Emerging applications of wireless sensor networks (WSNs) require real-time quality of service (QoS) guarantees to be provided by the network. However, designing real-time scheduling and communication solutions for these networks is challenging since the characteristics of QoS metrics in WSNs are not well known yet. Due to the nature of wireless connectivity, it is infeasible to satisfy worst-case QoS requirements in WSNs. Instead, probabilistic QoS guarantees should be provided, which requires the definition of probabilistic QoS metrics.

To provide an analytical tool for the development of real-time solutions, in this project, the statistical properties in WSNs are investigated. These properties include end-to-end delay, energy consumption, lifetime, and event detection delay. To analyze these properties, a comprehensive and accurate cross-layer analysis framework, which employs a stochastic queueing model in realistic channel environments, is developed. This framework captures the heterogeneity in WSNs in terms of channel quality, transmit power, queue length, and communication protocols. Our analysis framework is designed to be comprehensive and adaptive to various MAC and routing protocols.

## Probabilistic End-to-End Delay Analysis

The probabilistic analytical framework is first applied to the most important QoS performance metric in WSNs, the end-to-end delay. Based on the framework, single-hop delay distributions are discovered, which are then used to derive the end-to-end delay distribution in WSNs. As a case study, the TinyOS CSMA/CA MAC protocol without Low-Power Listening (LPL), and a representative anycast cross-layer protocol are evaluated to show how the developed framework can analytically predict the distribution of end-to-end delay. Extensive testbed experiments and simulations are conducted to validate the developed model. The cross-layer framework can be used to identify the relationships between network parameters and the distribution of end-to-end delay and accordingly, to design real-time solutions for WSNs. This work has been documented in a paper published in RTSS '09, and a consequential journal paper in IEEE/ACM Transactions on Networking.

## Probabilistic Energy Consumption and Lifetime Analysis

Traditional energy analysis approaches only focus on the average energy consumed. However, for reliability analysis in such networks, the statistical information about energy consumption and lifetime is required. In this project, a stochastic analysis of the energy consumption in a random network environment is provided using the proposed framework. Accordingly, the distribution of energy consumption for nodes in WSNs during a given time period is found. It is also shown that when the time duration is long, the energy consumption asymptotically approaches the Normal distribution. This distribution of energy consumption is then utilized to investigate the distribution of node lifetime and network lifetime. As a case study, a representative anycast protocol is investigated for energy and lifetime analysis. Comprehensive testbed experiments and simulations are provided to validate the developed energy consumption model. By adopting several techniques to increase the simulation speed, long timescale simulations are conducted to validate the proposed lifetime analysis. The cross-layer framework is also used to identify relationships between the distribution of energy consumption and network parameters, such as network density, duty cycle, and traffic rate. A paper about this work has been published in SECON 2010, and a consequential journal paper is in the final revision stage before submission.

Our testbed in Schorr Center CPN Lab is capable to measure energy consumption

continuously for weeks. The gathered energy consumption measurements are used

to validate our proposed analytical model.

The results of energy consumptions from testbed experiments and simulations show that our model is accurate.

The energy consumption tends to be Normally distributed when the duration is large.

## Probabilistic Event Detection Analysis

Emerging applications of wireless sensor networks (WSNs) require real-time event detection to be provided by the network. In a typical event monitoring WSN, multiple reports are generated by several nodes when a physical event occurs, and are then forwarded through multi-hop communication to a sink that detects the event. To improve the event detection reliability, usually timely delivery of a certain number of packets is required. Traditional timing analysis of WSNs are, however, either focused on individual packets or traffic flows from individual nodes. In this work, a spatio-temporal fluid model is developed to capture the delay characteristics of event detection in large-scale WSNs. More specifically, the distribution of delay in event detection from multiple reports is modeled. Accordingly, metrics such as mean delay and soft delay bounds are analyzed for different network parameters. Motivated by the fact that queue build up in WSNs with low-rate traffic is negligible, a lower-complexity model is also developed. Testbed experiments and simulations are used to validate the accuracy of both approaches. The resulting framework can be utilized to analyze the effects of network and protocol parameters on event detection delay to realize real-time operation in WSNs. Please refer to our published paper in INFOCOM 2011 for more information.

## Probabilistic QoS Optimization in WSNs

One of the major contributions of this work is to provide aid for network and protocol designing. Due to the random nature of wireless communications, and low profile of sensor nodes, probabilistic QoS performances of WSNs are crucial for many applications. Therefore, to meet the probabilistic QoS requirements for such applications, our proposed probabilistic QoS analysis is used to optimize various aspects of the network and protocols.

Possible constraints include the following:

- Network density or total number of nodes. This is usually an important constraint when the total cost of the network is limited.
- Queue size for each node. This is usually limited by the hardware capacity of sensor nodes.
- Traffic rate. This constraint is usually requested by the applications.
- Transmission power. Low power will reduce the transmission range, while high power will consume a large amount of energy, reducing node and network lifetime.
- End-to-end delay, and reliability to achieve it.
- Node or network lifetime, and reliability to achieve it.
- Event detection delay, and reliability to achieve it.

The goal of the optimization problem is to find the values of these parameters, subject to the constraints, such that the desired parameter (one of the above) is optimized.

The following are examples of the problems we are interested to solve:

- Given constraints of the queue size, traffic rate, transmission power, and the desired end-to-end delay with a minimum reliability, find an optimal set of their values, such that the total number of nodes is minimized.
- Given constraints of the network density, queue size, traffic rate, and transmission power, find an optimal set of their values, such that the network lifetime is maximized with a given reliability.

The development of this optimization framework is undergoing. The framework is supposed to capture various network deployments and protocols. As a case study, the anycast protocol with random node deployment will be assessed.