Distributed (Cloud) Storage Systems (DSS) exhibit heterogeneity in several dimensions such as the volume (size) of data, frequency of data access and the desired degree of reliability. Ultimately, the complex interplay between these dimensions impacts the latency performance of cloud storage systems. To this end, the authors propose and analyze a heterogeneous distributed storage model in which n storage servers (disks) store the data of R distinct classes. Data of class i is encoded using a (n; ki) erasure code and the (random) data retrieval requests can also vary from class to class. They present a queuing theoretic analysis of the proposed model and establish upper and lower bounds on the average latency for each data class under various scheduling policies for data retrieval.