The problem of performing software tests using Testing-as-a-Service cloud environment is considered and formulated as an~online cluster scheduling on parallel machines with total flowtime criterion. A mathematical model is proposed. Several properties of the problem, including solution feasibility and connection to the classic scheduling on parallel machines are discussed. A family of algorithms based on a new priority rule called the Smallest Remaining Load (SRL) is proposed. We prove that algorithms from that family are not competitive relative to each other. Computer experiment using real-life data indicated that the SRL algorithm using the longest job sub-strategy is the best in performance. This algorithm is then compared with the Simulated Annealing metaheuristic. Results indicate that the metaheuristic rarely outperforms the SRL algorithm, obtaining worse results most of the time, which is counter-intuitive for a metaheuristic. Finally, we test the accuracy of prediction of processing times of jobs. The results indicate high (91.4%) accuracy for predicting processing times of test cases and even higher (98.7%) for prediction of remaining load of test suites. Results also show that schedules obtained through prediction are stable (coefficient of variation is 0.2-3.7%) and do not affect most of the algorithms (around 1% difference in flowtime), proving the considered problem is semi-clairvoyant. For the Largest Remaining Load rule, the predicted values tend to perform better than the actual values. The use of predicted values affects the SRL algorithm the most (up to 15% flowtime increase), but it still outperforms other algorithms.