  Patience Sort sorts a sequence of numbers with a minimal number of queues
that work according to the First-In-First-Out (FIFO) principle. More precisely,
if the length of the longest descreasing subsequence of the input sequence is
$L$, then Patience Sort uses $L$ queues. We ask how much one can improve order
with $k$ queues, where $k < L$? We address this question for two measures of
sortedness: number of down-steps and length of the longest descreasing
subsequence. For the first measure, we give an optimal algorithm. For the
second measure, we give an algorithm that reduces the LDS from $L$ to $L - k +
1$, and we provide a sequence with LDS $L$ that can't be reduced to an LDS
lower than $L - k + 1$ with $k$ queues. Moreover, we study the mergeability of
two sequences of numbers, providing an optimal linear algorithm for two queues
with LDS $\leq 2$. The research was inspired by a problem arising in car
manufacturing.
