Performance analysis of interfaces between networks and a recursive solution to two-dimensional QBD processes
Abstract
Analysis of the interface between two different types of networks is a problem of significant current interest. For example, the interface between an ATM network and an Ethernet requires careful design to minimize delay while avoiding jamming the Ethernet with many short frames. In this dissertation we address two problems concerning these interfaces: how to characterize and control the traffic flowing from one network into another, and how to model the interaction between two networks. For the first problem, a MAP/G/1/ N model with a batch service policy is developed. The MAP (Markovian Arrival Process) is a rich class of point processes which contains many well known arrival processes as special cases, including Poisson processes, PH-renewal processes, Markov-modulated Poisson processes, etc. The capacity constraint of N and the batch service policy introduce a new level of difficulty into problems of this type. In addition, a QBD (quasi-birth-death) model of a CSMA/CD network is extended to analyze the delay characteristics of an Ethernet with a constant-load retransmission strategy. This delay analysis by itself is important in the design of a CSMA/CD network with real-time traffic. Also, the results can be used to model a service process in the above MAP/G/1/N queue. Applying the MAP/G/1/N model and the QBD model along with a three moment-matching method for PH-distributions, we have successfully analyzed an ATM/Ethernet interface. Note, though, that the application of the MAP/G/1/ N model is not limited to this type of interface. For the second problem, we use a two-dimensional QBD process to investigate how coupled queues interact with each other. A novel state splitting method is developed and applied. Consequently, we find a complete recursive solution for the non-boundary states, and a partial solution for the boundary states, of the two-dimensional QBD process.
Degree
Ph.D.
Advisors
Coyle, Purdue University.
Subject Area
Electrical engineering|Computer science
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