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Stochastic networks with complex structures are key modelling tools for manyimportant applications. In this paper, we consider a specific type of network:the retrial queueing systems with priority. This type of queueing system isimportant in various applications, including telecommunication and computermanagement networks with big data. For this type of system, we propose adetailed stochastic decomposition approach to study its asymptotic behaviour ofthe tail probability of the number of customers in the steady-state for retrialqueues with two types (Type-1 and Type-2) of customers, in which Type-1customers (in a queue) have non-preemptive priority to receive service overType-2 customers (in an orbit). Under the assumption that the service times ofType-1 customers have a regularly varying tail and the service times of Type-2customers have a tail lighter than Type-1 customers, we obtain tail asymptoticproperties for the number of customers in the queue and in the orbit,respectively, conditional on the server's status, in terms of a detailedstochastic decomposition approach. Tail asymptotic properties are often used askey tools for approximating various performance metrics and constructingnumerical algorithms for computations.

Tail Asymptotics for the $M_1,M_2/G_1,G_2/1$ Retrial Queue with Priority