The prime objective of this paperis 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.