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Heavy Traffic Limits for the Extreme Waiting Time in Multi-phase Queueing Systems

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Abstract

The main object of this research is a functional limit theorem under conditions of heavy traffic in multi-phase queueing systems. In this paper, limit theorems are proved for extreme values of important probabilistic characteristics of a queueing system, as well as maxima and minima of a waiting time and cumulative waiting time of a customer are investigated and illustrative numerical examples of simulation of multi-phase queueing systems are presented.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225, Vilnius, Lithuania

    Saulius Minkevičius & Edvinas Greičius

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  1. Saulius Minkevičius
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  2. Edvinas Greičius
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Correspondence to Edvinas Greičius.

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Minkevičius, S., Greičius, E. Heavy Traffic Limits for the Extreme Waiting Time in Multi-phase Queueing Systems. Methodol Comput Appl Probab 21, 109–124 (2019). https://doi.org/10.1007/s11009-018-9641-4

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  • DOI: https://doi.org/10.1007/s11009-018-9641-4

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