Stability And Brownian Model For Multiclass Queueing Networks

This dissertation studies the stability and diffusion approximation of multiclass queue-ing networks. The main results may be summarized as follows:1. The stability of a class of multi-stations queueing networks is investigated. Using linear Lacunae functions to find the sufficient condition under which queue length of only one station is zero. By mathematics induction to reduce the numbers of stations until two. Together with piecewise lines Lyapunov functions, we obtain a sufficient condition of stability of the network under the work-conserving service disciplines.2. Under priority service discipline, the diffusion approximations for a three-stations reentrant networks and a class of the re-entrant networks were studied. Using piecewise lines Lyapunov functions, we get a sufficient condition of weakly stable for the network. Based on weak stability,we turn the queue length into a certain format. by stochastic analysis theorem, We derive a sufficient condition for the existence of the diffusion approximation for the queue networks when the traffic tensity is 1 for each station.3. By bringing in random vector of the size of batch, the batch processing fluid model was established. Under batch FIFO service disciplines and batch priority service disciplines, We demonstrate the batch processing fluid model is identical with the fluid model of a standard queuing network. Based on the stability of the standard queuing network, we state the stability of batch processing queueing networks, Which offer an appealing method for studying the batch processing queuing networks.4. Giving a new service disciplines which is limited Priority Service Disciplines. under the service disciplines,We studied the stability of the multiclass queueing networks. Turning the fluid model of the standard queuing networks into the fluid model of a special batch processing queuing networks. By the method of establishing the stability condition for the batch processing queuing networks, we demonstrate that the stability of the queueing networks with limited Priority Service Disciplines is identical with the stability of a standard queuing networks under a priority serviced discipline.5. Based on limit, theorems of the standard queuing networks this paper defined a class of batch processing queuing networks, and derive the diffusion limit for queue length of each service station under FIFO service disciplines when the traffic intensity more than one.