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In this article the model of central network element home location register/home subscriber server (HLR/HSS) in mobile networks GSM and UMTS is presented. The model is based on queueing discipline earliest deadline first (EDF). The EDF method operates with dynamical priorities and takes into account the deadlines of arriving tasks. Moreover, focused on the considered case of HLR/HSS, the approach for a mathematical description of non-preemptive queueing method EDF is offered.