Input Queued Switches: Cell Switching vs. Packet Switching

Input Queued(IQ) switches have been very well studied in the recent past. The main problem in the IQ switches concerns scheduling. The main focus of the research has been the £xed length packet-known as cells-case. The scheduling decision becomes relatively easier for cells compared to the variable length packet case as scheduling needs to be done at a regular interval of £xed cell time. In real traf£c dividing the variable packets into cells at the input side of the switch and then re-assembling these cells into packets on the output side achieve it. The disadvantages of this cell-based approach are the following: (a) bandwidth is lost as division of a packet may generate incomplete cells, and (b) additional overhead of segmentation and reassembling cells into packets. This motivates the packet scheduling: scheduling is done in units of arriving packet sizes and in non-preemptive fashion. In [7] the problem of packet scheduling was £rst considered. They show that under any admissible Bernoulli i.i.d. arrival traf£c a simple modi£cation of Maximum Weight Matching (MWM) algorithm is stable, similar to cell-based MWM [1-4]. In this paper, we study the stability properties of packet based scheduling algorithm for general admissible arrival traf£c pattern. We £rst show that the result of [7] extends to general re-generative traf£c model instead of just admissible traf£c, that is, packet based MWM is stable. Next we show that there exists an admissible traf£c pattern under which any work-conserving (that is maximal type) scheduling algorithm will be unstable. This suggests that the packet based MWM will be unstable too. To overcome this dif£culty we propose a new class of “waiting” algorithms. We show that “waiting”-MWM algorithm is stable for any admissible traf£c using ¤uid limit technique [6]