By Klee V. (ed.)

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**Extra resources for Convexity**

**Sample text**

Because of the overhead involved in checking the load on each CPU, a front-end processor will distribute incoming jobs randomly; that is, an incoming job will have a 50% chance of being assigned to CPU A, and a 50% chance of being assigned to CPU B. The design question is whether the random allocation strategy can lead to a severe imbalance in processor load. ). The system does not yet exist, so it is not possible to obtain a sample path. However, since the job routing is equally likely, routing inputs can be generated by flipping a fair coin.

Therefore, the definition of “better service” is not straight-forward. Modeling and analysis of systems that are subject to uncertainty is the topic of this book. The mathematical models that we develop to analyze such systems are called stochastic processes. “Stochastic” is a synonym for random. The words used in the previous paragraph were carefully chosen. System refers to a physical entity, such as The Darker Image, which may be real or conceptual (yet to be constructed). Systems are subject to uncertainty, which we cannot completely control.

In some contexts the height h2 may be interpreted as the probability of a value falling in this interval. Using an indicator function to represent a histogram may seem unnecessarily complicated, but the simple idea of an indicator function turns out to be a powerful representation that we exploit later in the book. 3 shows several histograms where the intervals are plotted along the horizontal axis and the heights hj are plotted along the vertical axis. The intervals at each end, (c0, c1] and (ck–1, ck], are often omitted from a histogram when they are empty, and the widths of the other intervals, cj – cj–1, are typically identical.