Chapter 10

Models of the Nodes in the Packet Network

10.1 Introduction

10.1.1 Parameters of the Queuing System

A queuing system is a system that is designed for servicing any call (demands) arriving to the system in random (or not) moments of time. Both the traditional telephone exchange and the IP router are examples of the queuing system. Queuing theory is concerned with stochastic processes taking place in queuing systems. Its main objective is to work out analytical methods enabling the identification and determination of parameters describing queuing, for example the length of the queue, the number of servers, and so on, as well as finding the dependencies between these parameters and efficiency characteristics of queuing systems (for example, the average waiting time of calls in the queue, or the average number of occupied servers).

Figure 10.1 presents a basic model of the queuing system. The figure shows the server, input stream, output stream and the queue. Any device (or a system of devices) that services calls is called the server. When the server is occupied, calls wait in the queue. The input stream is the sequence of calls arriving to the system to be serviced, whereas the output stream is the sequence of calls leaving the system. Calls are serviced in the system by the server or a wider set of servers. In order to characterize the queuing system it is necessary to determine the statistical distributions defining time intervals between subsequent calls arriving to ...

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