Related papers: On a fractional queueing model with catastrophes
The presented study elaborates a multi-server catastrophic retrial queueing model considering preemptive repeat priority policy with phase-type (PH) distributed retrial times. For the sake of comprehension, the scenario of model operation…
In this paper, asymptotic properties of the loss probability are considered for an M/G/1/N queue with server vacations and exhaustive service discipline, denoted by an M/G/1/N -(V, E)-queue. Exact asymptotic rates of the loss probability…
We consider a fractional counting process with jumps of amplitude $1,2,\ldots,k$, with $k\in \mathbb{N}$, whose probabilities satisfy a suitable system of fractional difference-differential equations. We obtain the moment generating…
We consider a system of ordered cars moving in $\R$ from right to left. Each car is represented by a point in $\R$; two or more cars can occupy the same point but cannot overpass. Cars have two possible velocities: either 0 or 1. An…
The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
A multi-channel queueing system is considered. The arriving requests differ in their type. Requests of each type arrive according to a Poisson process. The number of channels required for service with the rate equal to 1 depends of the…
In this paper we study a class of Quasi-Skipfree (QSF) processes where the transition rate submatrices in the skipfree direction have a column times row structure. Under homogeneity and irreducibility assumptions we show that the stationary…
We study a model of a polling system, that is, a collection of $d$ queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is…
Changing time of simple continuous-time Markov counting processes by independent unit-rate Poisson processes results in Markov counting processes for which we provide closed-form transition rates via composition of trajectories and with…
In this paper we study a particular class of Piecewise deterministic Markov processes (PDMP's) which are semi-stochastic catastrophe versions of deterministic population growth models. In between successive jumps the process follows a flow…
We study an M/G/1-type queueing model with the following additional feature. The server works continuously, at fixed speed, even if there are no service requirements. In the latter case, it is building up inventory, which can be interpreted…
We analyze the time-dependent behavior of an $M/M/c$ priority queue having two customer classes, class-dependent service rates, and preemptive priority between classes. More particularly, we develop a method that determines the Laplace…
We consider a point process $i+\xi_i$, where $i\in \bZ$ and the $\xi_{i}$'s are i.i.d. random variables with variance $\sigma^{2}$. This process, with a suitable rescaling of the distribution of $\xi_i$'s, converges to the Poisson process…
We consider an M/M/1 feedback queue in which service attempts may fail, requiring the customer to rejoin the queue. Arriving customers act strategically, deciding whether to join the queue based on a threshold strategy that depends on the…
We study in this paper an $M/M/1$ queue whose server rate depends upon the state of an independent Ornstein-Uhlenbeck diffusion process $(X(t))$ so that its value at time $t$ is $\mu \phi(X(t))$, where $\phi(x)$ is some bounded function and…
We consider the Erlang A model, or $M/M/m+M$ queue, with Poisson arrivals, exponential service times, and $m$ parallel servers, and the property that waiting customers abandon the queue after an exponential time. The queue length process is…
We derive upper and lower bounds on the convergence behavior of certain classes of one-parameter quantum dynamical semigroups. The classes we consider consist of tensor product channels and of channels with commuting Liouvillians. We…
We investigate Markovian queues that are examined by a controller at random times determined by a Poisson process. Upon examination, the controller sets the service speed to be equal to the minimum of the current number of customers in the…
We introduce and study a new model: 0-automatic queues. Roughly, 0-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable…