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We study K-class single server retrial queueing system with classical retrial policy. If new arrival of class i=1,..., K finds the server busy, it joins to i-th infinite capacity orbit and then retry to attack server after random delay. Each class of customers is characterized by its own set of parameters (input rate, service time and orbit rate). Note, that only source of instability of such a system is an infinite growth of orbits size. Necessary and sufficient stability condition of presented system coincides with stability condition of corresponding multiclass infinite buffer queueing system. The talk illustrates the convergence of mean orbit size to mean queue size with a growth of orbit rates for stable regime in retrial system and corresponding queueing system, respectively.

Unlike multiclass retrial system with constant retrial rate, the growth of any orbit in a system with classical retrial policy affects to other orbits. Thus, the stability means, that all K orbits are stable and instability implies that all orbits go to infinity. That illustrates the solidarity property for orbits in presented system.

2018 September 22 - 14:40
20 min
Stochastic Modeling and Applied Research of TechnologY
1. Stochastic Modeling and Applications