Related papers: Joint Queue-Length Distribution for the Non-Preemp…
Score-based diffusion generative models have recently emerged as a powerful tool for modelling complex data distributions. These models aim at learning the score function, which defines a map from a known probability distribution to the…
The main contribution of this paper is to present a new sufficient condition for the subexponential asymptotics of the stationary distribution of a GI/GI/1-type Markov chain without jumps from level "infinity" to level zero. For simplicity,…
The MultiQueue is a relaxed concurrent priority queue consisting of $n$ internal priority queues, where an insertion uses a random queue and a deletion considers two random queues and deletes the minimum from the one with the smaller…
In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from…
In this paper we introduce a bivariate distribution on $\mathbb{R}_{+} \times \mathbb{N}$ arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively,…
We consider refined versions of Markov chains related to juggling introduced by Warrington. We further generalize the construction to juggling with arbitrary heights as well as infinitely many balls, which are expressed more succinctly in…
This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…
We study the generalization of the G/G/1 queue obtained by relaxing the assumption of independence between inter-arrival times and service requirements. The analysis is carried out for the class of multivariate matrix exponential…
In this paper, by the singular-perturbation technique, we investigate the heavy-traffic behavior of a priority polling system consisting of three M/M/1 queues with threshold policy. It turns out that the scaled queue-length of the…
The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two…
The queue system,with Poisson arrivals,constant service time and infinite servers, busy period distribution is intensively studied because, due to its probability density function quite easy interpretation, it may serve as a clue to…
Till today we dreamt of imperceptible delay in a network. The computer science research grows today faster than ever offering more and more services (computational representational, graphical, intelligent implication etc) to its user. But…
Recent studies indicate that in many situations service times are affected by the experienced queueing delay of the particular customer. This effect has been detected in different areas, such as health care, call centers and…
We propose a novel approach for solving inverse-problems with high-dimensional inputs and an expensive forward mapping. It leverages joint deep generative modelling to transfer the original problem spaces to a lower dimensional latent…
In this paper we describe a perfect simulation algorithm for the stable $M/G/c$ queue. Sigman (2011: Exact Simulation of the Stationary Distribution of the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209--213) showed how to build…
The paper considers the distribution of a general linear combination of central and non-central chi-square random variables by exploring the branch cut regions that appear in the standard Laplace inversion process. Due to the original…
We study the MAP/M/s+G queuing model with MAP (Markovian Arrival Process) arrivals, exponentially distributed service times, infinite waiting room, and generally distributed patience times. Using sample-path arguments, we propose to obtain…
This paper presents a comprehensive review of stochastic processes, with a particular focus on Markov chains and jump processes. The main results related to queuing systems are analyzed. Additionally, conditions that ensure the stability,…
Consider stochastic functional differential equations, whose coefficients depend on past histories. The solution determines a non-Markov process. In the present paper, we shall obtain the existence of smooth densities for joint…
We introduce a non-Markovian generalization of the classical M/M/1 queue by incorporating extended nonlocal time dynamics into Kolmogorov forward equations. We obtain the model by replacing the standard time derivative with an extended…