GI/M/1 Queuing System With Negative Customers And Working Vacations

The main theme of this paper is GI/M/1 queue model with negative customers and working vacations.At first,we study GI/M/1 queue model with negative customers and working vacations and vacation interruption. This paper first introduces negative customers to working vacations and vacation interruption queuing systems.The server rules are First Come First Served,exhaustive service and multiple vacations,and removal of customers at the tail.The server works at a low level rather than stop working during a working vacation.Bye use of "Imbedded Markov Chain" and "State Transfer Analyses",we obtain the stationary distribution of the queue length and its stochastic decomposition at arrival points and various performance measures such as mean queue length and mean waiting time. And then,we study GI/M/1/N queue model with negative customers and working vacations.This paper first introduces negative customers to working vacations queuing systems with finite buffer.Bye use of "Matrix-Geometric Solutions Approach" and "Supplemental Variables Method",we obtain steady-state distribution at pre-arrival epochs and arbitrary epochs,respectively.