UDC 519.21 The Analysis of Queueing System with Two Input Flows and Stochastic Drop Mechanism I. S. Zaryadov, A. V. Gorbunova Department of Applied Probability and Informatics Peoples’ Friendship University of Russia 6, Miklukho-Maklaya str., Moscow, Russia, 117198 The queueing system with two independent flows of requests with different types of priorities is considered. <...> The incoming flows are Poisson flows with different (non equal) rates. <...> The priority requests at the end of its service can drop non-priority ones with probability q (renovation probability) or just leaves the system with probability p = 1−q. <...> For general case the two-dimensional Markov process is introduced and the system of equilibrium equations for steady-state probability distribution is presented. <...> For special case, when drop probability q is equal to one, some probabilistic characteristics as the steady-state probability distribution of priority requests, the probability of idle period are obtained. <...> Also the analytical expressions for some characteristics of non-priority requests, such as probability of being dropped (or serviced), waiting time distribution for non-priority requests (in terms of Laplace-Stieltjes transformation and generating function) and mean waiting time, are obtained. <...> Key words and phrases: queueing system, two input flows, renovation probability, stochastic drop mechanism, time-probability characteristics. 1. <...> Introduction At the present time the questions how to ensure the specified quality of service (QoS) in data networks are very important. <...> One of the key performance indicators are the service traffic losses and the average transmission delay due to the unavoidable occurrence of bursts. <...> Problems associated with data loss may also occur due to servers failure, receipt of a special type of data that have a negative impact on the efficiency of the service and operation of the network element (device) [1–5]. <...> In order to regulate the intensity of the incoming data flow and to reduce the negative effects various control mechanisms to prevent network overload are introduced and under study. <...> Thus, for example, RED-like algorithms (Random Early Detection) [6,7] under overload situation or close thereto can control the degree of loading queue using some stochastic drop mechanism for incoming packets. <...> In the article the authors consider some modification of active queue management mechanism [8 <...>