Resistive switching (RS) is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start playing a role that cannot be neglected. A detailed understanding of switching mechanisms and reliability is essential. For this reason, we formulate a particle model based on the stochastic motion of oxygen vacancies. It allows us to investigate fluctuations in the resistance states of a switch with two active zones. The vacancies' dynamics are governed by a master equation. Upon the application of a voltage pulse, the vacancies travel collectively through the switch. By deriving a generalized Burgers equation we can interpret this collective motion as nonlinear traveling waves, and numerically verify this result. Further, we define binary logical states by means of the underlying vacancy distributions, and establish a framework of writing and reading such memory element with voltage pulses. Considerations about the discriminability of these operations under fluctuations together with the markedness of the RS effect itself lead to the conclusion, that an intermediate vacancy number is optimal for performance. of sneak paths around it are drastically reduced. As such, the concept has been picked up by various works, see e.g. [6,[18][19][20][21][22]. Conceptually, this setup is similar to having a single element with two active switching zones, one at each electrode-TMO boundary, as it will be applied in this work.Fluctuations can appear externally and internally. They have been studied for phenomenological memristor models , whose resistance is determined by a single internal scalar variable, which denotes the relative sizes of a high and low and high resistivity area. Internal fluctuations are incorporated by adding white noise to this variable, [23,24], with beneficial effects on the RS-effect, such as increasing the contrast between the resistive states. External fluctuations were studied in the form of noisy impulses switching the states, and depending on the setup can either have a positive [25,26] or detrimental effect [24]. As yet, no study of fluctuations has been conducted for a particle based model.Such an approach is essential to address many characteristics of RS. From experimental observations it is known that the functionality of a RS device is determined by the electrode-TMO interface and the distribution of oxygen vacancies [27][28][29]. In this setting, a one-dimensional lattice model in which a probability distribution of the vacancies evolves depending on the external voltage and the local resistance of each lattice site is proportional to its density of vacancies has been proposed in [30] for manganites, termed the voltage enhanced oxygen-vacancy migration model (VEOV-model) by the authors. The Schottky barriers are incorporated by enhancing the vacancies effect near the interfaces compared to the bulk, resulting effectively in a two active switching zo...