On the transient behavior of a finite birth-death process with an application

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Abstract

The transient distribution of the number in the system and the distribution of the length of a busy period for a finite birth and death process is derived by solving the system of linear equations of Laplace-Transforms and finding the inversions through the properties of tridiagonal symmetric matrices. It is proved that the distributions of a busy period is hyperexponential. The steady-state solution of the number of customers in the system is verified without any difficulty. The numerical solution of the number of customers in the system and the busy period is possible by the use of a high speed computer for which a multi-server queueing system with balking and reneging serves as an illustration. Some numerical comparisons are made with the randomization method.

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S. G. Mohanty is a Professor in the Department of Mathematics and Statistics at McMaster University, Hamilton, Canada. His research interests are enumerative combinatorics, nonparametric inference and queueing theory. Besides his publications in various journals of Mathematics, Statistics and Operations Research, he is the author of Lattice Path Counting and Applications, Academic Press (1979).

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A. Montazer-Haghighi is a Professor in the Department of Mathematics and Computer Science at Benedict College, Columbia, South Carolina. His research interests are applied probability and queueing theory. Besides his publications in journals of Mathematics and Operations Research, he is the author of several textbooks in Farsi and has published several translations of well-known published books on Mathematics and Probability Theory.

R. Trueblood is an Associate Professor in the Department of MIS/MSC at The University of Alabama in Huntsville, Huntsville, Alabama. His research interests are computer performance evaluation and data/knowledge systems. He has publications in various IEEE and ACM journals.

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