Modeling Background
Möbius Tool
Motivation
Performance and dependability modeling is an integral part of the design process of many computer and communication systems. A variety of techniques have been developed to address different issues of modeling. For example, combinatorial models were developed to assess reliability and availability under strong independence assumptions; queuing networks were developed to assess system performance; and Markov process-based approaches have become popular for evaluating performance with synchronization or dependability without independence assumptions. Finally, simulation has been used extensively when other methods fail.
As techniques for solving models advanced, formalisms (or formal languages for expressing models) were also developed. Each formalism has its own merits. Some formalisms afford very efficient solution methods; for example, BCMP [3] queuing networks admit product-form solutions, while superposed generalized stochastic Petri nets (SGSPNs) [15] afford Kronecker-based solution methods, and colored GSPNs (CGSPNs) [6] yield state-space reductions. Other formalisms, such as SPNs [25] and SPAs [18], provide a simple elegance in their modeling primitives, while a number of extensions, such as stochastic activity networks (SANs) [24], were developed for compactly expressing complex behaviors.
Along with formalisms, tools have been developed. A tool is generally built around a single formalism and one or more solution techniques, with simulation sometimes available as a second solution method. \cite{Sanders:PNPM:99} lists a number of such tools, such as DyQN-Tool+ \cite{Haverkort:RQSE:95}, which uses dynamic queuing networks as its high-level formalism; GreatSPN \cite{Chiola:PE:95}, which is based on GSPNs \cite{Marsan:TOCS:84}; UltraSAN \cite{Sanders:PE:95}, which is based on SANs \cite{Meyer:TPN:85}; SPNP \cite{Ciardo:MASCOTS:93}, which is based on stochastic reward networks \cite{Ciardo:SRN:93}; and TANGRAM-II \cite{Carmo:CPE:97}, which is an object- and message-based formalism for evaluating computer and communication systems. While all of these tools are useful within the domains for which they were intended, they are limited in that all parts of a model must be built in the single formalism that is supported by the tool. Thus, it is difficult to model systems that cross different domains and would benefit from multiple modeling techniques.
Möbius takes an integrated multi-formalism, multi-solution approach; the goal was to build a tool in which each model formalism or solver was, to the extent possible, modular, in order to maximize potential interaction. A modular modeling tool is possible because many operations on models, such as composition (described later), state-space generation, and simulation are largely independent of the formalism being used to express the model.
This approach has several advantages. First, it allows for novel combinations of modeling techniques. For example, to the best of our knowledge, the Replicate/Join model composition approach of [30] has been used exclusively with SANs. This exclusivity is artificial, and in the Möbius tool, Replicate/Join can be used with virtually any formalism that can produce a labeled transition system, such as PEPA [11].
The ability to add new components benefits researchers and users alike. Researchers can add a new component to the tool and expect it to be able to interact immediately with other components. Additionally, researchers have access to the work of others, and are able to extend and compare techniques. Users benefit by having access to the most recent developments in conjunction with previously existing techniques. They also benefit from having a modular, “toolbox” approach that allows them to choose the most appropriate tool or tools for the job.
