We have proposed a three-parameter renewal approximation to analyze splitting and superposition of autocorrelated processes. We define the index of dispersion for counts of an ordinary process used in a new and more accurate technique to estimate the third parameter. Then, we express this newly defined index of dispersion for the superposition in terms of the ordinary as well as the stationary ...

It has now been demonstrated in many studies that network traac exhibits properties consistent with Long Range Dependence (LRD) and self-similarity. While theoretical frameworks are currently being developed to estimate the performance of such systems, simulation will remain a valuable tool for validating these theoretical models, and providing insight into systems which are too complicated to ...

s for the Workshop on Extremes in Space and Time, May 31 On the extremal behavior of random variables observed at renewal times Bojan Basrak (University of Zagreb) This is joint work with Drago Špoljarić (University of Zagreb). We consider the asymptotic extremal behavior of iid observationsX1, X2, . . ., until a random time τ(t) which is determined by a renewal process, possibly dependent on X...

Data from the urban renewal experience in Syracuse, New York are used to examine the impact of race on patterns of intra-urban migration. The results show that, overall, the migration patterns exhibited an exponential decay in frequency with increasing distance. Both blacks and whites display this pattern, but blacks tend to cluster more closely around the point of origin. Indirect evidence is ...

We study multi-product and multi-item assemble-to-order systems under general assumptions on demand patterns and replenish leadtime distributions. We only assume that the demand process of each product being a renewal process, and the replenish leadtimes follow general distributions. Based upon techniques from renewal theory, we developed procedures for approximating key performance measures of...

Spermatogonial stem cells (SSCs) undergo self-renewal division and support spermatogenesis. Although several cytokines coordinate to drive SSC self-renewal, little is known about the mechanisms underlying this process. We investigated the molecular mechanism by reconstructing SSC self-renewal in vitro without exogenous cytokines. Activation of Ras or overexpression of cyclins D2 and E1, both of...

Abstract We propose dual form of Markov renewal equations. While the dual form is theoretically equivalent to the classical standard form of Markov renewal equation, it is shown to be a useful tool for analysis of recent stochastic models. To demonstrate the power of the dual form of Markov renewal equations, we apply one to tail asymptotic analysis of the stationary workload distribution for a...

In this paper, we consider a certain class of Markov renewal processes where the matrix of the transition kernel governing the Markov renewal process possesses some block-structured property, including repeating rows. Duality conditions and properties are obtained on two probabilistic measures which often play a key role in the analysis and computations of such a block-structured process. The m...

A weighted embedding for the generalized pontogram {Kn(t): 06t61} corresponding pointwise to a renewal process {N (s): 06s¡∞} via Kn(t)=n−1=2(N (nt)− tN (n)) is studied in this paper. After proper normalization, weak convergence results for the processes {Kn(t): 06t61} are derived both in sup-norm as well as in Lp-norm. These results are suggested to serve as asymptotic testing devices for dete...

Let {(Xi; Yi): i= : : : ;−1; 0; 1; : : :} be a doubly in nite renewal-reward process, where {Xi: i= : : :− 1; 0; 1; : : :} is an i.i.d. sequence of renewal cycle lengths and Yi= g(Xi−q; Xi−q+1; : : : ; Xi) is the lump reward earned at the end of the ith renewal cycle, with some function g :R q+1 → R . Starting with the rst renewal cycle (of duration X1) at the time origin, let C(t) denote the e...