A Note on the Effects of Service Time Distribution in the M/G/1 Queue

The M/G/1 queue is a classical model used to represent a large number of real-life computer and networking applications. In this note, we show that, for coefficients of variation of the service time in excess of one, higher-order properties of the service time distribution may have an important effect on the steady-state probability distribution for the number of customers in the M/G/1 queue. As a result, markedly different state probabilities can be observed even though the mean numbers of customers remain the same. This should be kept in mind when sizing buffers based on the mean number of customers in the queue. Influence of higher-order distributional properties can also be important in the M/G/1/K queue where it extends to the mean number of customers itself. Our results have potential implications for the design of benchmarks, as well as the interpretation of their results

Nutrient loads exported from managed catchments reveal emergent biogeochemical stationarity

Complexity of heterogeneous catchments poses challenges in predicting biogeochemical responses to human alterations and stochastic hydro?climatic drivers. Human interferences and climate change may have contributed to the demise of hydrologic stationarity, but our synthesis of a large body of observational data suggests that anthropogenic impacts have also resulted in the emergence of effective biogeochemical stationarity in managed catchments. Long?term monitoring data from the Mississippi?Atchafalaya River Basin (MARB) and the Baltic Sea Drainage Basin (BSDB) reveal that inter?annual variations in loads (LT) for total?N (TN) and total?P (TP), exported from a catchment are dominantly controlled by discharge (QT) leading inevitably to temporal invariance of the annual, flow?weighted concentration, Cf = (LT/QT). Emergence of this consistent pattern across diverse managed catchments is attributed to the anthropogenic legacy of accumulated nutrient sources generating memory, similar to ubiquitously present sources for geogenic constituents that also exhibit a linear LT?QT relationship. These responses are characteristic of transport?limited systems. In contrast, in the absence of legacy sources in less?managed catchments, Cf values were highly variable and supply limited. We offer a theoretical explanation for the observed patterns at the event scale, and extend it to consider the stochastic nature of rainfall/flow patterns at annual scales. Our analysis suggests that: (1) expected inter?annual variations in LT can be robustly predicted given discharge variations arising from hydro?climatic or anthropogenic forcing, and (2) water?quality problems in receiving inland and coastal waters would persist until the accumulated storages of nutrients have been substantially depleted. The finding has notable implications on catchment management to mitigate adverse water?quality impacts, and on acceleration of global biogeochemical cycles.Water ManagementCivil Engineering and Geoscience

Priorities and interactions of Sustainable Development Goals (SDGs) with focus on wetlands

Wetlands are often vital physical and social components of a country's natural capital, as well as providers of ecosystem services to local and national communities. We performed a network analysis to prioritize Sustainable Development Goal (SDG) targets for sustainable development in iconic wetlands and wetlandscapes around the world. The analysis was based on the information and perceptions on 45 wetlandscapes worldwide by 49 wetland researchers of the GlobalWetland Ecohydrological Network (GWEN). We identified three 2030 Agenda targets of high priority across the wetlandscapes needed to achieve sustainable development: Target 6.3-"Improve water quality"; 2.4-"Sustainable food production"; and 12.2-"Sustainable management of resources". Moreover, we found specific feedback mechanisms and synergies between SDG targets in the context of wetlands. The most consistent reinforcing interactions were the influence of Target 12.2 on 8.4-"Efficient resource consumption"; and that of Target 6.3 on 12.2. The wetlandscapes could be differentiated in four bundles of distinctive priority SDG-targets: "Basic human needs", "Sustainable tourism", "Environmental impact in urban wetlands", and "Improving and conserving environment". In general, we find that the SDG groups, targets, and interactions stress that maintaining good water quality and a "wise use" of wetlandscapes are vital to attaining sustainable development within these sensitive ecosystems. © 2019 by the authors

Priorities and interactions of Sustainable Development Goals (SDGs) with focus on wetlands

10.3390/w11030619Water (Switzerland)11361