In this paper, we study multi-resource maximin share fair allocation with time discount in a cloud computing system with heterogeneous servers. It primarily focuses on the allocation of computing resources in cloud computing systems when users are dealing with time-sensitive tasks. If users delay handling these tasks, their utility will decrease over time. In addition, users do not always stay in the computing system in this problem. For this problem, we propose a mechanism called maximin share fairness with time discount (MMS-TD) in a heterogeneous cloud computing system. We prove theoretically that the allocation returned by the mechanism is lexicographically max-min optimal, that the allocation satisfies the maximin share fairness, and that the mechanism is Pareto efficiency, proportionality, and strategy-proofness. In addition, we designed an algorithm to realize this mechanism and conducted simulation experiments with Alibaba cluster traces. The experimental results show that regardless of resource utilization or user utility, the MMS-TD mechanism consistently outperforms the other three similar mechanisms.