Large closed queueing networks in semi-Markov environment and its application

The paper studies closed queueing networks containing a server station and $k$ client stations. The server station is an infinite server queueing system, and client stations are single-server queueing systems with autonomous service, i.e. every client station serves customers (units) only at random instants generated by a strictly stationary and ergodic sequence of random variables. The total number of units in the network is $N$. The expected times between departures in client stations are $(N\mu_j)^{-1}$. After a service completion in the server station, a unit is transmitted to the $j$th client station with probability $p_{j}$ $(j=1,2,...,k)$, and being processed in the $j$th client station, the unit returns to the server station. The network is assumed to be in a semi-Markov environment. A semi-Markov environment is defined by a finite or countable infinite Markov chain and by sequences of independent and identically distributed random variables. Then the routing probabilities $p_{j}$ $(j=1,2,...,k)$ and transmission rates (which are expressed via parameters of the network) depend on a Markov state of the environment. The paper studies the queue-length processes in client stations of this network and is aimed to the analysis of performance measures associated with this network. The questions risen in this paper have immediate relation to quality control of complex telecommunication networks, and the obtained results are expected to lead to the solutions to many practical problems of this area of research.Comment: 35 pages, 1 figure, 12pt, accepted: Acta Appl. Mat

Carvalheiro2019Ecography_data

Dataset to run TREND function This file contains richness change values per cell obtained after running Multilevel.RAR_EXTR.r (https://github.com/lgcarvalheiro/richness.change/blob/master/Multilevel.RAR_EXTR.r) which were later used to run Trend.extractorV3 (https://github.com/lgcarvalheiro/richness.change/blob/master/Trend.extractorV3) and generate Figures published in Carvalheiro et al. 2019 (doi: 10.1111/ecog.04656) Note that bias due to differences in sampling effort is checked and corrected after running Trend.extractorV3, so this database is just an intermediate file and should not be used in other analyses or for plotting richness change values. For access to the original files (spatially and temporally explicit list of records) that were used to run Multilevel.RAR_EXTR.r please contact the authors. Dataset after running TREND function This file provides the corrected richness change values per cell for different time periods comparisons. This file was used to generate Fig 2 and Fig 3 of Carvalheiro et al. 2019 (doi: 10.1111/ecog.04656) and was used to run the analyses which generated Fig 4 of the same publication

The classical myth of Ulysses versus Palamedes: an early metaphor for the qualitative/quantitative debate?

Greek mythology, Qualitative, Quantitative, Methodology, Epistemology, Debate, Interpretation, Ulysses, Palamedes,