This paper considers a multiclass Markovian fluid queue with a buffer of infinite capacity. Input rates of fluid flows in respective classes and the drain rate from the buffer are modulated by a continuous-time Markov chain with finite states. We derive the joint Laplace-Stieltjes transform for the stationary buffer contents in respective classes, assuming the FIFO service discipline. Further w...

In this paper we introduce the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process components. We use the physical interpretation of a Rational Arrival Process (RAP), developed by Asmussen and Bladt, to consider such a Markov process. We exploit this interpretation to develop an analytic method for such a process, that parallels the analysis of a traditional QBD. We d...

We have considered a distribution inventory system with one warehouse and several retailers. Customer demand arrives at the retailers and the material flow between echelons is driven by reorder point/order quantity inventory control policies. Our objective is to calculate the long-run inventory statistics. The challenge in this system is to characterize the demand arrival process at the warehou...

This paper models a call center as a Markovian queue with multiple servers, where customer impatience, and retrials are modeled explicitly. The model is analyzed as a continuous time Markov chain. The retrial phenomenon is explored numerically using a real example, to demonstrate the magnitude it can take and to understand its sensitivity to various system parameters. The model is then used to ...

We consider a dual form of Markov renewal equation and derive limit results for the solution of it by analogy with the results for the standard form of Markov renewal equation. As an application of the derived results, we consider the tail asymptotics of the stationary workload distribution of the single-server queue with a Markovian arrival stream and show that our approach can give a simpler ...

We consider a Markovian multiserver queueing model with time dependent parameters where waiting customers may abandon and subsequently retry. We provide simple uid and di usion approximations to estimate the mean, variance, and density for both the queue length and virtual waiting time processes arising in this model. These approximations, which are generated by numerically integrating only 7 o...

1.1. Rationale The Jackson network [1] is a basic model favored as a useful beginning approach to many queueing network problems. Its appeal stems from not only its product-form solution for the joint distribution of the number of customers in each queue but also from the simplicity of the structures of the model. Markovian routing is one such structure. The purpose of this paper is to study so...

Statistical evidence suggests that the autocorrelation function (k) (k = 0; 1; : : :) of a compressed-video sequence is better captured by (k) = e ? p k than by (k) = k ? = e ? log k (long-range dependence) or (k) = e ?k (Markovian). A video model with such a correlation structure is introduced based on the so-called M jGj1 input processes. In essence, the M jGj1 process is a stationary version...