On Time-to-Buffer Overow Distribution in a Single-Machine Discrete-Time System with Finite Capacity.

A model of a single-machine production system with finite magazine capacity is investigated. The input ow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer overow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer overows is also given. Numerical examples are attached as well. [ABSTRACT FROM AUTHOR]