Queues Applied to Telecoms

8Teletraffic in Delay Systems

It’s the time spent in waiting rooms that turns sick people into patients.

Claude Frisoni (1954–)

In this chapter, we study the teletraffic of systems in which requests that cannot be processed immediately due to insufficient available resources are put on hold. They are processed one by one as resources for processing become available.

8.1. Delay system

8.1.1. Description

Let us consider a delay system with total accessibility: when all the resources of the system are busy, requests arriving from sources join a queue and wait there until a resource is free. No request should be asked to wait if a resource is free; in other words, all requests will be processed. There are no lost requests.

In a delay system, lost traffic or rejected traffic A_p is equal to 0. Carried traffic is therefore equal to offered traffic. However, the notion of the maximum capacity of spendable traffic must be posited to avoid infinite delay times.

With type-one pure chance traffic, the arrival of requests from an infinite number of sources is Poissonian and the duration of activity is distributed according to an exponential distribution. This model is called an Erlang delay system model. The distribution of delay times in such a system can be calculated according to the way requests are organized in the waiting room: FIFO, LIFO, random, etc.

With type-two pure chance traffic, requests arrive from a limited number of sources, and the duration of activity is distributed ...