Queues with the dropping function and general service time

Abstract

We present an analysis of queueing systems with the dropping function, infinite buffer and general distribution of the service time. Firstly, a stability condition, more general than the well-known ρ < 1, is proven. Secondly, the formulas for the queue size distribution, loss ratio and mean duration of the busy period, are derived. Thirdly, numerical examples are given, including optimizations of the shape of the dropping function with regard to the combined cost of the queue size and loss ratio.