Stochastic Modeling and Analysis of Telecoms Networks

Chapter 9Loss Systems

 

 

 

9.1. General

A loss system is a system that has fewer resources (servers and possibly, buffer) than potential users, and where all the customers arriving at a time when the system resources are taken, are lost. Therefore, we need to find out the adequate number of resources in order to loose as few requests as possible. In the following, we always denote by

– N(t), the number of customers who tried to enter the system up to t (those will be termed arrived customers);

– Y (t), the number of customers who have actually entered the system (called entered customers) before t. Therefore,

is the number of customers lost up to t.

– X(t), the number of customers present in the system (server + waiting line) at time t.

– S, the number of servers and C, the number of places in the waiting line.

EXAMPLE 9.1.– The second generation mobile phone network, known as GSM, is technically based on TDMA (Time Division Multiple Access). For a given frequency, we divide time into periods of equal and constant duration, known as slots. The slots are gathered in packets of eight to form a frame. The voice call is digitized in a way that routing a call amounts in fact to carrying information bits. To route a call, the octets of a call are grouped by packets, and we attribute to a call a slot set during the whole call duration. On Figure 9.1, the fourth slot is assigned to the ...