On Performance Measures of a Fuzzy Priority Queue in a Transient Regime using the L-R Method
Abstract
In this paper, we proposed the performance measures of a Markovian queue with non-preemptive priority under transient conditions in a fuzzy environment. We study the transient performance measures of an FM/FM/1 queue with absolute priority. We analyze the characteristics of this model in a fuzzy environment by the L-R method of a fuzzy number A~=<m, a, b>_{LR}, where m, a, b are exponential functions of time—considering arrivals and services as triangular fuzzy numbers. The L-R method turns out to be very short and more practical compared to other methods, such as the DSW method (Dong, Shah and Wong), the α-cuts method, or the centroid method, because it allows us to obtain the membership functions, modal values, and supports of different performance measures and facilitates the graphical representation of the results obtained. A numerical example illustrates the validity of the method and the results obtained using it.
Keywords: performance measures; non-preemptive priority; triangular fuzzy numbers; LR method.
Abstrak
Pada artikel ini, kami mengusulkan ukuran kinerja antrian Markovian dengan prioritas non-preemptive dalam kondisi transien di lingkungan fuzzy. Kami mempelajari ukuran kinerja transien dari antrian FM/FM/1 dengan prioritas mutlak. Kami menganalisis karakteristik model ini dalam lingkungan fuzzy dengan metode L-R dari bilangan fuzzy A~=<m, a, b>_{LR}, dengan m, a, b adalah fungsi eksponensial terhadap waktu dengan mempertimbangkan kedatangan dan pelayanan sebagai bilangan fuzzy segitiga. Metode L-R ternyata sangat singkat dan lebih praktis dibandingkan dengan metode lain, seperti: metode DSW (Dong, Shah dan Wong), metode α-cuts, atau metode centroid, karena metode ini memungkinkan kita untuk mendapatkan fungsi keanggotaan, nilai modus, dan supports dari ukuran kinerja yang berbeda dan memfasilitasi representasi grafis dari hasil yang diperoleh. Contoh numerik menggambarkan validitas dari metode dan hasil yang diperoleh dengan menggunakan metode yang kami usulkan.
Kata Kunci: ukuran kinerja; prioritas non-preemptive; bilangan fuzzy segitiga; metode LR.
2020MSC: 60K25, 03E72.
Keywords
References
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DOI: 10.15408/inprime.v6i2.41126
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