| D. P. Maki and M. Thompson. Mathematical Models and Applications. Prentice-Hall, Inc., first edition, 1973. ISBN 0-13-561670-0. |
....it becomes obvious that these models are all based on Markov chains that modulate a probability distribution function. A good introduction to Markovian mathematics and stochastic theory in general can be found in Bailey[19] while their appliance to modelling is explored in Maki and Thompson[20]. A review of the models used for VBR voice and video services is presented in Saitio[16] A popular model is the Markov Modulated Poisson Process (MMPP) The long tail on the PDF of a Poisson process makes it suitable for modelling the rare peaks that a bursty source can produce and for this ....
D. P. Maki and M. Thompson. Mathematical Models and Applications. Prentice-Hall, Inc., first edition, 1973. ISBN 0-13-561670-0.
....with this approach is the admittance of a stochastic element in the data. Thus, Y (t) does not exactly describe all the points y 1 ; y 2 ; y n . But the best (least amount of error) Y (t) is still desired. Numerous methods of minimum discrepancy exist to fit data to a linear function [1, 43] (commonly known as the method of least squares) and more complex functions [33] Periodic functions such as those necessary to model daily, weekly, and quarterly variations in workload on a computer system can be approximated accurately using fast Fourier transform techniques [33] Unfortunately, ....
....in queueing theory. Typical quantities that are provided from a queueing model are the average number of customers in the queue and the average time a customer spends in the service center. Typically, a queueing process can be described completely by characterizing three subprocesses of the queue [43]: arrival scheme: The arrival scheme (referred to as ) is a description of how often customers arrive. The arrival scheme is usually completely deterministic (the arrival times are precisely known) Adding a stochastic element to the arrival times makes the mathematics much more difficult. queue ....
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Maki, D. P., and Thompson, M. Mathematical Models and Applications. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1973.
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