Estimating Bird / Aircraft Collision Probabilities and Risk Utilizing Spatial Poisson Processes

In this article we give some characterizations of Poisson processes, the model which we consider is inspired by Kimeldorf and Thall (1983) and we generalize the results of Chandramohan and Liang (1985). More precisely, we consider an arbitrarily delayed renewal process, at each arrival time we allow the number of arrivals to be i.i.d. random variables, also the mass of each unit atom can be split into k new atoms with the ith new atom assigned to the process Di, i = 1, ···, k. We shall show that the existence of a pair of uncorrelated processes Di, Dj, i ≠ j, implies the renewal process is Poisson. Some other related characterization results are also obtained.

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A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

Mathematical Problems in Engineering ◽

10.1155/2017/3298605 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

Ekaterina Evdokimova ◽

Sabine Wittevrongel ◽

Dieter Fiems

Keyword(s):

Performance Measures ◽

Queueing Systems ◽

Poisson Processes ◽

Series Expansions ◽

Service Rate ◽

Single Server ◽

Queueing Model ◽

State Space Explosion ◽

Finite Queues ◽

Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

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Modeling wildfires via marked spatio-temporal Poisson processes

Environmental and Ecological Statistics ◽

10.1007/s10651-021-00497-1 ◽

2021 ◽

Author(s):

José J. Quinlan ◽

Carlos Díaz-Avalos ◽

Ramsés H. Mena

Keyword(s):

Poisson Processes ◽

Spatio Temporal

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Radial generation of n-dimensional poisson processes

Journal of Applied Probability ◽

10.1017/s0021900200028746 ◽

1984 ◽

Vol 21 (03) ◽

pp. 548-557

Author(s):

M. P. Quine ◽

D. F. Watson

Keyword(s):

Poisson Process ◽

Poisson Processes ◽

Three Dimensions ◽

Simulation Studies ◽

Simple Method ◽

Efficient Simulation ◽

Nearest Neighbours

A simple method is proposed for the generation of successive ‘nearest neighbours' to a given origin in ann-dimensional Poisson process. It is shown that the method provides efficient simulation of random Voronoi polytopes. Results are given of simulation studies in two and three dimensions.

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