Performance of Input-Queued Sparse-Crossbar Packet Concentrators

Packet concentrators are used in shared-memory and knockout switches to select and route packets into individual outputs. Recently, a switch model was introduced to investigate the intrinsic relationship between the switching complexity and traffic characteristics of packet concentrators. Using this model, it was shown that any bipartite packet concentrator with n inputs, m outputs and peak per input and per output rates of v and w packets/unit time respectively must use at least m ( n − mw v + ⌈ w v ⌉) crosspoints to route up to mw packets. In this paper, we establish that if the number of input packets to be concentrated per unit time is allowed to exceed mw, this model reduces to a GI/D/mw queueing system with work-conserving service discipline for any concentrator switch fabric, assuming i.i.d. packet arrivals and a suitable routing algorithm. We then derive formulas for the queue length and packet delay distributions and present an algorithm to route packets in any such concentrator with a minimum crosspoint complexity fabric. We establish the conditions for this concentrator system to be stable under the proposed routing algorithm. Furthermore, simulation results indicate that this algorithm is nearly work-conserving, thus facilitating a minimum crosspoint complexity concentrator with a performance similar to that of concentrators with much higher crosspoint complexity.