A cyclic renewal process is considered as an extension of an alternating renewal process, where each of the underlying independently and identically distributed (i.i.d.) nonnegative random increments is composed of multiple stages. Such a process may be appropriate for analyzing optimal preventive maintenance policies for production management, where a pair of two stages representing an uptime ...

In this work we provide sufficient conditions under which a general counting process stopped at a random time independent from the process belongs to the reliability decreasing reversed hazard rate (DRHR) or increasing failure rate (IFR) class. We also give some applications of these results in generalized renewal and trend renewal processes stopped at a random time.

We discuss new possibilities which the weakly regenerative approach (when a dependence between two adjacent regeneration cycles is allowed) opens in modeling and simulation of queueing network processes. First we extend the class of regenerative inputs constructing weak regeneration for a superposition of n independent, stationary renewal processes in which case generally, classical regeneratio...

In many tissues, a cellular hierarchy exists in which a small population of stem cells is responsible for the production of the mature cells of the organ. The stem cells maintain themselves through a process known as self-renewal. Similarly, tumors contain a minority population of cancer stem cells that maintain the tumor. Some factors that regulate this process of self-renewal are conserved fr...

Let W be the number of points in (0, t] of a stationary finitestate Markov renewal point process. We derive a bound for the total variation distance between the distribution of W and a compound Poisson distribution. For any nonnegative random variable ζ, we construct a “strong memoryless time” ζ̂ such that ζ − t is exponentially distributed conditional on {ζ̂ ≤ t, ζ > t}, for each t. This is used...

BACKGROUND Curriculum development in the health sciences usually entails a lengthy, in-depth review of most or all aspects of the curriculum. The review usually leads to the generation of a detailed report that is submitted to the Dean or executive committee of the faculty. Much has been written about the process of curriculum development but very little has been written about the important pro...

Consider a data network model in which sources begin to transmit at renewal time points {Sn}. Transmissions proceed for random durations of time {Tn} and transmissions are assumed to proceed at fixed rate unity. We study M(t), the number of active sources at time t, a process we term the activity rate process, since M(t) gives the overall input rate into the network at time t. Under a variety o...

Abstract A two-sided exit problem is solved for a difference of a compound Poisson process and a compound renewal process. The Laplace transforms of the joint distribution of the first exit time, the value of the overshoot and the value of a linear component at this instant are determined. The results obtained are applied to solve the two-sided exit problem for a particular case of this process...

The detection of encrypted stepping-stone attack is considered. Besides encryption and padding, the attacker is capable of inserting chaff packets and perturbing packet timing and transmission order. Based on the assumption that packet arrivals form renewal processes, and a pair of such renewal processes is also renewal, a nonparametric detector is proposed to detect attacking traffic by testin...

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two mai...