Geodesic
Sufficient ergodicity conditions for queueing systems with non-preemptive priority
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2019), pp. 5-14

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Known results in ergodicity of priority queues are based on the assumption, that interarrival times in each queue have exponential distribution. This paper relaxes this assumption, providing sufficient conditions for queues with two priority classes under assumption, that interarrival times in high priority class queue have hyperexponential distribution. Queues with non-preemptive priority are considered. To formulate desired conditions, we use Lindley's recursion for waiting times of each priority class queue. Using Lyapunov-Foster criteria, we obtain sufficient conditions for given recursion to be Harris-ergodic markov chain.
Keywords: nonpreemtive queues, hyperexponential interarrival times, ergodicity, Lyapunov-Foster criteria, Lindley recursion. 
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     author = {A. V. Mistryukov and V. G. Ushakov},
     title = {Sufficient ergodicity conditions for queueing systems with non-preemptive priority},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {5--14},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2019_1_a0/}
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A. V. Mistryukov; V. G. Ushakov. Sufficient ergodicity conditions for queueing systems with non-preemptive priority. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2019), pp. 5-14. http://geodesic.mathdoc.fr/item/VTPMK_2019_1_a0/