The notion of timely status updating is investigated in the context of cloud computing. Measurements of a time-varying process of interest are acquired by a sensor node, and uploaded to a cloud server to undergo some required computations. These computations have random service times that are independent and identically distributed across different uploads. After the computations are done, the results are delivered to a monitor, constituting an update. The goal is to keep the monitor continuously fed with fresh updates over time, which is assessed by an age-of-information(AoI) metric. A scheduler is employed to optimize the measurement acquisition times. Following an update, an idle waiting period may be imposed by the scheduler before acquiring a new measurement. The scheduler also has the capability to preempt a measurement in progress if its service time grows above a certain cutoff time, and upload a fresher measurement in its place. Focusing on stationary deterministic policies, in which waiting times are deterministic functions of the instantaneous AoI and the cutoff time is fixed for all uploads, it is shown that the optimal waiting policy that minimizes the long term average AoI has a threshold structure, in which a new measurement is uploaded following an update only if the AoI grows above a certain threshold that is a function of the service time distribution and the cutoff time. The optimal cutoff is then found for standard and shifted exponential service times. While it has been previously reported that waiting before updating can be beneficial for AoI, it is shown in this work that preemption of late updates can be even more beneficial.