Queueing Theory - Role of Poisson Process, Exponential Distributions

Role of Poisson Process, Exponential Distributions

A useful queueing model represents a real-life system with sufficient accuracy and is analytically tractable. A queueing model based on the Poisson process and its companion exponential probability distribution often meets these two requirements. A Poisson process models random events (such as a customer arrival, a request for action from a web server, or the completion of the actions requested of a web server) as emanating from a memoryless process. That is, the length of the time interval from the current time to the occurrence of the next event does not depend upon the time of occurrence of the last event. In the Poisson probability distribution, the observer records the number of events that occur in a time interval of fixed length. In the (negative) exponential probability distribution, the observer records the length of the time interval between consecutive events. In both, the underlying physical process is memoryless.

Models based on the Poisson process often respond to inputs from the environment in a manner that mimics the response of the system being modeled to those same inputs. The analytically tractable models that result yield both information about the system being modeled and the form of their solution. Even a queueing model based on the Poisson process that does a relatively poor job of mimicking detailed system performance can be useful. The fact that such models often give "worst-case" scenario evaluations appeals to system designers who prefer to include a safety factor in their designs. Also, the form of the solution of models based on the Poisson process often provides insight into the form of the solution to a queueing problem whose detailed behavior is poorly mimicked. As a result, queueing models are frequently modeled as Poisson processes through the use of the exponential distribution.

Read more about this topic:  Queueing Theory

Famous quotes containing the words role of and/or role:

    But however the forms of family life have changed and the number expanded, the role of the family has remained constant and it continues to be the major institution through which children pass en route to adulthood.
    Bernice Weissbourd (20th century)

    Today, only a fool would offer herself as the singular role model for the Good Mother. Most of us know not to tempt the fates. The moment I felt sure I had everything under control would invariably be the moment right before the principal called to report that one of my sons had just driven somebody’s motorcycle through the high school gymnasium.
    Mary Kay Blakely (20th century)