Open queuing network systems are useful in the computer industry. In this paper, a multi-node open network, with heterogeneous nodes, each node serving external as well as routed internal arrivals of jobs is considered. The nodes are prone to failures and repairs, the buffers are of finite size. An approximate performability model is developed based on an IPP departure process. External Poisson...

The long-term goal of this project is a complete and accurate understanding of the properties of acoustic pulses sent over mesoscale to global scales. In particular, I want to understand the forward problem for calculating travel times of the early ray arrivals and late mode arrivals in long-range acoustic transmissions and to understand the sampling associated with those arrivals. The better t...

In this paper, we are concerned with a time-inhomogeneous version of the Markovian Arrival Process. Under the assumption that the environment process is asymptotically time-homogeneous, we discuss a Poisson approximation of the counting process of arrivals when the arrivals are rare. We provide a rate of convergence for the distance in variation. Poisson-type approximation for the process resul...

In this paper, we are concerned with a time-inhomogeneous version of the Markovian Arrival Process. Under the assumption that the environment process is asymptotically time-homogeneous, we discuss a Poisson approximation of the counting process of arrivals when the arrivals are rare. We provide a rate of convergence for the distance in variation. Poisson-type approximation for the process resul...

We model a job in a parallel processing system as a sequence of stages, each of which requires a certain integral number of processors for a certain interval of time. With this model we derive the speedup of the system for two cases: systems with no arrivals, and systems with arrivals. In the case with no arrivals, our speedup result is a generalization of Amdahl’s Law. We extend the notion of ...

In a G/GI/c loss system with balking, reneging, or limited waiting space, deleting some of the arriving customers can either increase or decrease the fraction of the remaining arrivals who get served, depending on how customers are deleted. We present a model in which the random deletion of arrivals independently and with some fixed probability can never decrease the fraction of the remaining a...