On Discrete-time Queue With Vacation Schedule And Call-center Features Such As Negative Customer

Discrete-time queue model is being paid to more and more attention. This paper mainly research discrete-time queues with vacation schedule and call-center features such as negative customer, which mainly includes three contents:Firstly, a queue of Geo/Geo/1 type with N-policy, negative customer, feedback and multiple vacations is discussed. The equilibrium condition and concise expression of the steady-state distribution for the queue length are obtained by using QBD process and matrix-geometric solution method as well as the probability when the system is on vacation and busy. Meanwhile, the conditional stochastic decomposition structure of the queue length in steady state and the distribution of additional queue length caused by vacations are also acquired.Secondly, a queue of Geo/Geo/1 type with negative customer, policy set-up time and multiple vacations is studied. The equilibrium condition and concise expression of the steady-state distribution for the queue length are obtained by using QBD process and matrix-geometric solution method as well as the probability when the system is on vacation and busy. Meanwhile, the conditional stochastic decomposition structure of the queue length in steady state and the distribution of additional queue length caused by vacations are also acquired.Lastly, a Geo/Geo/1 queuing system with RCH strategy of negative customers and single vacations is studied. The equilibrium condition and concise expression of the steady-state distribution for the queue length are obtained by using QBD process and matrix-geometric solution method as well as the probability when the system is on vacation and busy. Meanwhile, the conditional stochastic decomposition structure of the queue length in steady state and the distribution of additional queue length caused by vacations are also acquired.