A framework for screening experiments and modelling in complex systems

Complex systems are pervasive in science and engineering. Some examples include complex engineered networks such as the internet, the power grid, and transportation networks. The complexity of such systems arises not just from their size, but also from their structure, operation (including control and management), evolution over time, and that people are involved in their design and operation. Our understanding of such systems is limited because their behaviour cannot be characterized using traditional techniques of modelling and analysis.

As a step in model development, statistically designed screening experiments may be used to identify the main effects and interactions most significant on a response of a system. However, traditional approaches for screening are ineffective for complex systems because of the size of the experimental design. Consequently, the factors considered are often restricted, but this automatically restricts the interactions that may be identified as well. Alternatively, the designs are restricted to only identify main effects, but this then fails to consider any possible interactions of the factors.

To address this problem, a specific combinatorial design termed a locating array is proposed as a screening design for complex systems. Locating arrays exhibit logarithmic growth in the number of factors because their focus is on identification rather than on measurement. This makes practical the consideration of an order of magnitude more factors in experimentation than traditional screening designs.

As a proof-of-concept, a locating array is applied to screen for main effects and low-order interactions on the response of average transport control protocol (TCP) throughput in a simulation model of a mobile ad hoc network (MANET). A MANET is a collection of mobile wireless nodes that self-organize without the aid of any centralized control or fixed infrastructure. The full-factorial design for the MANET considered is infeasible (with over 10^{43} design points) yet a locating array has only 421 design points.

In conjunction with the locating array, a ``heavy hitters'' algorithm is developed to identify the influential main effects and two-way interactions, correcting for the non-normal distribution of the average throughput, and uneven coverage of terms in the locating array. The significance of the identified main effects and interactions is validated independently using the statistical software JMP.

The statistical characteristics used to evaluate traditional screening designs are also applied to locating arrays.

These include the matrix of covariance, fraction of design space, and aliasing, among others. The results lend additional support to the use of locating arrays as screening designs.

The use of locating arrays as screening designs for complex engineered systems is promising as they yield useful models. This facilitates quantitative evaluation of architectures and protocols and contributes to our understanding of complex engineered networks.