In one embodiment, a task control block (TCB) for allocating cache storage such as cache segments in a multi-track cache write operation may be enqueued in a wait queue for a relatively long wait period, the first time the task control block is used, and may be re-enqueued on the wait queue for a relatively short wait period, each time the task control block is used for allocating cache segments for subsequent cache writes of the remaining tracks of the multi-track cache write operation. As a result, time-out suspensions caused by throttling of host input-output operations to facilitate cache draining, may be reduced or eliminated. It is appreciated that wait classification of task control blocks in accordance with the present description may be applied to applications other than draining a cache. Other features and aspects may be realized, depending upon the particular application.