Square time is optimal for simulation of one pushdown store or one queue by an oblivious one-head tape unit
To simulate a pushdown store or queue on-line by an oblivious one-head tape unit takes at least square time. Since each multitape Turing machine can be trivially simulated by an oblivious one-head tape unit in square time, this result is optimal.
scientific article; zbMATH DE number 3919822