Should I Stay or Should I Go? Maximizing Lifetime with Relays

Abstract

We consider the problem of maximizing the lifetime of a wireless connection between a transmitter and a receiver using mobile relays. Initially, all relays are positioned arbitrarily on the line between the transmitter and the receiver and have arbitrary battery capacities. Energy is consumed in proportion to the distance traveled for mobility and in proportion to an exponential function of the distance over which information is sent for communication. The objective is to find positions and thus transmission ranges for the nodes that maximize the lifetime of the network. We study two models, the single deployment model and the multiple deployment model. We show how to compute an optimal solution for the case of no movement cost for both models. When there is a cost for movement we develop some structure for multiple deployment model. We consider a discrete version of the single deployment model, in which relays are deployed on grid points. We provide two algorithms for this case: a dynamic programming algorithm and a binary search algorithm. We prove that both algorithms are FPTASs for the non-discrete problem, if batteries are not too small. We develop a number of heuristics for the multiple deployment model. Our simulations demonstrate the benefit of moving over remaining at initial locations.

Maximizing Barrier Coverage Lifetime with Mobile Sensors

“…The only previous result we are aware of that considered a battery model with movement and transmission on a line is by Phelan et al [14] who considered the problem of maximizing the transmission lifetime of a sender to a receiver on a line using mobile relays.…”

Modeling and Analyzing Duty-Cycling Pipelined-Scheduling MAC for Linear Sensor Networks

“…There are various promising applications of LSNs as introduced above. Existing research work on LSNs involves the framework and architecture design [3], [4], [14], protocol and algorithm design (including routing protocol [15]- [17], node placement and network coverage [18]- [20], MAC protocol and scheduling [5], [13], [21], [22], etc. ), and network modeling and analysis [18], [20], [23]- [25].…”

“…Specifically, for the LSNs modeling and analysis, Phelan et al [18] studied the problem of maximizing the wireless connection lifetime between a pair of stationary transmitter and receiver using mobile relays that are initially placed arbitrarily on the line between the transmitter and the receiver. In [20], an analytical model is developed to estimate the impact of the faulted nodes on the network coverage in LSNs.…”

“…Therefore, for a node in grade i, we have P (0,0)→(0,m) = p r (i)a m−1 + (1 − p r (i))a m , m ∈ [0, K − 1] (12) P (0,0)→(0,K) = p r (i)a ≥K−1 + a ≥K (13) For the transitions between two states in the same retransmission stage, the corresponding transition probabilities are shown below. (14), (15) and (16) correspond to the transitions in retransmission stage 0, and (17) and (18) correspond to the transitions in a non-zero retransmission stage.…”