Erlang service system with limited memory space under control of AQM mechanizm

Abstract

We investigate the M/G/n ≤ ∞/(0, V)-type Erlang loss service system with n ≤ ∞ independent service stations and Poisson arrival stream in which volumes of entering demands and their processing times are generally distributed and, in general, are dependent random variables. Moreover, the total volume of all demands present simultaneously in the system is bounded by a non-random value V (system memory capacity). The enqueueing process is controlled by an AQM-type non-increasing accepting function. Two different acceptance rules are considered in which the probability of acceptance is dependent or independent on the volume of the arriving demand. Stationary queue-size distribution and the loss probability are found for both scenarios of the system behavior. Besides, some special cases are discussed. Numerical examples are attached as well.