Consider the language of even-length palindromes $L = \{ WW^R \mid W \in \{0,1\}^* \}$. This language is surely context free and I need an NPDA to recognize it.
But, what if we replace the stack with a queue which supports insert and delete operations? Can a queue automaton accept $L$?
The construction of a PDA except with a FIFO instead of a LIFO data structure attached can mimic any single tape TM as follows: it keeps the cell contents in the queue along with two special markers for the end of the tape and for the head of the TM. Every time you make a move, you just go through the entire queue and re-push everything you pop, making whatever slight modification in head position and tape contents you require.
So this is computationally equivalent to a Turing Machine, so in particular it can recognize $L = \{ww^R \mid w \in \{0, 1\}^*\}$.
