Analysis And Application Of Repairable Queueing System With Rate Control And Two-stage Vacations

With the rapid development of modern science and technology,the popularization of automatic production system,enterprises pay great attention to how to improve the utilization rate of resources and enhance the strain capacity.In order to better solve the problem of serious accumulation of buffers in production system,rationally allocate workshop resources and cope with various random events in the system,based on the fault repairable queueing model,dynamic input rate controlled by threshold,variable failure rate,complete failure,working failure,start-up period and two-stage vacations policy are introduced.A queueing model is established which conforms to the regulation buffer stacking problem and the workpiece diversion strategy of stochastic production system.Firstly,in order to avoid the workpieces in the buffer of the production system staying a long time,the single machine repairable queueing system with dynamic input rate controlled by threshold,complete failure and variable failure rate is studied.The steady-state probability distribution of the repairable queueing model is obtained by quasi-birth-and-death process,matrix-geometric solution method and recursion method.The system performance indexes with threshold value h = 0 and h > 0 are given.Numerical experiments are carried out with programming software to describe the trend of performance indexes with system parameters and thresholds.By establishing the average cost function of unit time,the system is optimized.Secondly,considering that the start-up and debugging process of production equipment is complicated,the number of switching on and off should be reduced as far as possible,the M/M/1/ repairable queueing system with input rate controlled by threshold,working failure,start-up period(production preparation time)and two-stage vacations are studied.The equilibrium equation of the system is established to determine the infinitesimal generation of the three-dimensional Markov process.The probability vector of the system under steady state is obtained by matrix analysis method.At the same time,the performance indexes of the system such as throughput rate,mean length and probability of each state are given.The effectiveness and feasibility of the model are proved by numerical analysis.The average cost function per unit time of the system is established and the parameter value which minimizes the system cost is found.Finally,taking an automobile production factory as an example,the relevant data of automobile welding workshop is investigated on the spot to verify the data distribution.The repairable queueing model with input rate controlled by threshold and two-stage vacations is applied to practical problems through model fitting,and the workpiece diversion strategy in production systems is studied.By analyzing the interaction relationship between performance indicators related to the production line,a unit time revenue function for the production line workpiece diversion strategy is established,and the threshold for maximizing system revenue is found through the revenue function.