Computer and Communication Networks (paperback)

11.7. Summary

This chapter presented the mathematical foundation for basic analysis of computer networks developing packet queues, using Markovian and non-Markovian cases. Single queues are the simplest models for the analysis of a single node in a communication network. Little's theorem relates the average number of packets and the average time per packet in the system to the arrival rate.

Birth-and-death processes can help identify the activity within a packet queue. Queueing node models with several scenarios were presented: finite versus infinite queueing capacity, one server versus several servers, and Markovian versus non-Markovian systems. The non-Markovian models are further classified into systems with non-Markovian services and systems with non-Markovian traffic arrivals. On a non-Markovian service model, we assume independent interarrivals and service times, which leads to the M/G/ 1 system.

Burke's theorem is the fundamental tool analyzing networks of packet queues. By Burke's theorem, we can present solutions to a network of several queues. We applied Burke's theorem in-series queueing nodes and in-parallel queueing nodes. Jackson's theorem provides a practical solution to situations in which a packet visits a particular queue more than once through loops or feedback . Open Jackson networks have a product-form solution for the joint queue length distribution in the steady state. We can derive several performance measures of interest, because nodes can be treated independently. Jackson networks with no external arrivals or departures forming a closed network also have a product-form solution for the steady-state joint queue length distribution.

The next chapter presents quality-of-service (QoS) in networks, another important issue of networking. Recall that QoS is a significant parameter in routing packets requiring performance.