A discrete formulation of the theory of sojourn times in a two-state system

2001 ◽  
Vol 289 (3-4) ◽  
pp. 307-320 ◽  
Author(s):  
Marian Boguñá ◽  
Jaume Masoliver ◽  
George H. Weiss
Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1834
Author(s):  
Vlad Stefan Barbu ◽  
Alex Karagrigoriou ◽  
Andreas Makrides

Semi-Markov processes are typical tools for modeling multi state systems by allowing several distributions for sojourn times. In this work, we focus on a general class of distributions based on an arbitrary parent continuous distribution function G with Kumaraswamy as the baseline distribution and discuss some of its properties, including the advantageous property of being closed under minima. In addition, an estimate is provided for the so-called stress–strength reliability parameter, which measures the performance of a system in mechanical engineering. In this work, the sojourn times of the multi-state system are considered to follow a distribution with two shape parameters, which belongs to the proposed general class of distributions. Furthermore and for a multi-state system, we provide parameter estimates for the above general class, which are assumed to vary over the states of the system. The theoretical part of the work also includes the asymptotic theory for the proposed estimators with and without censoring as well as expressions for classical reliability characteristics. The performance and effectiveness of the proposed methodology is investigated via simulations, which show remarkable results with the help of statistical (for the parameter estimates) and graphical tools (for the reliability parameter estimate).


1980 ◽  
Vol 12 (04) ◽  
pp. 1000-1018 ◽  
Author(s):  
J. Walrand ◽  
P. Varaiya

Consider an open multiclass Jacksonian network in equilibrium and a path such that a customer travelling along it cannot be overtaken directly by a subsequent arrival or by the effects of subsequent arrivals. Then the sojourn times of this customer in the nodes constituting the path are all mutually independent and so the total sojourn time is easily calculated. Two examples are given to suggest that the non-overtaking condition may be necessary to ensure independence when there is a single customer class.


2021 ◽  
Vol 13 (10) ◽  
pp. 5582
Author(s):  
Daniele Conversi

This article argues that we need to look at living examples provided by non-state communities in various regions of the world that are, perhaps unwittingly, contributing to the maintenance of the Earth’s optimal thermal balance. These fully sustainable communities have been living outside the mainstream for centuries, even millennia, providing examples in the global struggle against the degradation of social–ecological systems. They have all, to varying degrees, embraced simple forms of living that make them ‘exemplary ethical communities’ (EECs)—human communities with a track record of sustainability related to forms of traditional knowledge and the capacity to survive outside the capitalist market and nation-state system. The article proceeds in three steps: First, it condenses a large body of research on the limits of the existing nation-state system and its accompanying ideology, nationalism, identifying this institutional–ideological complex as the major obstacle to tackling climate change. Second, alternative social formations that could offer viable micro-level and micro-scale alternatives are suggested. These are unlikely to identify with existing nation-states as they often form distinct types of social communities. Taking examples from hunter-gatherer societies and simple-living religious groups, it is shown how the protection and maintenance of these EECs could become the keystone in the struggle for survival of humankind and other forms of life. Finally, further investigation is called for, into how researchers can come forward with more examples of actually existing communities that might provide pathways to sustainability and resistance to the looming global environmental catastrophe.


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