Queuing Theory Applications to Communication Systems: Control of Traffic Flows and Load Balancing

Abstract

With the tremendous increase in traffic on modern communication systems, such as the World Wide Web, it has made it imperative that users of these systems have some understanding not only of how they are fabricated but also how packets, which traverse the links, are scheduled to their hosts in an efficient and reliable manner. In this chapter, we investigate the role that modern queueing theory plays in achieving this aim. We also provide up-to-date and in-depth knowledge of how queueing techniques have been applied to areas such as prioritizing traffic flows, load balancing and congestion control on the modern internet system. The Introduction gives a synopsis of the key topics of application covered in this chapter, i.e. congestion control using finite buffer queueing models, load balancing and how reliable transmission is achieved using various transmission control protocols. In Sect. 52.1, we provide a brief review of the key concepts of queueing theory, including a discussion of the performance metrics, scheduling algorithms and traffic variables underlying simple queues. A discussion of the continuous-time Markov chain is also presented, linking it with the lack of memory property of the exponential random variable and with simple Markovian queues. A class of queues, known as multiple-priority dual queues (MPDQ), is introduced and analyzed in Sect. 52.2. This type of queues consists of a dual queue and incorporates differentiated classes of customers in order to improve their quality of service. Firstly, MPDQs are simulated under different scenarios and their performance compared using a variety of performance metrics. Secondly, a full analysis of MPDQs is then given using continuous-time Markov chain. Finally, we show how the expected waiting times of different classes of customers are derived for a MPDQ. Section 52.3 describes current approaches to assigning tasks to a distributed system. It highlights the limitations of many task-assignment policies, especially when task sizes have a heavy-tailed distribution. For these so called heavy-tailed workloads, several size-based load distribution policies are shown to perform much better than classical policies. Amongst these, the policies based on prioritizing traffic flows are shown to perform best of all. Section 52.4 gives a detailed account of how the balance between maximizing throughput and congestion control is achieved in modern communication networks. This is mainly accomplished through the use of transmission control protocols and selective dropping of packets. It will be demonstrated that queueing theory is extensively applied in this area to model the phenomena of reliable transmission and congestion control. The final section concludes with a brief discussion of further work in this area, an area which is growing at a rapid rate both in complexity and level of sophistication.