Mathematics – Optimization and Control
Scientific paper
2011-05-20
Mathematics
Optimization and Control
6 pages, 2 figures, Extended version of IEEE ISIT 2011
Scientific paper
It has been well established that reverse-carpooling based network coding can significantly improve the efficiency of multi-hop wireless networks. However, in a stochastic environment when there are no opportunities to code because of packets without coding pairs, should these packets wait for a future opportunity or should they be transmitted without coding? To help answer that question we formulate a stochastic dynamic program with the objective of minimizing the long-run average cost per unit time incurred due to transmissions and delays. In particular, we develop optimal control actions that would balance between costs of transmission against those of delays. In that process we seek to address a crucial question: what should be observed as the state of the system We analytically show that just the queue lengths is enough if it can be modeled as a Markov process. Subsequently we show that a stationary policy based on queue lengths is optimal and describe a procedure to find such a policy. We further substantiate our results with simulation experiments for more generalized settings.
Abedini Navid
Gautam Natarajan
Hsu Yu-Pin
Ramasamy Solairaja
Shakkottai Srinivas
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