Solid-state drives (SSDs) have been added into storage systems for improving their performance, which will bring the heterogeneity into the storage medium. The throughput is one of the essential resources in heterogeneous storage systems, and how to allocate the throughput plays a crucial role in user performance. There are many types of research on the throughput allocation of heterogeneous storage systems. However, the throughput allocation of heterogeneous storage is facing new challenges in a dynamic setting, where users are not present in the system simultaneously, and enter the system dynamically. Drawing on economic gametheory, researchers have proposed many methods to tackle dynamic throughput allocation issues for heterogeneous storages, cross out enjoying Sharing Incentive (SI), Envy Freeness (EF), and Pareto Optimality (PO). However, they either relax constraints of fairness property to cause the allocation with weak fairness or interrupt some users present in the system to give up a piece of their allocations for new users entering the system, which will degrade these donors' performance. Moreover, all of existing methods will cause lower resource utilization due to constraints of users' dominant share equality. In this article, we propose a dynamic throughout allocation method based on gradual increase (DAGI), which can adapt to various workloads to make a fair allocation with a maximum resource utilization. Without relaxing constraints of fairness properties, when new users enter the system, DAGI can make a dynamic allocation with strong fairness by appropriately postponing the allocation of surplus throughputs, so this can provide an opportunity that DAGI can guarantee the final allocation with strong fairness when allocating remaining throughputs after all users are present in the system. Meanwhile, DAGI can gradually increase user allocation without reduction, which will not interrupt any users present in the system. Furthermore, DAGI can conduct a ...