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The solution of an infinite set of differential-difference equations occurring in polymerization and queueing problems

Published online by Cambridge University Press:  24 October 2008

A. Wragg
A. Wragg
Affiliation:
Mathematics Department, Royal College of Advanced Technology, Salford
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Abstract

The time-dependent solutions of an infinite set of differential-difference equations arising from queueing theory and models of ‘living’ polymer are expressed in terms of modified Bessel functions. Explicit solutions are available for constant values of a parameter describing the arrival rate or monomer concentration; for time-dependent parameter a formal solution is obtained in terms of a function which satisfies a Volterra type integral equation of the second kind. These results are used as the basis of a numerical method of solving the infinite set of differential equations when the time-dependent parameter itself satisfies a differential equation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 117 - 124
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

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