consider a status update system consisting of a sampler, a controller, a processing unit, a transmitter, and a sink. The sampler generates a sample upon receiving a request from the controller and the sample requires further processing before transmission, hence is computation-intensive. This is mathematically modeled by a server called process server. After processing the sample, the status update packet is generated and sent to the transmitter for delivery to the sink. This is mathematically modeled by a server called transmit server. The service time of each packet at the transmit and process servers follow geometric distributions. Moreover, we consider that the servers serve packets under the blocking policy, i.e., whenever a server is busy at the arrival time of a new packet, the new arriving packet is blocked and discarded. We analyze the average age of information (AoI) for two fixed policies, namely, 1) zero-wait-one policy and 2) zero-wait-blocking policy. According to the former policy, the controller requests sampling when there is no packet in the system. According to the zero-waitblocking policy, the controller requests a sample whenever the process server is idle. Furthermore, we develop an optimal control policy to minimize the average AoI using the tools of Markov decision process (MDP). In numerical results, we evaluate the performance of the policies under different system parameters. Moreover, we analyze the structure of the optimal policy.