Related papers: Exact Tail Asymptotics --- Revisit of a Retrial Qu…
We obtain asymptotic bounds for the tail distribution of steady-state waiting time in a two server queue where each server processes incoming jobs at a rate equal to the rate of their arrivals (that is, the half-loaded regime). The job…
The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon…
In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service…
A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this…
We study the tail asymptotic of the stationary joint queue length distribution for a generalized Jackson network (GJN for short), assuming its stability. For the two station case, this problem has been recently solved in the logarithmic…
The busy period for a queue is cast as the area swept under the random walk until it first returns to zero, $B$. Encompassing non-i.i.d. increments, the large-deviations asymptotics of $B$ is addressed, under the assumption that the…
When decomposing the total orbit into $N$ sub-orbits (or simply orbits) related to each of $N$ servers and through comparing the numbers of customers in these orbits, we introduce a retrial supermarket model of $N$ identical servers, where…
Two independent Poisson streams of jobs flow into a single-server service system having a limited common buffer that can hold at most one job. If a type-i job (i=1,2) finds the server busy, it is blocked and routed to a separate type-i…
We consider a two dimensional reflecting random walk on the nonnegative integer quadrant. This random walk is assumed to be skip free in the direction to the boundary of the quadrant, but may have unbounded jumps in the opposite direction,…
Many networking-related settings can be modeled by Markov-modulated infinite-server systems. In such models, the customers' arrival rates and service rates are modulated by a Markovian background process, additionally, there are infinitely…
In general, obtaining the exact steady-state distribution of queue lengths is not feasible. Therefore, we establish bounds for the tail probabilities of queue lengths. Specifically, we examine queueing systems under Heavy-Traffic (HT)…
A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized…
We investigate the tail behaviour of the steady state distribution of a stochastic recursion that generalises Lindley's recursion. This recursion arises in queuing systems with dependent interarrival and service times, and includes…
Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an $M/G/1$ retrial queue is investigated where…
This short communication considers an infinite-server system with overdispersed input. The objective is to identify the exact tail asymptotics of the number of customers present at a given point in time under a specific scaling of the model…
We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue…
This article deals with asynchronous server vacation and customer retrial facility in a multi-server queueing-inventory system. The Poisson process governs the arrival of a customer. The system is comprised of c identical servers, a…
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…
The interest to retrial queueing systems is due to their application to telephone systems. The paper studies multiserver retrial queueing systems with $n$ servers. Arrival process is a quite general point process. An arriving customer…
We deal with a discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process for short) on $\mathbb{Z}_+^2\times S_0$, where $S_0$ is a finite set, and give a complete expression for the asymptotic decay function of the…