A double quasi-birth-and-death (QBD) process is the QBD process whose background process is a homogeneous birth-and-death process, which is a synonym of a skip free random walk in the two dimensional positive quadrant with homogeneous reflecting transitions at each boundary face. It is also a special case of a 0-partially homogenous chain introduced by Borovkov and Mogul’skii [5]. Our main inte...

MOTIVATION Diversification rates and patterns may be inferred from reconstructed phylogenies. Both the time-dependent and the diversity-dependent birth-death process can produce the same observed patterns of diversity over time. To develop and test new models describing the macro-evolutionary process of diversification, generic and fast algorithms to simulate under these models are necessary. S...

We consider a class of stochastic networks with state-dependent arrival and service rates. The state-dependency is described via multi-dimensional birth/death processes, where the birth/death rates are dependent upon the current population size in the system. Under the uniform (in state) stability condition, we establish several moment stability properties of the system: (i) the unique invarian...

A new model is proposed for the analysis of CDMA systems. This model is a birth and death process whose birth process considers the new call arrival rate, the blocking rate, the effect of soft handoff and the effect of the band allocation strategy in multiband (multicarrier) CDMA systems. This model accurately predicts the distribution of the number of calls connected to a base station.

A new model is proposed for the analysis of CDMA systems. This model is a birth and death process whose birth process considers the new call arrival rate, the blocking rate, the effect of soft handoff and the effect of the hand allocation strategy in multiband (multicarrier) CDMA systems. This model accurately predicts the distribution of the number of calls connected to a base station.

Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the well-mixed case, can act as amplifiers or suppressors of selection by increasing or decreasing the fixation probability of a beneficial mutant. Properties of the ass...

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quant...

We prove under mild conditions that the Fleming-Viot process selects minimal quasi-stationary distribution for Markov processes with soft killing on non-compact state spaces. Our results are applied to multi-dimensional birth and death processes, continuous time Galton-Watson diffusion killing.