Abstract
Moving data across communication networks is often subject to deadline requirements. An example is early warning of disasters of natural origin, where sensor measurements at the disaster location must be communicated across a network within a predefined maximum delay in order for a consequent warning to be timely. In this work, we present a probabilistic model that allows for characterizing the delay experienced by sensor measurements in a wireless sensor network from source to sink depending upon the routing metric used for forwarding the data through the network. Using link delay probability distributions and the probabilities of following different paths to the sink, source-to-sink delay distributions are found for routing policies based on minimum hop-count, minimum mean delay and the Joint Latency (JLAT) protocol. An algorithm for calculating the end-to-end source to sink delay probability density function (PDF) is presented for the general case of networks that use routing tables whose input for routing decisions is the remaining time-to-deadline. The work provides a general tool for routing delay analysis, allowing for comparison of the deadline miss probability between different routing policies. An improved form of JLAT is proposed. Its deadline miss probability is found using the presented algorithm and compared to the ones determined for minimum hop-count, minimum mean delay and JLAT by means of an example.
Highlights
Consider a wireless sensor network (WSN) with nodes connected by edges
The method is valid for any routing policy in which the hop is determined based on the time en route of the data to be forwarded. (Fixed routing tables that ignore the time en route are special cases for which the method is valid.) The technique builds on a mathematical model we develop for the probability distribution of the time en route of data as it journeys from its source node towards the sink
The model is used in an iterative algorithm for determining the end-to-end delay probability distribution seen from a node to the sink, when data is forwarded on each hop by minimizing the probability of missing a deadline given the time en route spent already up to the current hop
Summary
Consider a wireless sensor network (WSN) with nodes connected by edges. All nodes may be sources of data, which is relayed from node to node in multihop fashion along the edges toward the desired destination nodes [1]–[5]. This can cause that the probability of missing the deadline is larger for P1 than for P2 even though the expected delay of P1 is smaller From this example, it is compelling to consider the probability density functions of paths delays (Fig. 1) for routing decisions, rather than statistical parameters about them, such as the mean value of those distributions. The model is used in an iterative algorithm for determining the end-to-end delay probability distribution seen from a node to the sink, when data is forwarded on each hop by minimizing the probability of missing a deadline given the time en route spent already up to the current hop. This paper is organized as follows: Section II presents a general model for calculating the delay probability distribution functions of paths and the DMP from a given node to the sink.
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