is frequency). The noise is generated by the magnetic moments of electrons in defect states which they occupy for a wide distribution of times before escaping. A trapped…
We establish the averaging property for a queuing process with one server, M(t)/GI/1. It is a new relation between the output flow rate and the input flow rate, crucial in the study of the Poisson Hypothesis. Its implications include the…
We consider a horizontal traffic queue (HTQ) on a periodic road segment, where vehicles arrive according to a spatio-temporal Poisson process, and depart after traveling a distance that is sampled independently and identically from a…
We investigate the generation of quantum operations for one-qubit systems under classical noise with 1/f^\alpha power spectrum, where 2>\alpha > 0. We present an efficient way to approximate the noise with a discrete multi-state Markovian…