Related papers: Fractional Erlang Queues
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…
Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…
The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…
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 derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse L\'evy-subordinator. If the time change is inverse $\alpha$-stable, the time-derivative…
The paper deals with a sharing economy system with various management factors by using a bulk input G/M/1 type queuing model. The effective management of operating costs is vital for controlling the sharing economy platform and this…
Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We study the queuing model of an agent trying to execute a task of…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
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…
In this paper, we demonstrate through the use of matrix calculus a transparent analysis of fractional inhomogeneous Markov models for life insurance where transition matrices commute. The resulting formulae are intuitive matrix…
The performance of non-preemptive M/M/1 queueing system with two priority is analyzed. By using complementary variable method to make vector Markov process and analyzing the state-change equations of the queueing system, the generating…
The subject of this paper is the problem of estimating service time distribution of the $M/G/\infty$ queue from incomplete data on the queue. The goal is to estimate $G$ from observations of the queue--length process at the points of the…
We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…
Explicit results are derived using simple and exact methods for the joint and marginal queue-length distributions for the M/M/c queue with two non-preemptive priority levels. Equal service rates are assumed. Two approaches are considered.…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
To offer a view into the rapidly developing theory of fractional diffusion processes we describe in some detail three topics of present interest: (i) the well-scaled passage to the limit from continuous time random walk under power law…
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…