Abstract
A gated service single vacation M/G/1 queue with setup and closedown periods, and different customer arrival rates, is studied in this paper. The probability generating function of the number of systems for customers who are at the initial moment of service period is analyzed by using a total probability theorem, and the stability condition of the system is obtained. The stationary distribution of the queue length is solved by the regeneration cycle method. The stochastic decomposition of queue length in the steady state is calculated, and the service cycle is obtained. Moreover, classified discussions are established in order to solve the steady-state distribution for the waiting time. The variation of system performance indicators with parameters is analyzed by performing numerical experiments.
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The research was supported by the National Natural Science Foundation of China (61973261) and the Natural Science Foundation of Jilin Province (20210101151JC).
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Sun, Y., Ma, Z. & Xu, T. A gated service single vacation M/G/1 queue system with setup and closedown times and different customer arrival rates. Acta Math Sci 46, 407–426 (2026). https://doi.org/10.1007/s10473-026-0122-5
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DOI: https://doi.org/10.1007/s10473-026-0122-5
Keywords
- different arrival rates
- regeneration cycle method
- stochastic decomposition theorem
- stationary queue length