As cloud platforms become increasingly popular, accurately understanding I/O behaviors in modern cloud storage is of paramount importance for system design and optimization. This paper sheds new light on the correlation of inter-arrival times of both read and write requests at the block level in four representative cloud storage workloads - AliCloud, Systor'17, MSRC and FIU. Our study reveals that I/O arrivals at the block level are very complex in modern cloud storage. There is a certain degree of correlation in the long-term timescale for request arrival intervals in AliCloud and Systor'17_read. Request arrival intervals in MSRC, FIU and Systor'17_write, however, are almost uncorrelated. The Gaussianity test confirms that I/O burstiness appears to be Gaussian in AliCloud_write and Systor'17_read, but the burstiness is non-Gaussian in other workloads. Importantly, we unfold the existence of self-similarity in cloud storage workloads with a certain degree of correlations, via visual evidence, the autocorrelation structure of the aggregated process of I/O request sequences, and Hurst parameter estimates. We further design an alpha-stable workload model for synthetic I/O generation, and the experimental results demonstrate that our model has an edge over conventional models in terms of accurately emulating I/O burstiness.