Mean-variance performance optimization of response time in a tandem router network with batch arrivals

The end-to-end performance of a simple wireless router network with batch arrivals is optimized in an M/G/1 queue-based, analytical model. The optimization minimizes both the mean and variance of the transmission delay (or 'response time'), subject to an upper limit on the rate of losses and finite capacity queueing and recovery buffers. Losses may be due to either full buffers or corrupted data. The queueing model is also extended to higher order moments beyond the mean and variance of the response time. The trade-off between mean and variance of response time is assessed and the optimal ratio of arrival-buffer size to recovery-buffer size is determined, which is a critical quantity, affecting both loss rate and transmission time. Graphs illustrate performance in the near-optimal region of the critical parameters. 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 resend 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.