Communication Networks An Optimization, Control, and Stochastic Networks Perspective

We have learned about Discrete-Time Markov Chains (DTMCs) and discrete-time queueing systems in Chapter 3. In this chapter, we will look at continuous-time queueing systems, which were first developed to analyze telephone networks but has broader applications in communication networks, manufacturing, and transportation. The focus of this chapter is on the basics of continuous-time queueing theory and its application to communication networks. As in the case of discrete-time queueing systems, continuous-time queueing systems will be analyzed by relating them to Markov chains. For this purpose, we will first introduce Continuous-Time Markov Chains (CTMCs) and related concepts, such as the global balance equation, the local balance equation, and the Foster–Lyapunov theorem for CTMCs. Then, we will introduce and study simple queueing models including the M/M/1 queue, the M/GI/1 queue, the GI/GI/1 queue, and the Jackson network, as well as important concepts such as reversibility and insensitivity to service time distributions. Finally, we will relate CTMCs and queueing theory to the study of connection-level stability in the Internet, distributed admission control, telephone networks, and P2P file-sharing protocols. The following questions will be answered in this chapter.