Long Tailed Distributions

Abstract

By “long tailed distributions” ([2], Chapter 10) we mean that we have different classes of customers, with one class of customer taking a long time in a server. We will consider only two classes of customer: (1) normal, or those who take a regular, or normal, time in a server; and (2) long, or those who usually take a much longer time in a server. The long tailed distribution relates to the fact that there is a positive probability that a customer will take a long time in the server. We will model this situation as having two different arrival rates, one for the “normal” customers and another for those who take a long time in the servers. Also, there will be two different service rates. The results will depend on whether we are using fuzzy probabilities or fuzzy arrival/service rates.