Abstract:

A queue of Geo／Geo／1 model with N-policy, negative customers, feedback and multiple vacations is discussed. The starting time of service is determined by N-policy. Negative customers needn’t accept service, only removing the positive customer who is accepting service one by one. When a negative customer arrives and the system is on vacation, it will automatically disappear. Just after completion of its service, the positive customer may feeds back for the next service with certain probability. The equilibrium condition and concise expression of the steady-state distribution for the queue length are obtained by using QBDprocess and matrix-geometric solution method as well as the probability when the system is on vacation or 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.

Key words: discrete-time queue; negative customer; N-policy; matrix-geometric solution; conditional stochastic decomposition