Work

Dynamic Analysis of a Standby System with Retrial Strategies and Multiple Working Vacations

Year: 2024

Type: article

Abstract: In this paper, we developed a new standby system that combines a retrial strategy with multiple working vacations, and we performed a dynamic analysis of the system. We investigated its well−posedness and asymptotic behavior using the theory of the C0−semigroup in the functional analysis. First, the corresponding model was transformed into an abstract Cauchy problem in Banach space by introducing the state space, the main operator, and its domain of definition. Second, we demonstrated that the model had a unique non−negative time−dependent solution. Using Greiner’s boundary perturbation idea and the spectral properties of the corresponding operator, the non−negative time−dependent solution strongly converged to its steady−state solution. We also provide numerical examples to illustrate the effect of different parameters on the system’s reliability metrics.

Source: Mathematics

DOI: 10.3390/math12243999

Authors: Changjiang Lai, Ehmet Kasim, Ahmadjan Muhammadhaji

Institution: Xinjiang University

Language: English

Topic: Advanced Queuing Theory Analysis

Subfield: Management Information Systems

Field: Business, Management and Accounting

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: Natural Science Foundation of Xinjiang Province