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The paper deals with a sharing economy system with various management factors by using a bulk input G/M/1 type queuing model. The effective management of operating costs is vital for controlling the sharing economy platform and this research builds the theoretical background to understand the sharing economy business model. Analytically, the techniques include a classical Markov process of the single channel queueing system, semi-Markov process and semi-regenerative process. It uses the stochastic congruent properties to find the probability distribution of the number of contractors in the sharing economy platform. The obtained explicit formulas demonstrate the usage of functional for the main stochastic characteristics including sharing expenses due to over contracted resources and optimization of their objective function.AMS Classification: 60G10, 60J10, 60K15, 60K25, 60K20, 90B05, 90B22, 90B50, 90C15 * The paper has been submitted to an international journal in Economics area and currently under review.

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Abstract-This paper is dealing with improving the software reliability by using the systematic innovation method that is recently invented. The mathematical modeling shows the theoretical software protection scheme in the security perspective. If software application modules are represented as backups under proposed architecture, the system can be solved by using the stochastic maintenance models with replacement policies. This practical approach of technology enhancement in software engineering is demonstrated in the framework of optimized software allocation problems with unreliable backups.Index Terms-Systematic innovation, security system, stochastic architecture design, duality principle, TRIZ, TIPS.