Provided are a method, system, and program automatic adjustment of time a consumer waits to access data from a queue during a waiting phase and transmission phase at the queue. A determination is made as to whether a queue is in a waiting phase or a transmission phase for data in response to waiting for a waiting phase wait time when initiating an operation to access data from the queue. During the waiting phase data is not available in the queue for reading. An incremental wait time is waited in response to determining that the queue is in the waiting phase. A determination is made as to whether the queue is in the waiting phase or the transmission phase in response to waiting the incremental wait time. A total wait time is recorded in response to determining that the queue is in the transmission phase. The at least one recorded total wait time is used to determine the waiting phase wait time to use when initiating the operation to access data from the queue.