Analysis Of A Variety Of Complex Queuing Systems With Feedback

In this paper,we study a queueing system with feedback and multiple adapted vacations and a queueing system with feedback and geometric abandonments.The multiple adapted vacation policy is that after serving all customers,the server may choose to remain idle or take a vacation with a certain probability.If at the end of this vocation the system is empty,then the sever reconsiders whether to take a vacation or not.Geometric abandonments are that during server vacations,customer in the system will be impatient and leave the system because of waiting too long,and the number of leaving customers follows a geometric distribution.Model 1 considers a queue model with feedback,start-up,vacation interruption and multiple adapted vacations,and obtains the stationary probability generating func-tion(PGF)of the length of the queue in the system,the Laplace-Stieltjes transform(LST)of waiting time distribution and a series of performance indexes.Model 2 s-tudies a queuing model with feedback,vacations and geometric abandonments.We derive the PGF of the queue length,the LST of waiting time distribution of a cus-tomer in the steady state and the probability that the server is in different states.The last model discusses a queue model with countable feedback,vacations and geometric abandonments.Besides the performance indexes discussed in previous two models,we also discuss the LST of sojourn time distribution of a customer in the steady states.