M/m/l/nâ†'m/m/c/k Queuing System And Its Application In Anchorage Planning

In the social civilization highly developed today, people often encounter some queuing phenomenon, for example, in the crossroads vehicles wait for passing; in subway station, railway station, bus station, passengers waiting for on, etc. With the increase of population and economic development, various queuing system is also becoming more and more complex, how to make people facilities to accept the service satisfaction? This is the queuing theory to solve.Queuing theory was originated from the problem of telephone calls, when the birth and death process were introduced, queuing theory is applied more and more widely. Because of queuing network model is very close to the reality, it becomes the key of queuing theory research in the present. The product type solution of all kinds of queuing network model are derived by many scholars, but for the limited capacity of tandem network system, people more use approximation method to get the approximation numerical solution of the index for the system.At present, since many scholars only take the capacity is limited at the second stage of service-center for two-stage tandem queuing system into consideration, but they haven't proposed that both of the capacity is limited for the two stage service-center. Based on the research of pioneers, the main purpose of this paper is about two-stage tandem queuing system—M/M/l/Nâ†'M/M/c/K, which capacity is both limited for the two stage service-center. There are five chapters in this paper. The first chapter was mainly introduced some backgrounds and significance of the problem, the research for present situation of domestic and foreign country and the main research mentality and content of this paper. The second chapter is the theoretical knowledge, which is prepared for the research of the third chapter. The knowledge of Queuing System was introduced, put out the knowledge of matrix analysis method and quasi birth and death process, then discussed two circumstances of two-stage tandem queuing system, which are the wait space both unlimited and both zeros. The third chapter is the innovation of this paper. It has make improvement of the predecessor's model, proposed M/M/l/Nâ†'M/M/c/K queuing system model, and used stochastic process, probability theory, matrix analysis theory to get it some of queuing index. Such as, the queuing index, the hinder time and its distribution of the first stage of service-center, the smooth and steady distribution and its algorithm of the system. The fourth chapter is empirical analysis, which is mainly about linked theory with practice, applied the knowledge of queuing system model of M/M/l/Nâ†'M/M/c/K to the planning of anchorage for Yan Tai port in west coastal. First, get the port system idealist, and consider it into a single stage queuing system-M/M/n, then simulate this model and count the result. Second, use the model of this paper to study this problem, simulate it also, compare the results, we can discover the latter is more reasonable, so the model for this paper has its value.