Abstract
Most modern high-performance information processing systems are scalable. Performance improvement in scalable computing systems is achieved by increasing the same type of modules (for example, computing nodes). In the Top 500 list (56 edition, November 2020), 93% of high-performance systems are cluster-based and have high scalability. The number of nodes in these systems can be measured in hundreds of thousands. On the other hand, increasing the resource exacerbates the problem of reliability and complicates the organization of effective functioning. The analysis of the reliability and potential capabilities of computer systems is an urgent problem. Within the framework of the Queuing Theory, a model of the functioning of scalable computer systems in case of failures, taking into account the switching time, is considered. The solutions uses the apparatus of generating functions and combinatorial methods. The paper offers analytical solutions for probability distribution of system states in the case of a model with three parameters for transient and stationary modes of operation. It is shown that the solutions of the three-parameter model are reduced to the solutions of the two-parameter model, if the switching time is not taken into account.
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This work was carried out under state contract with ISP SBRAS (grants No 0242-2021-0011) and under Russian Foundation for Basic Research (grants No 20-07-00039).
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Pavsky, V.A., Pavsky, K.V. (2022). Mathematical Model with Three Parameters for Calculating Probabilities of States of Scalable Computer Systems. In: Solovev, D.B., Kyriakopoulos, G.L., Venelin, T. (eds) SMART Automatics and Energy. Smart Innovation, Systems and Technologies, vol 272. Springer, Singapore. https://doi.org/10.1007/978-981-16-8759-4_24
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DOI: https://doi.org/10.1007/978-981-16-8759-4_24
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