Mathematics – Optimization and Control
Scientific paper
2010-08-27
Mathematics
Optimization and Control
19 pages, 7 figures
Scientific paper
We consider a dynamic vehicle routing problem in wireless networks where messages arriving randomly in time and space are collected by a mobile receiver (vehicle or a collector). The collector is responsible for receiving these messages via wireless communication by dynamically adjusting its position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the delay performance in such networks. We show that the necessary and sufficient condition for the stability of such a system (in the bounded average number of messages sense) is given by {\rho}<1 where {\rho} is the average system load. We derive fundamental lower bounds for the delay in the system and develop policies that are stable for all loads {\rho}<1 and that have asymptotically optimal delay scaling. Furthermore, we extend our analysis to the case of multiple collectors in the network. We show that the combination of mobility and wireless transmission results in a delay scaling of {\Theta}(1/(1- {\rho})) with the system load {\rho} that is a factor of {\Theta}(1/(1- {\rho})) smaller than the delay scaling in the corresponding system where the collector visits each message location.
Çelik Güner D.
Modiano Eytan
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