Logarithmic delay for N × N packet switches under the crossbar constraint

We consider the fundamental delay bounds for scheduling packets in anN×N packet switch operating under the crossbar constraint. Algorithms that make scheduling decisions without considering queue backlog are shown to incur an average delay of at least O(N). We then prove that O(log(N)) delay is achievable with a simple frame based algorithm that uses queue backlog information. This is the best known delay bound for packet switches, and is the first analytical proof that sublinear delay is achievable in a packet switch with random inputs. The algorithm can be implemented with O(N log(N)) total operations per timeslot. Similar results for switches with speedup are provided, and complexity and delay tradeoffs are considered.