Some Research Results Of Discrete Time Vacation Queueing System

Queuing theory in electronic communication, logistics management, transportation,medical assistance, banking service, production line, and many otherareas have widely application. In the 1970s, for effectively using idle time view,the thought of server taking vacation is introduced to the queuing system. thereare many reasons causing server taking vacation, such as the server engaging inauxiliary work and adding energy for the machine, or giving the machine maintenanceetc. In this M.D. thesis, we investigate three types discrete time vacationqueuing systems, including a discrete time Geom^[x]/G/1 queueing with modifiedT vacation policy and set-up time, general randomized working vacationpolicy for a Geom/Geom/1 queueing and a discrete time Geom/G/1 queueingwith multiple adaptive vacations policy and general decrementing service rule.The main results obtained of this paper can be summarized as follows:In chapter 2, we discuss the discrete time Geom^[x]/G/1 queueing with modifiedT vacation policy and set-up time. We derive the generating functions andthe mean values for the steady state system size and waiting time, and also getthe generating functions and expects of the busy period, vacation period andvacation cycle.Chapter 3 studies a discrete-time Geom/Geom/1 queueing with generalrandomized working vacation policy. By using the quasi birth and death chainand matrix-geometric solution approaches, we derive the generating functionsand the expected values of the steady state queue length and sojourn time.In addition, we obtain the generating functions and the average values of theregular busy period, busy cycle and vacation period.Chapter 4 studies a discrete time Geom/G/1 queueing with multiple adaptivevacations policy and general decrementing service rule. The generatingfunctions of the steady state queue length, waiting time and their stochasticdecomposition property are derived via the embedded Markov chain methodand regeneration cycle approach. Several common vacation policies are special cases of the vacation policy presented in this study, and some numerical resultsare shown to compare the mean queue length and waiting time of special cases.