Related papers: The stability condition of BMAP/M/$\infty$ queues
Multiserver-job systems, where jobs require concurrent service at many servers, occur widely in practice. Much is known in the dropping setting, where jobs are immediately discarded if they require more servers than are currently available.…
Lyapunov drift and Lyapunov optimization are powerful techniques for optimizing time averages in stochastic queueing networks subject to stability. However, there are various definitions of queue stability in the literature, and the most…
This paper studies the workload distribution of a finite-capacity queue driven by a spectrally one-sided Markov additive process (MAP). Our main result provides the Laplace-Stieltjes transform of the workload at an exponentially distributed…
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 purpose of this paper is to analyze the so-called back-off technique of the IEEE 802.11 protocol in broadcast mode with waiting queues. In contrast to existing models, packets arriving when a station (or node) is in back-off state are…
We consider stability and network capacity in discrete time queueing systems. Relationships between four common notions of stability are described. Specifically, we consider rate stability, mean rate stability, steady state stability, and…
We consider a Markovian single server queue with impatient customers. There is a customer abandonment cost and a holding cost for customers in the system. We consider two versions of the problem. In the first version, customers pay a reward…
In this paper we consider the problem of maximum throughput for tandem queueing system. We modeled this system as a Quasi-Birth-Death process. In order to do this we named level the number of customers waiting in the first buffer (including…
The single server queue with multiple customer types and semi-Markovian service times, sometimes referred to as the $M/SM/1$ queue, has been well-studied since its introduction by Neuts in 1966. In this paper, we apply an extension of this…
In this article, we consider a continuous review (s, S) inventory system with failures of demand fulfillment (service) modeled as a Markov-modulated retrial queueing system. The inventory system features a single product that experiences…
In recent years a number of models involving different compatibilities between jobs and servers in queueing systems, or between agents and resources in matching systems, have been studied, and, under Markov assumptions and appropriate…
We consider exponential single server queues with state-dependent arrival and service rates which evolve under influences of external environments. The transitions of the queues are influenced by the environment's state and the movements of…
Demand for studying queueing systems with multiple servers providing correlated services was created about 60 years ago, motivated by various applications. In recent years, the importance of such studies has been significantly increased,…
A FORTRAN program to simulate the operation of infinite servers queues is presented in this work. Poisson arrivals processes are considered but not only. For many parameters of interest in queuing systems study or application, either there…
We consider a GI/G/c/K-type retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has $c$ identical servers and can accommodate the maximal number of $K$ jobs. If a…
This paper considers the mean waiting times in discrete-time preemptive-resume and nonpreemptive priority single-server queues fed by K independent batch Markovian arrival streams with geometrically distributed idle periods. While being…
This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a `multiplicative transition'). For this model we…
Some important results on the variance of the $M|G|\infty$ queue busy period are presented. Often, this parameter depends on the whole structure of the service time distribution. So, the importance of the bounds presented, depending only on…
Let $X$ be the constrained random walk on ${\mathbb Z}_+^2$ with increments $(1,0)$, $(-1,0)$, $(0,1)$ and $(0,-1)$; $X$ represents, at arrivals and service completions, the lengths of two queues working in parallel whose service and…
This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in…