AI 中文总结
研究传感器网络中发送方和接收方能量消耗，考虑含能量包和数据包的模型，证明了马尔可夫链稳态分布有乘积形式解，给出遍历性条件，还证明了计算流值数值算法的收敛性和正确性。
AI 中文摘要
我们考虑一种包含能量包和数据包的新型模型，其中数据包的传输在发送方和接收方节点都需要能量。能量包是表示发送和接收一个数据包所需能量量子的离散焦耳数。两种类型的包都存储在队列中。能量包队列模拟电池。没有能量时，发送方的发射会延迟，当数据包到达没有足够能量的接收方时会丢失。这种机制意味着几个队列之间存在新的复杂同步。尽管复杂，但我们证明在一些经典假设下，马尔可夫链的稳态分布具有乘积形式解。我们给出遍历性的充分条件，并证明计算流值的数值算法的收敛性和正确性。
英文摘要
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.
