Nightclub bar dynamics: statistics of serving times

In this work, we investigate the statistical properties of drink serving in a nightclub bar, utilizing a stochastic model to characterize pedestrian dynamics within the venue. Our model comprises a system of n agents moving across an underlying square lattice of size l representing the nightclub venue. Each agent can exist in one of three states: thirsty, served, or dancing. The dynamics governing the state changes are influenced by a memory time, denoted as {\tau}, which reflects their drinking habits. Agents' movement throughout the lattice is controlled by a parameter {\alpha} which measures the impetus towards/away from the bar. When {\alpha} = 0, a power-law distribution emerges due to the non-objectivity of the agents. As {\alpha} moves into intermediate values, an exponential behavior is observed, as it becomes possible to mitigate the drastic jamming effects in this scenario. However, for higher {\alpha} values, the power-law distribution resurfaces due to increased jamming. We also demonstrate that the average concentration of served, thirsty, and dancing agents provide a reliable indicator of when the system reaches a jammed state. Subsequently, we construct a comprehensive map of the system's stationary state, supporting the idea that for high densities, {\alpha} is not relevant, but for lower densities, the optimal values of measurements occurs at high values of {\alpha}. To complete the analysis, we evaluate the conditional persistence, which measures the probability of an agent failing to receive their drink despite attempting to do so. In addition to contributing to the field of pedestrian dynamics, the present results serve as valuable indicators to assist commercial establishments in providing better services to their clients, tailored to the average drinking habits of their customers.