The Geom/Geom/1Working Vacation Queue With N Policy And Bernoulli Feedback

Queuing system with working vacations is an emerging research hotspot in queuingsystems in recent years. At the same time,literatures regarding queuing modelsincorporating N policy are extensively discussed by researchers worldwide. Inaddition,feedback is another feature which has been widely studied in queuing system.In this paper,we study queuing systems taking together the above mentioned features.In this paper, we will study a Geom/Geom/1queue with working vacations, Npolicy and Bernoulli feedback. This is a brand new queuing model with workingvacations. Using quasi-birth-and-death chain and matrix-geometric solution method,we obtain the expressions of the steady-state distributions for the queue length.Furthermore, we indicate the conditional stochastic decomposition structures of queuelength and waiting time in the stationary state and obtain the distributions foradditional queue length and additional delay.Firstly, we briefly introduced the historic and current state of vacation queues, Npolicy and feedback queues.Secondly, we have described a Geom/Geom/1queue with working vacations andquasi-birth-and-death process and matrix-geometric solution method.Thirdly, we have researched a Geom/Geom/1queue with working vacations andBernoulli feedback. Using quasi-birth-and-death chain and matrix-geometric solutionmethod, we obtain the expressions of the steady-state distributions for the queue length.Furthermore, we indicate the conditional stochastic decomposition structures of queuelength and waiting time in the stationary state and obtain the distributions foradditional queue length and additional delay.Fourthly, a working vacation Geom/Geom/1queuing system with N-policy andBernoulli feedback is considered. Using quasi-birth-and-death chain andmatrix-geometric solution method, we obtain the expressions of the steady-statedistributions for the queue length. Furthermore, we indicate the conditional stochasticdecomposition structures of queue length and waiting time in the stationary state and obtain the distributions for additional queue length and additional delay.