The analysis of systems executing a set of transactions composed by a number of tasks is required in some application domains, such as distributed systems or many audio/video streaming systems. This paper deals with the time response analysis of such systems, considering periodic uniprocessor transactions, and tasks, characterized by their fixed priority and execution time, connected in series through bounded buffers. The scheduling policy allows several transaction jobs to be active at a time, which is possible by putting intermediate task results in the buffers. When the output buffer of a task is full, the task becomes blocked and priority inversion arises. An analysis method is described that allows to calculate the worst-case response time of the transactions in order to be compared with their end-to-end deadlines. Besides, the results of the method application show how task priorities or buffer sizes influence the transaction response times.