To meet the increasing requirement for high speed switches, a multiple input-queued (MIQ) switch is explored. Rather than handling the scheduling problem heavily focused on by many researchers, a proposed dynamic queue allocation algorithm is used to handle non-uniform or hot-spot traffic. Although the performance of the original algorithm is analyzed by N.K. Sharma and M.R. Pinnu (see Parallel Computing, vol.23, p.777-81, 1997) and the orderly property is enhanced by us, Wu and Lin, (see Parallel Computing, vol.24, p.2143-8, 1998), the correctness of the algorithm has not been proven yet. In this report, with the help of the inherent properties of FIFO queues, we prove that the algorithm, and the related MIQ switch, is free from deadlock.