| In our daily lives,congestion often occurs,such as telephone busy,banking services,traffic jams,etc.Queueing theory is an effective tool to solve such problems.In the research process of queueing theory,the relevant vacation systems and retrial systems have been extensively studied.This paper investigates some retrial and working vacation systems under different queueing strategies.This paper first introduces the background and research significance of the queueing model with retrial and working vacation,and briefly describes some queueing rule strategies involved in the study.Then the Markov process and matrix geometric solution are used to analyze and calculate the M/M/1 queueing model with retrial,working vacation,orbit search and balking.We derive the stationary probability distribution and some performance measures.Then we give the conditional stochastic decomposition for the queue length in the orbit when the server is busy.And using MATLAB software to carry out numerical analysis,then give the analysis of the optimal situation.After that,the M/M/1 queueing model with retrial,working vacation and feedback is analyzed.We obtain the necessary and sufficient condition for system to be stable.At the same time,the model is numerically analyzed by MATLAB and given the conditional stochastic decomposition for the queue length in the orbit when the server is busy.Finally,the retrial and working vacation queueing model with collision is studied.The steady queue length of the system steady state and the probability that the server is busy are also calculated.Then we show the effect of the model parameters on the system's characteristics by some numerical examples.The innovation of this paper is that our paper uses Markov process and matrix geometric solution method to combine orbit search,balking,feedback and collision strategy on the basis of classical retrial and working vacation model,which generalizes the classic model and make the queueing model be more realistic. |
PDF Full Text Request