On the role of Rouche's theorem in queueing analysis

On the role of Rouche's theorem in queueing analysis

0.00 Avg rating0 Votes
Article ID: iaor19992893
Country: United States
Volume: 23
Issue: 1/4
Start Page Number: 281
End Page Number: 291
Publication Date: Jan 1996
Journal: Queueing Systems
Authors: ,
Keywords: M/G/1 queues
Abstract:

In analytic queueing theory, Rouché's theorem is frequently used, and when it can be applied, leads quickly to tangible results concerning ergodicity and performance analysis. For more complicated models it is sometimes difficult to verify the conditions needed to apply the theorem. The natural question that arises is: Can one dispense with this theorem, in particular when the ergodicity conditions are known? In the present study we consider an M/G/1-type queueing problem which can be modelled by N coupled random walks. It is shown that it can be fully analysed without using Rouché's theorem, once it is known that the relevant functional equation has a unique solution with prescribed regularity properties.

Reviews

Required fields are marked *. Your email address will not be published.