Parallel sample path construction techniques for discrete event systems: K-constructability and applications

The fundamental sample path constructability problem in discrete event systems is the following: for a finite parameter set Θ={θ₀, θ₁,..., θ_M }, given a sample path under θ₀, we need to construct sample paths under all remaining parameter values. A condition for solving this problem is known as the constructability condition. This condition, however, depends on the initial state assumptions for the observed and each of the constructed sample path. In this paper, we first review the general problem setting and the two main solution approaches known to date, i.e., the standard clock (SC) approach and augmented system analysis (ASA). Then, we provide an extension under which a weaker form of constructability is established, which is independent of initial state conditions. This is referred to as K-constructability. In this case, a sample path may not be constructable for up to K event occurrences, but subsequently does satisfy constructability. We also present an application to the general problem of traffic smoothing where it is shown that constructability is violated, but K-constructability holds