Important feature in the theory of the Telecommunication networks is the Erlang's Loss formula which computes the probability that a "call offered to a group of circuits finds that all circuits are busy".

Introduction

Lets assume a M/M/r/r queuing system. Namely a system of r servers circuits where the arrival process and the service time follow a Poisson distribution with mean arrival rate l and mean service time 1/m respectively. The system does not provide waiting room. Thereby all blocked calls are cleared.

It can be proved that the probability that all servers are busy is given by the Erlang B formula which is defined as follows: , where a=l/m denotes the traffic load, whose units are Erlangs. It might be worth mentioning that the Erlang's Loss Formula (Erlang B) also computes the probabilities of blocking for M/G/r/r queuing systems, where the service times are independent identically distributed according to some general distribution G.

It is useful to note the recursive form for the Erlang B formula, which simplifies the numerical evaluation: , where E(r,a) is the probability of blocking, "a" the traffic offered in Erlangs, "r" the number of circuits and E(0,a)=1.

Some useful characteristics can be observed by examining the Erlang B formula:

• 1. For a given blocking probability, the traffic carried by the system increases as the number of circuits increases.
• 2. For a given number of circuits, blocking probability increases as traffic load increases.

Interactive Erlang B Calculator

Calculate Erlang B loss probabilities for a range of offered traffic and circuit groups directly in your browser.

Parameters

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Max Circuits Number

Max Offered Traffic

Min Erlang Loss Prob. 1e-

Traffic Axis Step

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Results

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