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Digital Library

of the European Council for Modelling and Simulation

 

Title:

Uniform In Time Bounds For “No-Wait” Probability In Queues Of Mt/Mt/S Type

Authors:

Alexander Zeifman, Anna Korotysheva, Yacov Satin, Galina Shilova, Rostislav Razumchik, Victor Korolev, Sergey Shorgin

Published in:

 

 

(2016).ECMS 2016 Proceedings edited by: Thorsen Claus, Frank Herrmann, Michael Manitz, Oliver Rose, European Council for Modeling and Simulation. doi:10.7148/2016

 

 

ISBN: 978-0-9932440-2-5

 

30th European Conference on Modelling and Simulation,

Regensburg Germany, May 31st – June 3rd, 2016

 

Citation format:

Alexander Zeifman, Anna Korotysheva, Yacov Satin, Galina Shilova, Rostislav Razumchik, Victor Korolev, Sergey Shorgin (2016). Uniform In Time Bounds For “No-Wait” Probability In Queues Of Mt/Mt/S Type, ECMS 2016 Proceedings edited by: Thorsten Claus, Frank Herrmann, Michael Manitz, Oliver Rose  European Council for Modeling and Simulation. doi:10.7148/2016-0676

 

DOI:

http://dx.doi.org/10.7148/2016-0676

Abstract:

In this paper we present new analytical results concerning long-term staffing problem in high-level telecommunication service systems. We assume that a service system can be modelled either by a classic Mt/Mt/S queue, or Mt/Mt/S queue with batch service or Mt/Mt/S with catastrophes and batch arrivals when empty. The question under consideration is: how many servers guarantee that in the long run the probability of zero delay in a queue is higher than the target probability at all times? Here the methodology is presented, which allows one to construct uniform in time upper bound for the value of S in each of the three cases and does not require the calculation of the limiting distribution. These upper bounds can be easily computed and are accurate enough whenever the arrival intensity is low, but become rougher as the arrival intensity is further increased. In the numerical section one compares the accuracy of the obtained bounds with the exact vales of S , obtained by direct numerical computation of the limiting distribution.

 

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