Fluid Limits of Optimally Controlled Queueing Networks

Research Article Fluid Limits of Optimally Controlled Queueing Networks

Closed Queueing Networks in Heavy Traac: Fluid Limits and Eeciency

We address the behavior of stochastic Markovian closed queueing networks in heavy traac, i.e., when the population trapped in the network increases to innnity. All service time distributions are assumed to be exponential. We show that the uid limits of the network can be used to study the asymptotic throughput in the innnite population limit. As applications of this technique, we show the eecie...

Fluid Queueing Networks

We introduce a new method to investigate stability of work-conserving policies in multiclass queueing networks. The method decomposes feasible trajectories and uses linear programming to test stability. We show that this linear program is a necessary and sufficient condition for the stability of all work-conserving policies for multiclass fluid queueing networks with two stations. Furthermore, ...

Heavy TraÆ Limits for Some Queueing Networks

Heavy Traffic Limits for Some Queueing Networks

Using a slight modification of the framework in Bramson [7] and Williams [52], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single station systems operating under first-in first-out (FIFO), generalized headof-the-line proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines. The next two ...