A risk hypothesis and risk measures for throughput capacity in systems

A basic risk hypothesis, expressed as a risk equation, for system throughput capacity (I), and governing all non-growth, non-evolving, agent-directed systems, is proposed and derived. The equation relates throughput capacity, resources and risk relative to the system environment, for efficient environments. The risk equation may be combined with, and thus enhances, a resource-sharing equation relating throughput capacity, resources and the time required to execute complex coordinated sharing procedures, an equation derived in an earlier paper. The basic risk equation shows how expected I increases [decreases] linearly with positive [negative] risk of loss of I in efficient environments. The conventional standard deviation risk measure with respect to the mean, from financial systems, may be used. A proposed, new, usually equivalent measure, called the mean-expected loss risk measure with respect to the hazard-free case, is shown to be more appropriate for systems in general. The concept of an efficient system environment is also proposed. All quantities used in the equation are precisely defined and their units specified. The equation reduces to a numerical expression, and can be subjected to experimental test. The equation clarifies and quantifies basic principles, enabling designers and operators of systems to reason correctly about system risk.