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Flow cytometers and other particle analyzing devices require the reliable detection of particles for counting, classification, sorting, and other applications. Using miniaturized microfluidic devices opens up new application possibilities, but also poses new challenges for reliable signal detection. Simplifying flow cytometers by eliminating scattering as the second signal channel changes the statistics for fluorescence particle detection due to the now unknown number and position of particles in the fluorescence signal. Furthermore, in applications such as particle sorters, the detection delay must be kept short, and cost considerations may limit the available signal processing power. In this paper, we investigate the statistics of a simple thresholded peak detection algorithm with a defined spatial resolution that satisfies these needs. We define a signal system with statistical properties in accordance with measurements obtained from a miniaturized fluorescence particle detection device. For this model, we derive properties, such as spatial resolution, rate of particle interference, and false positives and false negatives due to noise. Using these properties allows us to predict the device performance during the design phase and therefore optimizes the particle detection device for specific applications to reduce device cost, while still maintaining crucial performance figures. In order to evaluate the applicability of the signal model in a real application, we compare the theoretical amplitude distributions with experimental results.