What is it about?
The end-to-end performance of a tandem router network with batch arrivals is optimized in an M/G/1 queue-based, analytical model, subject to a specified upper limit on the rate of losses and finite capacity queueing and recovery buffers. 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. 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. 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. 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, yielding a different penalty.
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Why is it important?
For low latency networks, like wireless 5G, the optimisation of time response across routers is essential.
Perspectives
Our forthcoming research will address time-dependent optimization by stochastic control and, even more interestingly, worst-case design approaches with design tradeoffs amongst minimal transmission times, maximum sustainable data rates and lowest possible packet loss. In addition, we will generalize the present model to Markov modulated Poisson (MMPP) arrivals, which can better represent the correlated nature of modern telecommunications traffic; or even further, to a MAP (Markovian Arrival Process). Whilst a Poisson point process is frequently realistic for node arrival streams since many users are often connected, none of which dominate, the arrival stream from a single user is often not well approximated by a renewal process since inter-arrival times tend to be correlated. Queues with Markov modulated, geometrically batched arrivals have been solved at equilibrium. Finally, the effect of network transmission protocols such as TCP may have a dominant effect on our models’ parameters and structure. If the time varying effect on arrival rate turns out to be highly significant, we may consider fluid models for queuing rather than discrete-state queues to represent the nodes in the same optimization framework.
Professor Louis F Pau
CBS Group of Institutions
Read the Original
This page is a summary of: Mean-variance performance optimization of response time in a tandem router network with batch arrivals, Cluster Computing, March 2007, Springer Science + Business Media,
DOI: 10.1007/s10586-007-0016-9.
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