相关论文: Asymptotic behavior of the loss probability for an…
The paper studies asymptotic behavior of the loss probability for the $GI/M/m/n$ queueing system as $n$ increases to infinity. The approach of the paper is based on applications of classic results of Tak\'acs (1967) and the Tauberian…
This paper provides the asymptotic analysis of the loss probability in the $GI/M/1/n$ queueing system as $n$ increases to infinity. The approach of this paper is alternative to that of the recent papers of Choi and Kim [2000] and Choi et al…
In this paper continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ queueing system where the service time probability distribution, slightly different in a…
This paper studies the asymptotic behavior of the steady-state waiting time, W_infty, of the M/G/1 queue with subexponenential processing times for different combinations of traffic intensities and overflow levels. In particular, we provide…
We consider the $M/G/1$ queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, as well as the unconditional distribution, in various asymptotic limits.…
We consider an $M/M/1$ queueing system with impatient customers with multiple and single vacations. It is assumed that customers are impatient whenever the state of the server. We derive the probability generating functions of the number of…
In this article statistical bounds for certain output characteristics of the $M/GI/1/n$ and $GI/M/1/n$ loss queueing systems are derived on the basis of large samples of an input characteristic of these systems, such as service time in the…
In this paper, we study the asymptotic behavior of the tail probability of the number of customers in the steady-state $M/G/1$ retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly…
When an explicit expression for a probability distribution function $F(x)$ can not be found, asymptotic properties of the tail probability function $\bar{F}(x)=1-F(x)$ are very valuable, since they provide approximations or bounds for…
In this paper, we consider the number of both arrivals and departures seen by a tagged customer while in service in a classical $M/M/1$ processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system…
We give a simple derivation of the distribution of the maximum L of the length of the queue during a busy period for the M/M/1 queue with lambda<1 the ratio between arrival rate and service rate. We observe that the asymptotic behavior of…
We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service…
We introduce a queueing system that alternates between two modes, so-called {\it working mode} and {\it vacation mode}. During the working mode the system runs as an $M^{X}/G/1$ queue. Once the number of customers in the working mode drops…
The $M/GI/m/n$ queueing system with $m$ homogeneous servers and the finite number $n$ of waiting spaces is studied. Let $\lambda$ be the customers arrival rate, and let $\mu$ be the reciprocal of the expected service time of a customer.…
In this article a special case of an M/G/2-queue is considered, where the two servers are exposed to two types of jobs that are distributed among the servers via a random switch. In this model the asymptotic behaviour of the workload buffer…
We calculate asymptotics of the distribution of the number of customers in orbit in a two-class priority retrial $M/G/1$-type queueing model. In this model, priority customers wait in line while non-priority customers join an orbit and…
The present paper provides some new stochastic inequalities for the characteristics of the $M/GI/1/n$ and $GI/M/1/n$ loss queueing systems. These stochastic inequalities are based on substantially deepen up- and down-crossings analysis, and…
We study critical GI/G/1 queues under finite second moment assumptions. We show that the busy period distribution is regularly varying with index half. We also review previously known M/G/1/ and M/M/1 derivations, yielding exact asymptotics…
In this paper, by the singular-perturbation technique, we investigate the heavy-traffic behavior of a priority polling system consisting of three M/M/1 queues with threshold policy. It turns out that the scaled queue-length of the…
The main contribution of this paper is to present a new sufficient condition for the subexponential asymptotics of the stationary distribution of a GI/GI/1-type Markov chain without jumps from level "infinity" to level zero. For simplicity,…