scholarly journals A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1239
Author(s):  
Yi Peng ◽  
Jinbiao Wu
Keyword(s):  
Communication Networks ◽  
Queueing System ◽  
Stopping Times ◽  
Stochastic Decomposition ◽  
Martingale Method ◽  
Computer Communication ◽  
Fluid Queues ◽  
Random Jumps ◽  
Stochastic Fluid ◽  
Decomposition Properties

Motivated by modelling the data transmission in computer communication networks, we study a Lévy-driven stochastic fluid queueing system where the server may subject to breakdowns and repairs. In addition, the server will leave for a vacation each time when the system is empty. We cast the workload process as a Lévy process modified to have random jumps at two classes of stopping times. By using the properties of Lévy processes and Kella–Whitt martingale method, we derive the limiting distribution of the workload process. Moreover, we investigate the busy period and the correlation structure. Finally, we prove that the stochastic decomposition properties also hold for fluid queues with Lévy input.

scholarly journals Sojourn Times in A Queueing System with Breakdowns and General Retrial Times

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2882
Author(s):  
Ivan Atencia ◽  
José Luis Galán-García
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Queueing System ◽  
Retrial Queue ◽  
Stochastic Decomposition ◽  
Discrete Time System ◽  
Main Research ◽  
Extensive Analysis ◽  
Complete Study ◽  
Number Of Customers

This paper centers on a discrete-time retrial queue where the server experiences breakdowns and repairs when arriving customers may opt to follow a discipline of a last-come, first-served (LCFS)-type or to join the orbit. We focused on the extensive analysis of the system, and we obtained the stationary distributions of the number of customers in the orbit and in the system by applying the generation function (GF). We provide the stochastic decomposition law and the application bounds for the proximity between the steady-state distributions for the queueing system under consideration and its corresponding standard system. We developed recursive formulae aimed at the calculation of the steady-state of the orbit and the system. We proved that our discrete-time system approximates M/G/1 with breakdowns and repairs. We analyzed the busy period of an auxiliary system, the objective of which was to study the customer’s delay. The stationary distribution of a customer’s sojourn in the orbit and in the system was the object of a thorough and complete study. Finally, we provide numerical examples that outline the effect of the parameters on several performance characteristics and a conclusions section resuming the main research contributions of the paper.

Rational Controllers in Computer/Communication Networks

2008 ◽  
Vol 41 (2) ◽  
pp. 15427-15432
Author(s):  
Pierre T. Kabamba ◽  
Wen-Chiao Lin ◽  
Semyon M. Meerkov ◽  
Choon Yik Tang
Keyword(s):  
Communication Networks ◽  
Computer Communication Networks ◽  
Computer Communication ◽  
Rational Controllers

Graph Mining Techniques

2013 ◽  
pp. 446-464 ◽  
Author(s):  
Ana Paula Appel ◽  
Christos Faloutsos ◽  
Caetano Traina Junior
Keyword(s):  
Social Networks ◽  
Communication Networks ◽  
Real World ◽  
Biological Networks ◽  
Graph Mining ◽  
Recommendation Systems ◽  
Computer Communication Networks ◽  
Computer Communication ◽  
Good Pattern ◽  
As Graph

Graphs appear in several settings, like social networks, recommendation systems, computer communication networks, gene/protein biological networks, among others. A large amount of graph patterns, as well as graph generator models that mimic such patterns have been proposed over the last years. However, a deep and recurring question still remains: “What is a good pattern?” The answer is related to finding a pattern or a tool able to help distinguishing between actual real-world and fake graphs. Here we explore the ability of ShatterPlots, a simple and powerful algorithm to tease out patterns of real graphs, helping us to spot fake/masked graphs. The idea is to force a graph to reach a critical (“Shattering”) point, randomly deleting edges, and study its properties at that point.

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