Queues Applied to Telecoms

7The Teletraffic of Loss Systems

To save one’s credit, one must hide one’s losses.

Jean de la Fontaine (1621–1695)

In Chapter 6, we examined distributions of requests and durations of activity. However, the principal objective of teletraffic is the evaluation of the number of resources needed to provide customers with a satisfactory quality of service. This chapter has the objective of evaluating this quantity using the distributions of the numbers of busy resources for different scenarios involving loss systems.

For type-one pure chance traffic (PCT-1), two scenarios can exist:

• – infinite number of resources n: Poisson distribution;
• – finite number of resources n: truncated Poisson distribution or Erlang distribution.

For type-two pure chance traffic (PCT-2), two scenarios can also exist:

• – number of resources n ≥ N sources: binomial distribution.
• – number of resources n < N sources: truncated binomial or Engset¹ distribution.

7.1. Loss systems

7.1.1. Definitions

DEFINITION 7.1.– What we call a perfect system is a system in which free resources are always accessible.

Given Definition 7.1, the system can allocate one of its unoccupied resources. A perfect system is also called a system with perfect access, or with total accessibility.

DEFINITION 7.2.– What we call an imperfect system is a system in which an unoccupied resource is not always necessarily accessible.

In the case of this imperfect system, there can be internal blockages, of which we can distinguish two ...