ON TIME-TO-BUFFER OVERFLOW DISTRIBUTION IN A SINGLE-MACHINE DISCRETE-TIME SYSTEM WITH FINITE CAPACITY-Reference-Cited by-同舟云学术

ON TIME-TO-BUFFER OVERFLOW DISTRIBUTION IN A SINGLE-MACHINE DISCRETE-TIME SYSTEM WITH FINITE CAPACITY

Published:2020-03-18 Issue:2 Volume:25 Page:289-302
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
language:
Short-container-title:

Author:

Kempa Wojciech M.¹^ORCID

Affiliation:

1. Silesian University of Technology, Faculty of Applied Mathematics, Kaszubska 23, 44-100 Gliwice, PolandSilesian University of Technology, Faculty of Applied Mathematics, Kaszubska 23, 44-100 Gliwice, Poland

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.

Publisher

Vilnius Gediminas Technical University

Subject

Modelling and Simulation,Analysis

Reference21 articles.

1. An introduction to numerical transform inversion and its application to probability models;J. Abate,2000

2. Discrete-Time Models for Communication Systems Including ATM

3. First-passage-time and busy-period distributions of discrete-time Markovian queues:Geom(n)/Geom(n)/1/N

4. Time ot buffer overflow in a MMPP queue;A. Chydziński,2007

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Level-Crossing Characteristics of an Actively Managed Buffer;Journal of Sensor and Actuator Networks;2024-04-15