Computation-as-a-Service (CaaS) offerings have gained traction in the last few years due to their effectiveness in balancing between the scalability of Software-as-a-Service and the customisation possibilities of Infrastructure-as-a-Service platforms. To function effectively, a CaaS platform must have three key properties: (i) reactive assignment of individual processing tasks to available cloud instances (compute units) according to availability and predetermined time-to-completion (TTC) constraints; (ii) accurate resource prediction; (iii) efficient control of the number of cloud instances servicing workloads, in order to optimize between completing workloads in a timely fashion and reducing resource utilization costs. In this paper, we propose three approaches that satisfy these properties (respectively): (i) a service rate allocation mechanism based on proportional fairness and TTC constraints; (ii) Kalman-filter estimates for resource prediction; and (iii) the use of additive increase multiplicative decrease (AIMD) algorithms (famous for being the resource management in the transport control protocol) for the control of the number of compute units servicing workloads. The integration of our three proposals\ into a single CaaS platform is shown to provide for more than 27% reduction in Amazon EC2 spot instance cost against methods based on reactive resource prediction and 38% to 60% reduction of the billing cost against the current state-of-the-art in CaaS platforms (Amazon Lambda and Autoscale).