Abstract:

Based on the operation mechanism of the factory order assembly system, this paper constructed and analyzed a fluid model driven by the M/M/1 queue with two type of mixed vacations and $N$ policy. Firstly, the driving system is described and the infinite small generators of the Markov process are decomposed into a blocky Jacobian matrix form. Then the three-dimensional Markov process of the fluid queue is established, the differential equations satisfied by the stationary joint distribution are obtained, and the mathematical expression of the stationary buffer content is deduced using matrix geometric solution and Laplace transformation. Then the expected buffer content is derived by Laplace-Stieltjes transformation. Finally, the influence of parameters changing on the performance indicators is illustrated by numerical analysis.

Key words: fluid model, N policy, two-stage vacation, buffer content