Storage allocation affects important performance measures of distributed storage systems. Most previous studies on the storage allocation consider its effect separately either on the success of the data recovery or on the service rate (time) where it is assumed that no access failure happens in the system. In this paper, we go one step further and incorporate the access model and the success of data recovery into the service rate analysis. In particular, we focus on quasi-uniform storage allocation and provide a service rate analysis for both fixed-size and probabilistic access models at the nodes. Using this analysis, we then show that for the case of exponential waiting time distribution at individuals storage nodes, minimal spreading allocation results in the highest system service rate for both access models. This means that for a given storage budget, replication provides a better service rate than a coded storage solution.