Optimization of a tandem M/GI/1 router network with batch arrivals

An optimization methodology is developed for a tandem router network with batch arrivals. The end-to-end performance, computed as the mean transmission delay in a simple analytical model, is minimized subject to an upper limit on the rate of losses and finite capacity queueing and recovery buffers. The optimal ratio of arrival-buffer size to recovery-buffer size is determined, which is a critical quantity that affects both loss rate and transmission time. Losses may be due to either full buffers or corrupted data. Losses at a full buffer are inferred by a time-out whereas corrupted data is detected immediately on receipt of a packet at a router, causing a N-ACK to be sent upstream. Recovery buffers hold successfully transmitted packets so that on receiving a N-ACK, the packet, if present, can be retransmitted, avoiding an expensive re send from source. The impact of the retransmission probability is investigated similarly: too high a value leads to congestion and so higher response times, too low and packets are lost forever, yielding a different penalty. Graphs are shown to illustrate performance in the near-optimal region of the critical parameters.