Some results for inhomogeneous birth-and-death process with application to staffing problem in telecommunication service systems

This paper proposes some analytical results that may facilitate long-term staffing problem in high-level telecommunication service systems (such as information call centers) in which rates of processes, that govern their behaviour, depend on time. We assume that except for arrivals of requests and their service there happen periodic system breakdowns (possibly with very long inter-breakdown periods). The staffing objective is immediate service of a given percentage of incoming requests. A natural model for such a time-varying processes is an innhomogeneous birth-death process for which we propose some general theoretical results concerning its ergodicity conditions and limiting behaviour. As an example we show that if the service system is modelled by multiserver queue Mt/Mt/S with state-dependent periodic arrivals, services and breakdown rates, then using obtained results one can calculate the quantities needed for the solution of optimization problem. Accuracy of approximation is briefly discussed. © 2015 IEEE.

Authors
Zeifman A.1 , Korotysheva A.2 , Razumchik R. 3 , Korolev V.4 , Shorgin S.5
Language
English
Pages
243-246
Status
Published
Number
7382436
Volume
2016-January
Year
2016
Organizations
  • 1 Vologda State University, Institute of Informatics Problems FRC CSC RAS, ISEDT RAS, Russian Federation
  • 2 Vologda State University, Institute of Informatics Problems FRC CSC RAS, Russian Federation
  • 3 Institute of Informatics Problems FRC CSC RAS, Peoples' Friendship University, Russian Federation
  • 4 Lomonosov Moscow State University, Institute of Informatics Problems FRC CSC RAS, Russian Federation
  • 5 Institute of Informatics Problems FRC CSC RAS, Russian Federation
Keywords
catastrophes; inhomogeneous birth-and-death process; limiting characteristics; rate of convergence; weak ergodicity
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/4024/
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