The expectation of a random variable is its average value, where each value is weighted according to the probability that it comes up. The expectation is also called the expected value or the mean of the random variable. For example, suppose we select a student uniformly at random from the class, and let R be the student’s quiz score. Then E [R] is just the class average —the first thing everyo...

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Block-flexure is the most common mode of toppling failure in natural and excavated rock slopes. In such failure, some rock blocks break due to tensile stresses and some overturn under their own weights and then all of them topple together. In this paper, first, a brief review of previous studies on toppling failures is presented. Then, the physical and mechanical properties of experimental mode...

Many service systems exhibit service slowdowns when the system is congested. Our goal in this paper is to investigate this phenomenon and its effect on system performance. We modify the Erlang-A model to account for service slowdowns and carry out the performance analysis in the Quality-and-Efficiency Driven (QED) regime. We find that when the load sensitivity is low, the system can achieve QED...

The strong coupling of software and physical processes in the emerging field of cyber-physical systems (CPS) motivates the development of new methods to respond to failures in both the cyber and physical domains. To this end, we propose a study of existing work on handling failures from various disciplines. If these models and methods are applicable to CPS, appropriate extensions should be made...