A storage device communicates with a host device that generates an original packet. The storage device includes a memory device including a die having multiple planes, and a controller. The controller includes; an operation checker that receives the original packet indicating a simultaneous parallel work request that occupies at least two planes among the multiple planes, wherein the operation checker sets a simultaneous parallel identifier associated with the original packet to generate a modified packet, an operation distributor that stores the modified packet in at least one virtual output queue of a virtual queue cluster, and a scheduler that transmits the modified packet to at least one plane among the multiple planes occupied by the simultaneous parallel work request according to a scheduling policy.