Queue size distribution and capacity optimum design for Geo/G/1 queueing system with delayed D-policy

This paper considers the discrete-time Geo/G/1 queueing system with delayed.D-policy.By using the total probability decomposition technique,we study the transient and equilibrium properties of the queue length from the beginning of the any initial state,obtain both the recursion expressions of the z-transformation of the transient queue length distribution at any time n~+ and the recursion expressions of the steady state queue length distribution,and then we give the stochastic decomposition of the queue length in equilibrium.The important relations between the steady state queue length distributions at different epochs(n~-,n,n~+) are discovered.Finally,by numerical examples we discuss the sensitivity of the steady state queue length distribution towards system parameters and illustrate the important value of the expressions of the steady state queue length distribution for calculating conveniently in the system capacity design.