A catastrophic queueing model with delayed action

We consider an M
 X
 /M/c queue with catastrophes and state-dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these properties and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we obtain the Laplace transform of the transition probability for the absorbing M
 X
 /M/c queue.

M X = M = c Queue with catastrophes and state-dependent control at idle time

This paper is largely a review. It considers two main methods used to study stability and to obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable state space. An approach is described to the construction of perturbation estimates for the main five classes of such chains associated with queuing models. Several specific models are considered for which the limit characteristics and perturbation bounds for admissible “perturbed” processes are calculated.

https://www.mdpi.com/2227-7390/8/2/253/pdf

Two approaches to the construction of perturbation bounds for continuous-time Markov chains

In this paper, we present the extension of the analysis of time-dependent limiting characteristics the class of continuous-time birth and death processes defined on non-negative integers with speci...

Ergodicity and truncation bounds for inhomogeneous birth and death processes with additional transitions from and to origin

A class of inhomogeneous Markovian queuing systems with possible catastrophic failures and group arrival of customers in the case of empty queue is considered; basic estimates of the rate of convergence and stability for this class are obtained.

On a class of Markovian queuing systems described by inhomogeneous birth-and-death processes with additional transitions

In this paper we consider an M/M/c queue modified to allow both mass arrivals when the system is empty and the workload to be removed. Properties of queues which terminate when the server becomes idle are firstly developed. Recurrence properties, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no mass exodus. All of these results are then generalized to allow for the removal of the entire workload. In particular, we obtain the Laplace transformation of the transition probability for the absorptive M/M/c queue.

/pdf/the-m-m-c-queue-with-mass-exodus-and-mass-arrivals-when-2dhbocdw76.pdf

Junping Li

Papers

The M/M/c queue with mass exodus and mass arrivals when empty