1. A system, comprising: a memory; and a processor coupled to the memory, wherein the processor performs operations, the operations comprising: receiving, by a storage controller that includes a cache, a command from a host, wherein a set of criteria corresponding to read and write response times for executing the command have to be satisfied for a stringent requirements application, and wherein destage task control blocks maintained in the storage controller store information about processes as data to be written is passed from the host through the cache to storage devices coupled to the storage controller; and adjusting destage rate corresponding to ranks corresponding to a plurality of volumes stored in the storage devices coupled to the storage controller, wherein the set of criteria corresponding to the read and write response times for executing the command are satisfied, and wherein the adjusted destage rate corresponding to the ranks is determined by simulating execution of a benchmark, and wherein the simulating comprises: determining whether read peaks are at a lower rate of input/output (I/O) operations than a rate of I/O operations at which the cache starts to fill and new writes need to wait for destages from the cache to complete; and in response to determining that the read peaks are at a lower rate of I/O operations than a rate of I/O operations at which the cache starts to fill and new writes need to wait for destages from the cache to complete, decreasing number of destage task control blocks to reduce the destage rate, wherein: a destage rate adjustment application determines which ranks are allocated to the stringent requirements application, and wherein a maximum number of destage task control blocks for a rank is set by performing: if the rank is a stringent requirements rank then a maximum number of destage task control blocks allowed for the stringent requirements rank is set to a number that is less than a default number; and if the rank is not a stringent requirements rank then the maximum number of destage task control blocks allowed for the rank that is not a stringent requirements rank is set to the default number.