🤖 AI Summary
This study addresses the challenges of queue synchronization and energy management in sensor networks where both transmitters and receivers are subject to energy constraints. The authors develop a joint queueing model that integrates energy packets and data packets, wherein data transmission consumes discrete units of energy, and insufficient energy leads to transmission delays or reception failures. Innovatively, under bilateral energy constraints, they formulate a queueing network model admitting a product-form stationary solution. By leveraging Markov chain theory and queueing analysis, they establish sufficient conditions for system ergodicity. Furthermore, they propose a convergent and correct numerical algorithm that efficiently computes the stationary distribution and key traffic performance metrics.
📝 Abstract
We consider a new type of model with energy packets and data packets where the transmission of a data packet requires energy on both the sender and the receiver nodes. Energy packets is a discrete number of Joules representing the quantum of energy needed to send and receive a data packet. Both types of packets are stored in queues. The energy packet queue models a battery. Without energy on the sender, the emission is delayed until energy is available. When a sent packet arrives on a receiver which does not have enough energy, it is lost. This mechanism implies a new complex synchronization between several queues. Despite this complexity, we prove that under some classical assumptions the steady-state distribution of the Markov chain has a product form solution. We state sufficient conditions for ergodicity and we also prove the convergence and the correctness of a numerical algorithm to compute the values of the flows.