Some analysis results associated with the optimization problem for a discrete-time finite-buffer NT-policy queue

Abstract

The prime objective of this paper is to give some analysis results concerning the discrete-time finite-buffer NT-policy queue, which can be utilized to determine the optimal threshold values. By recording the waiting time of the leading customer in server’s vacation period, the model is successfully described as a vector-valued Markov chain. Meanwhile, depending on the special block structure of the one-step transition probability matrix, the equilibrium queue length distribution is calculated through a more effective UL-type RG-factorization. Due to the number of customers served in the busy period does not have the structure of a Galton-Watson branching process, analysis of the regeneration cycle is regarded as a difficult problem in establishing the cost structure of the queueing system. However, employing the concept of i-busy period and some difference equation solving skills, the explicit expression for the expected length of the regeneration cycle is easily derived, and the stochastic decomposition structure of the busy period is also demonstrated. Finally, numerical results are offered to illustrate how the direct search method can be implemented to obtain the optimal management policy.