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This paper analyzes the performance, for a particular strategy, of a head-per-track type auxiliary storage system in a real-time environment. The prototype system of either fixed-head disks or drums incorporates a hardware queuer. This device attempts to always select first that request for a data transfer which will incur the shortest rotational latency relative to all other possible waiting file access requests. The queueing analysis is concerned with the tradeoff which is experienced in practice between throughput of a stochastic service device and the response time for each service request. An exact analysis of the system is shown to be totally unmanageable. Therefore, the approach is to estimate the results via physical arguments. We obtain an approximate stationary distribution for the waiting time of a file access request in the system.