On fluid modeling of networks and queues

Data communication networks have been experiencing tremendous growth in size, complexity, and heterogeneity over the last decade. This trend poses a significant challenge to the modeling, simulation, and analysis of the networks. In this dissertation, we take the fluid model as the way to attack the issue and apply it to network simulation, and to the analysis of queues. Traditional discrete-event packet-based approaches to simulating computer networks become computationally infeasible as the number of network nodes or their complexity increases. An alternative approach, in which packet-based traffic sources are replaced by fluid sources, has been proposed to address this challenge. We quantitatively characterize the amount of computational effort needed by a simulation scheme using the notion of a simulation\u27s event rate, and derive expressions for the event rate of a packet and fluid flow at both the input and output sides of a queue. We show that the fluid-based simulation of First In First Out (FIFO) networks requires less computational effort when the network is small. However, the so-called “ripple effect” can result in fluid-based simulations becoming more expensive than their packet-based counterparts. Replacing FIFO with weighted fair queuing reduces the ripple effect, however the service rate re-distribution process incurs extra event rate. We then propose time-stepped hybrid simulation (TSHS) to deal with the scalability issue faced by traditional packet-based discrete event simulation method and fluid-based simulation methods. TSHS is a framework that offers the user the flexibility to choose the simulation time scale so as to trade off the computational cost of the simulation with its fidelity. Simulation speedup is achieved by evaluating the system at coarser time-scales. The potential loss of simulation accuracy when fine time-scale behavior is evaluated at a coarser time-scale is studied both analytically and experimentally. In addition, we compare an event-driven TSHS simulator to the time-driven version, and find out that the time-driven TSHS simulator out-performs event-driven simulator due to TSHS simulation model\u27s time-driven nature and the simplicity of time-driven scheme. In this dissertation, we also apply the fluid model, together with the theory of stochastic differential equations, to the queueing analysis. We formulate and solve a number of general questions in this area using sample path methods as an important part of the process. Relying on the theory of stochastic differential equations, this approach brings to bear a heretofore ignored but quite effective problem solving methodology