UDC 519.21 Time Characteristics of Queuing System with Renovation and Reservice I. S. Zaryadov, A. A. Scherbanskaya Probability Theory and Mathematical Statistics Department Peoples’ Friendship University of Russia 6, Miklukho-Maklaya str., Moscow, Russia, 117198 This article is devoted to time characteristics of queuing system with recurrent input flow, one server, exponential service time distribution and infinite queue. <...> It means that a packet at the moment of the end of its service with some probability may just leave the system or with complementary probability will drop all other packets in the system and return for service. <...> Assuming that we know the steady-state probability distribution of number of packets (calculated with help of embedded by the moments of arrival Markov chain) the main emphasis of the article will be on system time characteristics such as steady-state distributions of time in system for serviced or dropped packets, average time characteristics—mean service time, mean waiting time for a dropped, serviced and an arbitrary packet. <...> Key words and phrases: renovation, reservice, general input flow, time characteristics, serviced packet, dropped packet. 1. <...> According to this mechanism a packet under service at the moment of the end of service with some probability may drop all other packets from a buffer or with complementary probability just leave the system. <...> The article is structured as follows: in the next section system notation is presented, then some formulae for steady-state distribution and service and loss probabilities are given. <...> The section after that presents time characteristics of served and dropped (loss) packets. <...> A(x) — arrival distribution function. 2. µ, µ > 0 — the parameter of exponential service distribution function. 3. α(·) — Laplase-Stieltjes transformation (LST) of A(x) function. 4. p — the probability that a served packet will leave the queuing system without dropping other packets. <...> Pp. 61–66 5. q = 1 − p — the probability of renovation with reservice — the packet at the moment of the end of the service will drop all other packets in the system and return to the buffer (and due to buffer emptiness will be immediately served again). 6. p− chain) that a packet at the moment of arrival will find k, k 0, packets in the system. k , k 0, — the steady-state <...>