On Time-to-Buffer Overflow Distribution in a Single-Machine Discrete-Time System With Finite Capacity

Abstract

A model of a single-machine production system with finite magazine capacity is investigated. The input flow 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 overflow 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 overflows is also given. Numerical examples are attached as well.

Level-Crossing Characteristics of an Actively Managed Buffer

“…On the other hand, the level-crossing characteristics were investigated in several other papers using methods of queuing theory, [37][38][39][40][41][42][43]. Unfortunately, all of the models from [37][38][39][40][41][42][43] lack the active management component, which is central here.…”

“…On the other hand, the level-crossing characteristics were investigated in several other papers using methods of queuing theory, [37][38][39][40][41][42][43]. Unfortunately, all of the models from [37][38][39][40][41][42][43] lack the active management component, which is central here. The AQM component is also absent in all the studies conducted so far on models of a sensor node with the N-policy, [31][32][33][34][35][36].…”