Fluid Queue Model For On-off Sources With Abandonments

In this paper, based on the general fluid-queue model, we further improved thecommonly used fluid queue with on-off sources to be the fluid queue for on-off sourceswith abandonments. We studied the heavy-traffic limits and Brownian limits processesexpression for the considered model, we get the queue length expression under the EDsystem.Firstly introduces the related basic theory of the queue, we define theM1topology andJ1topology in the space D, and introduce central limit theorem, functional central limittheorem, two-sided reflection map conception and continuous-mapping theorem. Then wedescribed the general fluid queue models in detail, and use the basic theory to get the fluidlimits and the heavy-traffic limits for the general fluid queue.Secondly, we describes the fluid queues for on-off sources with abandonments, showsthe mathematical expression for the relevant quantity in the model, By using functionalcentral limit theorem,two-sided reflection map conception and continuous-mapping theorem,we get the heavy-traffic and Brownian limit processes expression for the considered model,and get the queue length expression under the ED system. Where Brownian limit processes isdistributed in the Brownian motion with deviation; And queue length of the model underthe ED system process is a Ornstein-Uhlenbeck (OU) diffusion process. In order to achievevisual effect, the waiting time and queue length are numerically simulated by Matlabsoftware.Finally we extended a single On-off sources to multiple On-off sources, mainlydiscussed the heavy-traffic and Brownian limit processes expression of the fluid queue formultiple on-off sources with abandonments, where Brownian limit processes is distributed inthe Brownian motion with deviation.