Bernoulli Feedback Queue With Negative Customers

The queue system with negative customers has been widely paid attention to andbecome object of study since Gelenbe firstly put forward negative customers policy. Forexample, foreign aid of some work will make the system provide better service for thecustomers. However, some external signals will influence the people’s acceptance ofservice. The arrival of negative customers is one of the restrictive factors of system inqueuing model. At the same time, the feedback system is also the key factor in theproduction and real life, which changes the service mechanism of classical queuing system.Therefore, it is very important that negative customers and feedback mechanism should beadded to the queuing model.The paper conducts a theoretical research on the queue system with negativecustomers as well as Bernoulli feedback system, constructs three different models andgives each one numerical analysis.Firstly, the paper carries out a research on an M/M/c working vacations queue. On avacation, the waiters do not stop working, but the service for customer is lower than thenormal service rate, work off strategies serve exhaustive multiple work off. Through thematrix-geometric solution method, the paper gains concise expressions of the steady statedistributions, and the result of stochastic decomposition of the queue length and waitingtime are given.Secondly, the paper deals with the M/M/c/N repairable queue system, whichcomprehensively considers the negative customers, customer impatient, feedback andvariable repairable failure rate. A level of dependency of quasi birth and death process wasset up. The reliability index of the model is obtained by the means of the steady-statedistributions. Meanwhile, the impact of index on the reliability is represented.Finally, the paper analyses the M/M/s/k+M retry queue system, According to themodels of the system, the state transition probability matrix is given. With matrixgeometric solution method, the balance equation is established and the probability of thesystem is obtained in the busy period and working holiday period. The article analyze the influence of the change of system parameters on performance index by means of Matlab.