Sorting by Shuffling Methods and a Queue

We consider sorting by a queue that can apply permutation from given set over its content. This gives us device \(\mathbb {Q}_{\varSigma }\) corresponding to any shuffling method \(\varSigma \) since every such is associated with of permutations. Two variations these devices are considered - }^{\prime and }^{\text {pop}}\). These require the entire content be unloaded after applied or each pop operation, respectively.