This paper addresses two key challenges in real-time systems: determining whether a system can handle its peak processing load without losing any inputs, and finding the exact worst-case response times for each device. The authors define a condition that must be met to ensure the system can handle the peak load and describe a method to compute exact worst-case response times. When this condition is not met, they show how adding buffers can help. They also discuss the use of multiple processors in real-time systems. A real-time system consists of multiple devices connected to a computer, each with a minimum time between inputs and a maximum allowable response time. The system's performance depends on the processing time for each input, which can vary but is bounded. Inputs are processed in priority levels, with higher-priority inputs pre-empting lower-priority ones. The worst-case response time for a device is determined by the sum of the processing times of all higher-priority inputs that occur before the current input is processed. The authors define the worst-case load as the maximum sustained processing load, which occurs when all inputs arrive periodically with the minimum interval and each input requires the maximum processing time. They then derive an exact formula for the worst-case response time, which accounts for the number of higher-priority inputs that occur within the response time interval. This formula is used to compute the worst-case response time for each device. The paper also discusses the use of buffers to handle cases where the worst-case response time exceeds the input repetition time. The number of buffers required is determined based on the worst-case response time and the input repetition time. The authors show that in some cases, the number of buffers can be reduced by adjusting the processing order of inputs. Finally, the paper discusses the use of multiple processors in real-time systems. When the system's load is too high for a single processor, multiple processors can be used to distribute the load and reduce the response time. The authors show that the load equation can be adjusted to account for multiple processors, and that the worst-case response time can be computed using this adjusted equation. They also discuss the challenges of analyzing real-time systems with multiple processors and the importance of ensuring that the system meets its real-time constraints.This paper addresses two key challenges in real-time systems: determining whether a system can handle its peak processing load without losing any inputs, and finding the exact worst-case response times for each device. The authors define a condition that must be met to ensure the system can handle the peak load and describe a method to compute exact worst-case response times. When this condition is not met, they show how adding buffers can help. They also discuss the use of multiple processors in real-time systems. A real-time system consists of multiple devices connected to a computer, each with a minimum time between inputs and a maximum allowable response time. The system's performance depends on the processing time for each input, which can vary but is bounded. Inputs are processed in priority levels, with higher-priority inputs pre-empting lower-priority ones. The worst-case response time for a device is determined by the sum of the processing times of all higher-priority inputs that occur before the current input is processed. The authors define the worst-case load as the maximum sustained processing load, which occurs when all inputs arrive periodically with the minimum interval and each input requires the maximum processing time. They then derive an exact formula for the worst-case response time, which accounts for the number of higher-priority inputs that occur within the response time interval. This formula is used to compute the worst-case response time for each device. The paper also discusses the use of buffers to handle cases where the worst-case response time exceeds the input repetition time. The number of buffers required is determined based on the worst-case response time and the input repetition time. The authors show that in some cases, the number of buffers can be reduced by adjusting the processing order of inputs. Finally, the paper discusses the use of multiple processors in real-time systems. When the system's load is too high for a single processor, multiple processors can be used to distribute the load and reduce the response time. The authors show that the load equation can be adjusted to account for multiple processors, and that the worst-case response time can be computed using this adjusted equation. They also discuss the challenges of analyzing real-time systems with multiple processors and the importance of ensuring that the system meets its real-time constraints.