Optimal threshold policy for opportunistic network coding under phase type arrivals

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Date
2016
Authors
Gunasekara, Charith
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Abstract
Network coding allows each node in a network to perform some coding operations on the data packets and improve the overall throughput of communication. However, network coding cannot be done unless there are enough packets to be coded so at times it may be advantageous to wait for packets to arrive. We consider a scenario in which two wireless nodes each with its own buffer communicate via a single access point using network coding. The access point first pairs each data packet being sent from each node and then performs the network coding operation. Packets arriving at the access point that are unable to be paired are instead loaded into one of the two buffers at the access point. In the case where one of the buffers is empty and the other is not network coding is not possible. When this happens the access point must either wait for a network coding opportunity, or transmit the unpaired packet without coding. Delaying packet transmission is associated with an increased waiting cost but also allows for an increase in the overall efficiency of wireless spectrum usage, thus a decrease in packet transmission cost. Conversely, sending packets un-coded is associated with a decrease in waiting cost but also a decrease in the overall efficiency of the wireless spectrum usage. Hence, there is a trade-off between decreasing packet delay time, and increasing the efficiency of the wireless spectrum usage. We show that the optimal waiting policy for this system with respect to total cost, under phase-type packet arrivals, is to have a separate threshold for the buffer size that is dependent on the current phase of each arrival. We then show that the solution to this optimization problem can be obtained by treating it as a double ended push-out queueing theory problem. We develop a new technique to keep track of the packet waiting time and the number of packets waiting in the two ended push-out queue. We use the resulting queueing model to resolve the optimal threshold policy and then analyze the performance of the system using numerical approach.
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Queueing Theory, Network Coding, Markov Decision Process
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