Polling Models with Two-Stage Gated Service: Fairness versus Efficiency ∗

We consider an asymmetric cyclic polling system with general service-time and switchover time distributions with so-called two-stage gated service at each queue, an interleaving scheme that aims to enforce fairness among the different customer classes. For this model, we (1) obtain a pseudo-conservation law, (2) describe how the mean delay at each of the queues can be obtained recursively via the so-called Descendant Set Approach, and (3) present a closed-form expression for the expected delay at each of the queues when the load tends to unity (under proper heavy-traffic scalings), which is the main result of this paper. The results are strikingly simple and provide new insights into the behavior of two-stage polling systems, including several insensitivity properties of the asymptotic expected delay with respect to the system parameters. Moreover, the results provide insight in the delay-performance of two-stage gated polling compared to the classical one-stage gated service policies. The results show that the two-stage gated service policy indeed leads to better fairness compared to onestage gated service, at the expense of a decrease in efficiency. Finally, the results also suggest simple and fast approximations for the expected delay in stable polling systems. Numerical experiments demonstrate that the approximations are highly accurate for moderately and heavily loaded systems

Single-Server Queues with Spatially Distributed Arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time

Astrobiology and the possibility of life on Earth and elsewhere…

Astrobiology is an interdisciplinary scientific field not only focused on the search of extraterrestrial life, but also on deciphering the key environmental parameters that have enabled the emergence of life on Earth. Understanding these physical and chemical parameters is fundamental knowledge necessary not only for discovering life or signs of life on other planets, but also for understanding our own terrestrial environment. Therefore, astrobiology pushes us to combine different perspectives such as the conditions on the primitive Earth, the physicochemical limits of life, exploration of habitable environments in the Solar System, and the search for signatures of life in exoplanets. Chemists, biologists, geologists, planetologists and astrophysicists are contributing extensively to this interdisciplinary research field. From 2011 to 2014, the European Space Agency (ESA) had the initiative to gather a Topical Team of interdisciplinary scientists focused on astrobiology to review the profound transformations in the field that have occurred since the beginning of the new century. The present paper is an interdisciplinary review of current research in astrobiology, covering the major advances and main outlooks in the field. The following subjects will be reviewed and most recent discoveries will be highlighted: the new understanding of planetary system formation including the specificity of the Earth among the diversity of planets, the origin of water on Earth and its unique combined properties among solvents for the emergence of life, the idea that the Earth could have been habitable during the Hadean Era, the inventory of endogenous and exogenous sources of organic matter and new concepts about how chemistry could evolve towards biological molecules and biological systems. In addition, many new findings show the remarkable potential life has for adaptation and survival in extreme environments. All those results from different fields of science are guiding our perspectives and strategies to look for life in other Solar System objects as well as beyond, in extrasolar worlds