Several Kinds Of Queuing Systems With Disasters

This thesis studies several kinds of queuing systems with disasters. First, the paper considers the M/M/C(1≤C≤ ∞) queuing models as the system needs start-up time, the customers arrive with impatience and the system runs with disasters. This thesis focuses on the research of four kinds of queuing models accompanied by disaster occurring. Those are as follows:(1) M/M/1 queuing model with the start-up working period, impatient customer characteristics and disasters; (2) M/M/1 queuing system with disasters which can only occur in the busy period; (3) M/M/C queuing model with the start-up working period, impatient customer characteristics and disasters; (4) M/M/∞ queuing model with the start-up working period, impatient customer characteristics and disasters. Then, on this basis, this thesis also studies comprehensive queuing model with single working vacation, N-strategy and disasters.This thesis has three main steps according to the research of each model. Firstly, the paper establishes the equilibrium equations by using Markov process theory when the system is steady. Applying supplementary variable method and generating function, we get the probabilities that the system is in the maintenance period, start-up period and the busy period respectively, conditional stationary queue, and its corresponding generating function. Furthermore, a series of important system indexes are obtained in the steady state. Then, by using Little formula, the paper gets the average sojourn time of a customer in the system. By using total probability formula, the paper calculates the average sojourn time of a customer in the three states, and discusses the special circumstances of the average sojourn time in the critical state. Finally, this thesis analyses the influence of some parameters on the system indexes by numerical calculation.