Theories And Methods On Queue-length Distribution For Queueing System Under N-policy With Application

The stoachatic service queueing system has been widely used in modeling the production system and traffic system as well as computer communication system. The queuing system withN -policy obtains much attention, which is an effective method of making use of resources and saving cost of operation. Many papers study the queueing system withN -policy from the performance measures as well as the design and optimation of the system. The results get the PGF (probability generation function) of the steady-state queue-length distribution and expected queue-length, et al. Furthermore, the optimal control policy is investigated. But, the queue-lenth distribution characters at instantaneous and steady-state are fewer researched. This paper considers the queue-length distribution characters for the production queueing-like system under N -policy in detial. Combing the steady-state queue-lenth distribution, the paper studies the quanlity control policy for the queueing-like production system under N -policy.Firstly, consider the discrete-time Geom / G / 1queue underN -policy vacation with Bernoulli feedback queue. The recursion expression of the U -transformation of the transient queue-length distribution at any time, and also the expressions of the distribution and stochastic decomposition of the queue-length at a random point in equilibrium are obtained. The optimal control polices are also investigated.Secondly, this paper considers the M / G / 1 queue underN -policy with delayed startup and closedown. By the total probability decomposition technique, the recursion expression of theL -transformation of the transient queue-length distribution at any timet , furthermore, the expressions of the distribution and stochastic decomposition of the queue length at a random point in equilibrium are obtained. The statistical character of stationary queue-length distribution and additional queue-length distribution are investigated based on numerical examples. A maximum entropy method is used for estimating the queue length distribution.Thirdly, this paper studies a like- queue production system under bi-level control policy. By a concise decomposition method, the transient and steady-state queue-length distribution and the control policies are obtained.Next, the paper considers the bach arrival queueing production system under N -policy. By the stochastic decomposition, the recursion expressions of queue-length distribution are obtained. Based on the simulation approach, the statistical properties of steady-state queue-length distribution are also investigated, which shows that it is important for the design and optimization of the system.Finaly, in terms of the quality management, the manufacturing system described by the Markov queue underN -policy is discussed. By setting up steady-state system equations, the stationary solution is obtained. Furthermore, under the policy named"barrier inspection", the system queueing characteristics and quality control characteristics are investigated. Then, in view of these performance indexes, the optimal model is proposed according to the minimizing average cost of unit. And the optimal combined control policy is gained through numerical method based on the nature of cost function.