A product-form network for systems with job stealing policies

What is it about?

We introduce a new product-form queueing network model where servers are always busy. This is obtained by defining a job movement policy that admits instantaneous migrations of jobs from non-empty waiting buffers to empty ones. This class of networks tends to maximize the system throughput and can be used to model situations where successive refinements on jobs improve the processes quality but are not strictly required to obtain a result.

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Photo by DeepMind on Unsplash

Photo by DeepMind on Unsplash

Why is it important?

Since their discovery more than 60 years ago, product-form models have played an important role in the quantitative analysis of computer and telecommunication systems as well as in the understanding of some important natural phenomena. Complex models of computer systems are often difficult to study from a numerical and analytical perspectives because of the state-space explosion problem. Product-form solutions are one of the most significant tools for overcoming this problem as a matter of fact, in many relevant applications, they are the only way to perform an exact quantitative analysis. In particular, product-from solutions enable the factorization of the system in different components, allowing the study of these components in isolation accounting nevertheless for their interactions and for their effect on the whole system.