This article is cited in 2 papers

Discrete-time $\mathrm{Geo}/G/1/\infty$ LIFO queue with resampling policy

L. A. Meykhanadzhyan^a, R. V. Razumchik<sup>bc

a</sup> Financial University under the Government of the Russian Federation, 49 Leningradsky Prosp., Moscow 125993, Russian Federation
^b Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
^c Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation

Abstract: Consideration is given to the problem of estimation of the true stationary mean response time in the discrete-time single-server queue of infinite capacity, with Bernoulli input, round-robin scheduling, and inaccurate information about the service time distribution which is considered to be general arithmetic. It is shown that the upper bound for the true value may be provided by the mean response time in the discrete-time single-server queue with LIFO (last in, first out) service discipline and resampling policy. The latter implies that a customer arriving to the nonidle system assigns new remaining service time for the customer in the server. For the case when the true service time distribution is geometric and the error in the service times is of multiplicative type, conditions are provided which, when satisfied, guarantee that the proposed method yields the upper bound across all possible values of the system's load.

Keywords: discrete time, inverse service order, inaccurate service time, round robin scheduling, resampling policy.

Received: 15.10.2019

DOI: 10.14357/19922264190410