This paper proposes a model for the claim occurrence, reporting, and handling process of insurance companies. It is assumed that insurance claims occur according to a Markovian arrival process. An incurred claim goes through some stages of a claim reporting and handling process, such as Incurred But Not Reported (IBNR), Reported But Not Settled (RBNS) and Settled (S). We derive formulas for the...

Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set X and that f(X) is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times λn along which we will be able to estimate the conditional expectation E(f(Xλn+1)|X0, . . . , Xλn) from the observ...

This paper introduces an analytical method for approximating the performability of a firm realtime system modeled by a multi-server queue. The service discipline in the queue is earliestdeadline- first (EDF), which is an optimal scheduling algorithm. Real-time jobs with exponentially distributed relative deadlines arrive according to a Poisson process. All jobs have deadlines until the end of s...

We characterize the conditions under which an absorbing Markovian finite process (in discrete or continuous time) can be transformed into a new aggregated process conserving the Markovian property, whose states are elements of a given partition of the original state space. To obtain this characterization, a key tool is the quasi-stationary distribution associated with absorbing processes. It al...

Process algebras are one of the main tools for modeling and analyzing concurrent systems. However, they can be used to describe only the functional aspect of system behavior. Recently, the relevance of integrating performance evaluation within the process of speciication, design and implementation of concurrent systems has been widely recognized. Hence, an eeort has been made in order to handle...

Process algebras are one of the main tools for modeling and analyzing concurrent systems. However, they can be used to describe only the functional aspect of system behavior. Recently, the relevance of integrating performance evaluation within the process of speciication, design and implementation of concurrent systems has been widely recognized. Hence, an eeort has been made in order to handle...

Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in...

Integrated-time Markovian process calculi rely on actions whose durations are quantified by exponentially distributed random variables. The Markovian bisimulation equivalences defined so far for these calculi treat exponentially timed internal actions like all the other actions, because each such action has a nonzero duration and hence can be observed if it is executed between a pair of exponen...

Measurement-based traac characterization has come to acquire a great deal of importance in high-speed networks. In this paper, we segregate the traac behaviour into the macrody-namics and microdynamics depending on the time scales at which the process is observed. We examine the validity of the Markovian assumption which is commonly made for modeling the macrodynamics of correlated traac in net...

In this paper, we show how to utilize the expectation-maximization (EM) algorithm for efficient and numerical stable parameter estimation of the batch Markovian arrival process (BMAP). In fact, effective computational formulas for the E-step of the EM algorithm are presented, which utilize the well-known randomization technique and a stable calculation of Poisson jump probabilities. Moreover, w...