On Queue Model Based On Markov Skeleton Process And Its Applications In Web Information System

With the rapid development of Internet technology, a variety of Web information systems have emerged and the analyses of their performance have become urgent and practical needs. Based on the operational mechanism of Web information system, this thesis establishes a systematic model of performance analysis and researches the vacation-queuing model of Web server using the Markov skeleton-processing theory. Firstly, this thesis probes the Web information system's rules and characteristics together with the general process of transmitting and transacting information, and builds a systematic model of performance analysis, regarding a Web information system as an abstract queuing network system. Secondly, the Markov skeleton-processing theory in queuing system is analyzed and summarized. Finally, the vacation queuing model of Web server is also under research. All the previous researches assume that the intervals of customers' inputs are random variables distributed independently and identically (the distribution of negative exponential), and the system is portrayed by the classical queuing models, such as M/M/N. In the actual network information systems, however, some customers' inputs are usually of great difference from the classical models. Consequently, it is necessary that a more general queuing model be researched. In this thesis 4 queuing models are focused on, namely, GI/G/N queuing system with synchronous single vacation, GI/G/N queuing system with synchronous multiple vacation, GI/G/N queuing system with d-policy vacation and GI/G/N queuing system with asynchronous multiple vacation. By means of the Markov skeleton process theory, the transient distribution of the queue length of these queuing models is achieved. In this thesis, the arrival intervals and the service time in the model are independent of each other though kept to the general distribution, and various vacation regulations are adopted so that the practical problems can be portrayed better in the model.The major findings of this thesis include:(1) The multiple server vacation queuing model of Web information system is established. The system model in this thesis broadens the existing modeling assumptions, that is, Web requests and the Web service time are not required to keep to the distribution of negative exponential. Besides, the GI/G/N model is introduced to portray the system so that some previous defects of logical modeling in Web information system are corrected.(2) With the Markov skeleton process theory, the equations are put forward that accord with the transient distribution of the queue length of GI/G/N queuing system with synchronous single vacation, and it proves that the probability distribution is the smallest non-negative solution of these equations.(3) With the Markov skeleton process theory, the equations are presented that accord with the transient distribution of the queue length of GI/G/N queuing system with synchronous multiple vacation, and it proves that the probability distribution is the smallest non-negative solution of these equations.(4) With the Markov skeleton process theory, the equations are brought forward that accord with the transient distribution of the queue length of GI/G/N queuing system with d-policy vacation, and it proves that the probability distribution is the smallest non-negative solution of these equations.(5) With the Markov skeleton process theory, the equations are proposed that accord with the transient distribution of the queue length of GI/G/N queuing system with asynchronous multiple vacation, and it proves that the probability distribution is the smallest non-negative solution of these equations.