  In a batch of synchronized queues, customers can only be serviced all at once
or not at all, implying that service remains idle if at least one queue is
empty. We propose that a batch of $n$ synchronized queues in a discrete-time
setting is quasi-stable for $n \in \{2,3\}$ and unstable for $n \geq 4$. A
correspondence between such systems and a random-walk-like discrete-time Markov
chain (DTMC), which operates on a quotient space of the original state-space,
is derived. Using this relation, we prove the proposition by showing that the
DTMC is transient for $n \geq 4$ and null-recurrent (hence quasi-stability) for
$n \in \{2,3\}$ via evaluating infinite power sums over skewed binomial
coefficients.
  Ignoring the special structure of the quotient space, the proposition can be
interpreted as a result of P\'olya's theorem on random walks, since the
dimension of said space is $d-1$.
