A Study Of Some Geom/Geom/(Geom/Geom)/H Dual Input Queue Systems

In modern society, discrete time queue system is used extensively by people incomputer technology public services and communication network systems and so on. Inrecent years, especially discrete time queue system with many servers gradually hasbecome research focus. Based on the previous research theory of GI/M/1type, the paperstudies about Geom/Geom/(Geom/Geom)/H double input queueing system. The maincontent is as follows:First of all, research the Geom/Geom/(Geom/Geom)/H double input queue system.By using quasi birth and death chain theory, derive the system state transition probabilitymatrix. We obtain the equilibrium conditions of the system and the steady-stateprobability distribution by using the matrix solution method. Further, deduce steady statecaptain distribution, steady state of the average captain and average server and otherperformance indexes. The paper analyzes the results.Secondly, research the Geom/Geom/(Geom/Geom)/H double input queue systemwith impatient customer. And describe the research models detailedly. Taking the Markovchain as the theoretical basis, get one-step state transition probability matrix. And thesteady-state probability equations are obtained by Markov process method. The method ofblocking matrix is used to derive the obvious iterative formula of the steady-stateprobability vectors. We use matrix geometric solution and derive the queue lengthdistribution and server disappear probability and other performance index. Further, wemake numerical examples using MATLAB, and derive some numerical examples. Thenwe observe that the influence of system performance is showed by parameters in thesystem.Finally, introduce balking and reneging and multiple working vacation into theGeom/Geom/(Geom/Geom)/H double input queueing system. Combined with the modelsof the system, we give the state transition probability matrix. With matrix geometricsolution method, establish the balance equation and obtain the probability of the system inthe busy period and working holiday period and the probability of having to wait and otherperformance index.