Automated surveillance is critically important in the current scenario of heightened security concerns. Therefore, there has been a surge in the development of surveillance systems. Surveillance systems employ sensors to capture various environmental aspects in order to reason about the dynamically changing situation. Due to their cheap availability, the number of sensors used in modern systems is quite large. While processing the large amount of sensor data, the system faces many bottlenecks in terms of processor and memory requirements. Despite many efforts to propose efficient system architectures, they all ignore the study of the dynamic behavior of the system and the impact of various factors on system performance. In this work, we develop an analytical model to evaluate the performance of surveillance systems. Using the proposed model, we obtain closed form equations for event miss probability and response time as a function of system parameters. The results obtained from the model are validated with those obtained from the simulator. Finally we explore the different trade-offs among the system parameters and performance metrics.