Detailed proof of ergodicity condition for the multi-server retrial queueing system with heterogeneous servers and phase type distribution of service
https://doi.org/10.67268/1812-5093-2026-34-1-118-124
EDN: PBYKZA
Abstract
Detailed proof of ergodicity for a multi-server retrial queueing system with heterogeneous servers, service times having a phase-type distribution with different irreducible representations and customer arrival defined by a Markovian arrival process is given. The proof consists of the use of the asymptotically quasi-Toeplitz Markov chains and Markov renewal processes theory
About the Authors
M. Liu
Belarusian State University
Belarus
Belarus
Minsk
A. N. Dudin
Belarusian State University
Belarus
Belarus
Minsk
References
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Review
For citations:
Liu M., Dudin A.N. Detailed proof of ergodicity condition for the multi-server retrial queueing system with heterogeneous servers and phase type distribution of service. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2026;34(1):118-124. https://doi.org/10.67268/1812-5093-2026-34-1-118-124. EDN: PBYKZA
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