# Relationship of the two distributions

Introduction This document is the continuation of entitled An approximation of the random variable to decision making process that involve risk and uncertainty conditions. Now the application queue Poison own situations queuing theory to process of providing services that are characterized by the random arrival of customers to the system, represented by a probability distribution Poison add reed, with rates stockings service that obey a negative exponential probability distribution. The application queues Poison queuing theory allows abstracting and queue management system modeling medical services characterized by the arrival of patients, independent of each other randomly, which is void the arrival of two or more patients simultaneously, with average rates of service that are due to a negative exponential distribution, which have a discipline of patient care FIFO, LIFO, SIRO, GD with one or more servers and a tail service demand generally regarded as infinite.

The development of the proposed theme includes characterization of the probability distributions of Poison and exponential negative, the explanation of the Poison price and the in solving problems of queuing theory. Additionally, included, queuing theory for the description of the basic concepts, notation and terminology used, the basic models and their application in decision making process queue management system in the management of medical services. The probability distributions of Poison and negative exponential are often used in problems of queuing theory; Poison distribution represents a number of independent events that our at a constant rate within a specified time interval, expreed in units ranging, for example, from seconds to years.

### Specified with queue management system

Allows modeling as diverse as the number of calls queue management system arriving at a telephone exchange, the number of bacteria breeding in a certain population, time that can last a closed because of a landslide route, the number of people arriving situations a self or the amount of insurance requested an negative exponential distribution represents the length of intervals between events furring that are distributed wording to Poison Canvas, distribution. The Poison relates the Poison and negative exponential in treating problems of queuing theory; then an overview of each of these distributions and concepts and models included in this theory, in order to bring forward the review of specific situations of health waiting in queue line management that allow queuing basic your application forward. Application of Poison queues in decision making process in the management of medical services. Poison distribution Lethe a random variable representing independent random events that our at a constant speed over time or space.

It is said that the random variable has a Poison distribution with the following probability queue management system distribution Canals, It is said in this way that the random with parameter Meyer. For details of the derivation of the formula for the Poison distribution see Canals. The above definition corresponds to a probability distribution, since it satisfies the following axioms of a probability space. The Poison probability distribution of sample space is the set of integers. The probability associated with each sample point is obtained by replacing directly on the probability distribution formula presented. The function is always positive because each of the three factors that.

They define it is also positive for any value Odin avoidance with the following arguments an exponential function is always positive, also because the parameter implies that for any k, and finally the factorial of a positive integer is always greater than or equal to one. Using developments in power series and applying properties of the sum, over all values queue management system of the sample space, waiting in queue line we have, sum of probabilities over the sample space, properties of the sum a random variable with Potion distribution parameter, E VAR where Denotes the expected value of the random variable, this indicator also known as the average name, and VARdenotes the variance of the random variable.