Exponential furthermoreat represents the probability of occurrence of an event in a time interval infinitesimal tithe probability that in a certain area of opportunity continuous time interval in which queue management an event can occur several times the event of interest occurs more than once decreases the decrease of the same queue management probability that in a certain area of opportunity is observed a certain event is the same in all the various areas the number of times that an event is realized in a certain area of opportunity is independent the number of times an event occurred in an 'other area.a v.a. Exponential satisfies all these conditions furthermore the lack of memory makes queue management the same reasonable to model the arrival split times that are not related, in those for so the arrival of a queue system online customer does not favor or disadvantage other arrivals.
Equipped with a very simple and intuitive
Most elementary tail models consider that the revenue and expenditure of the system fall out according to a birth and death process the term birth refers the arrival of a new unit and the term death at the start of a queue system online unit served. It represents the number of elements n t of a population, and assumes that, for each generic time t, can be on one event birth and death, and that, given a population of n t= n, the time interval until the net birth is a random variable exponential with parameter n, while the time interval until the net death is an exponential random variable with parameter in. In this content, the parameters n and in the can be interpreted as, respectively, the average birth rate coefficient births and death mortality rate when the population is composed of n individuals. Graphical. Exponential have no memory the coefficients associated with the arrows press instead.
Duty number and queue management
For each state n is defined probability was the probability that the number of users in system at time t, n t, is equal to n in general, the state probability function are the instant of time considered, but if the system reaches a stead state to become independent from the instant t. Note that assume that there is the stationary distribution is not a 'hypothesis limiting example, as in man practical cases, it is enough simply to evaluate the stationary distribution in rather than the probability in t, assuming that the system has been in operation for a time sufficient large to achieve this equilibrium condition.
Under this condition, the system of differential equations is a system of equations homogeneous linear to determine the stationary solution in fact just take the limit for t → ∞ of both members of each of the differential equations usually a resource is not used in isolation more often different resources interconnected queue management to build a single system, which can be represented as a network in which individual resources are nodes and where the branches indicate the flows of users from a resource other.
As an example consider the case of a production line, formed b a series of workstations. Entering the first queue management station of the line, the piece is placed on hold in front the first machine, when it has finished processing goes immediately to the second, and so on until the completion of the technological cycle when the finished product comes out b the system.