Discrete-time Queue System In Preemptive Priority And Dependent Case

Classical random service system (queuing system), originated from the research of the telephone communication using the mathematic theory by Danish mathematician Erlang at beginning of the 20th century. The theory of random service system has acquired enormous development in past years, and became one of the most vigorous research fields in applying probability and the random operations research. Not only does it have a comparatively complete theoretical system, but also has extensive application in such each field as military, economy, production, management, traffic, etc. Classical random service system, including the forms such as M/M/1, M/G/1,GI/G/1, GI/M/n, has been made deep research by many experts whose majors are the applying probability and the random operations and got many perfect results.In recent years, a lot of scholars began to extend the classical models to the other research fields through various ways and studied some more complicated models on the basis of classical queuing theories. These amplification includes the following several respect mainly: Firstly, it is considered that the general assumption the customers'arrival and the service time of the queue models. For example, some scholars suppose the arrival process of the customers as Markov renew process or PH process; Secondly, some scholars consider the queuing system with the priority classes of customers. At last, the vacation and repairable system is also considered as a part of complicated queuing system.This paper studies various of discrete-time queuing models, including two-state arrival in preemptive priority case, two-state bulk arrival in preemptive case and the discrete-time queue with arrival processes state dependent queue length. Approach used from chapter2 to chapter5 in this paper is mainly the theory of probability analysis and embedded Markov chains which is presented by Kendall. Main feature of embedded Markov chains is that the random point process needn't be a Markovian process and only acquire Markovian quality in series of stopping time. That extent the require of random point process in the classical queuing model.Our research work include 5 chapters: in chapter1, we provide introduction and preliminary knowledge used in this paper, including research background, development of queuing theory, some results of discrete-time queue and main results of this paper. In chaper2, we introduce some methods on studying queuing models that include embedded Markov chains, supplemental variables method and matrix-geometric method. In chapter3 and chapter4, we discuss two different customers'arrival models in preemptive priority case, and it is given that the distribution of the queue length, the waiting time and busy time in the system. Then, we compare it with the classical models. In chapter5, we consider discrete-time queue with arrival process state dependent queue length and derive some perfect results.