In recent years, an increasing number of real-time applications have become more sensitive to the freshness of information, which requires that packets reach the receiver as promptly as possible. As a measure of information freshness, it is of great interest to measure the age of information (AoI) on multi-source networks. In this paper, we propose a new queueing system: the systems with N sources, Single buffer, Non-source-aware, and LCFS-S (NSLS-Q system). To simplify the study, we first studied the queueing system for Two sources, Single buffer, Non-source-aware, and LCFS-S (TSLS-Q system). We then generalize the conclusions to the NSLS-Q system. We model the queueing system using a stochastic hybrid system (SHS) to solve for the age of information in the queueing system. In this, Markov chains are used to represent the state transitions. We then compared the system with other queueing systems through numerical results. The results show that the queue model performs better in terms of AoI compared to the traditional queue model.