Tight bounds for the maximum throughput of time-multiplex switches

The throughput of a time-multiplex switch can be maximized by resolving transmission conflict such that the maximum number of packets are switched in each slot. We propose an upper-bound and a lower-bound for the maximum throughput of time-multiplex switches. These bounds are given in closed-form expressions, they are very tight, and they are significantly tighter than the bounds proposed by Mehmet-Ali, Youssefi and Nguyen (see ibid., vol.42, no.12, p.3189, 1994).