What probability distribution describes search?

Abstract. Typically, search research papers assume that target acquisition is described by an exponential distribution. We investigate when this assumption is valid. It is obvious that two people are more effective than one person at finding a target, but how can that be quantified? The network imaging sensor (NIS) and time-dependent search parameter (TDSP) models quantify how much more effective multiple observers are at finding a target than a single individual for a wide variety of scenarios. We reference and summarize evidence supporting the NIS and TDSP models and demonstrate how NIS model results can be expressed in terms of a reduced hyperexponential distribution for scenarios where observer and target are stationary. Target acquisition probabilities are determined by analysis and confirmed by computer simulations and perception experiments. Search by multiple stationary observers looking for a stationary target is described by the hyperexponential distribution. Stationary scenarios with multiple observers are more accurately modeled by hyperexponential rather than exponential distributions. Hyperexponential distributions are an example of phase-type distributions used in queuing and in the performance evaluation of computer networks and systems. The observation that search, queuing, and computer networks share phase-type distributions facilitates cross fertilization between these fields.

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