Communication Networks An Optimization, Control, and Stochastic Networks Perspective

In Chapter 2, we assumed that the transmission rates xr are positive, and we derived fair and stable resource allocation algorithms. In reality, since data are transmitted in the form of packets, the rates xr are converted to discrete window sizes, which results in bursty (non-smooth) arrival rates at the links in the network. In addition, many flows in the Internet are very short (consisting of only a few packets), for which the convergence analysis in the previous chapter does not apply. Further, there may also be flows which are not congestion controlled. Because of these deviations, the number of incoming packets at a link varies over time and may exceed the link capacity occasionally even if the mean arrival rate is less than the link capacity. So buffers are needed to absorb bursty arrivals and to reduce packet losses. To understand the effect of bursty arrivals and the role of buffering in communication networks, in this chapter we model packet arrivals at links as random processes and study the packet level performance at a link using discrete-time queueing theory. This chapter is devoted to answering the following questions.