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

Abstract

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 vectorvalued Markov chain. Meanwhile, depending on the special block structure of the one-step transition probability matrix, the equilibrium queue length distri-bution 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.

Queue Size Distribution on a New ND Policy Geo/G/1 Queue and Its Computation Designs

“…random variables and represent the busy period initiating with a customer in the classical Geo/G/1 queue with the PGF B(z) � S(pz + pzB(z)) and mean E(B) � (E(S)/(1 − ρ)). en, according to the Galton-Watson branching process approach [11] (an effective method to analyze the busy period when the service time periods of the customers are independent random variables), the remaining busy period B ς can be decomposed as…”

Time Sensitive Analysis of Antagonistic Stochastic Processes and Applications to Finance and Queueing

“…The two policies combined are known as an NT-Policy model. There are quite a few papers on NT-Policy (cf., [2,3,25,27,39]) including one [29] by Lee et al about a "supreme triadic" (N,D,T)-Policy. While it is of interest to find a probabilistic information about the first passage time t ν and status of the system at t ν , it is of further importance to obtain the distribution of the queueing process at any time t during the interval [0, t ν ).…”