Transient solution of a non-empty chemical queueing system

Transient solution of a non-empty chemical queueing system

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Article ID: iaor200971589
Country: Germany
Volume: 70
Issue: 1
Start Page Number: 77
End Page Number: 98
Publication Date: Aug 2009
Journal: Mathematical Methods of Operations Research
Authors: , ,
Keywords: numerical analysis
Abstract:

In this paper, we illustrate that a power series technique can be used to derive explicit expressions for the transient state distribution of a queueing problem having ‘chemical’ rules with an arbitrary number of customers present initially in the system. Based on generating function and Laplace techniques Conolly et al. (1997) have obtained the distributions for a non-empty chemical queue. Their solution enables us only to recover the idle probability of the system in explicit form. Here, we extend not only the model of Conolly et al. but also get a new and simple solution for this model. The derived formula for the transient state is free of Bessel function or any integral forms. The transient solution of the standard M/M/1/8 queue with λ = μ is a special case of our result. Furthermore, the probability density function of the virtual waiting time in a chemical queue is studied. Finally, the theory is underpinned by numerical results.

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