student from 01.01.2024 until now
Russian Federation
The purpose of the work is to understand how different channel speeds affect the efficiency of the queuing system if catastrophic failures occur in the system (channels completely and permanently fail). Unlike classic models with reliable and equally powerful devices, in the systems under consideration, the efficiency of maintenance is determined not only by the load level, but also by which channel is susceptible to failure. Models of this type make it possible to more adequately describe real processes, however, despite their high practical significance, they remain insufficiently studied. In the work, the total system performance is fixed (µ1 + μ2 = 10), which allows us to study in isolation the effect of the ratio of channel capacities on the system characteristics. Both the symmetrical configuration (5, 5) and variants with different channel capacities are considered. (4-6; 3-7; 2-8; 1-9). The probability of channel failure varies in the range p = 0.1-0.6. Two scenarios are analyzed separately: failure of a less productive channel and failure of a more productive channel. The behavior of the queuing system at various load levels, including limit modes, is analyzed. T he probability of service Q and the probability of rejection Prej in the stationary mode are used as performance indicators. The calculation results show that if a less productive channel fails, then systems with channels of different speeds in some cases work more efficiently than systems with the same channels. The paper provides examples of such systems, analyzes the results obtained, and outlines areas for further research. The obtained conclusions can be used in the design and modeling of fault-tolerant systems, including three-channel systems described by the methods of queuing theory.
QUEUING SYSTEM, DEVICES OF DIFFERENT PERFORMANCE, CATASTROPHIC FAILURES, PROBABILITY OF FAILURE, HETEROGENEITY OF PERFORMANCE
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