Year: 2026
Type: article
Abstract: We focus on a queueing model in which the sizes of arriving jobs are stochastically dependent and each job may be denied service with a probability determined by the queue size (active management). Both of these effects are known to occur in computer networking and many other real-world realizations of queueing systems. For such a model, we perform a thorough transient and stationary analysis of the job departure process and the job rejection process. The results include theorems on the expected number of jobs that depart within a specified time interval, the departure intensity at a given time, the stationary departure rate, the expected number of jobs rejected within a specified interval, the transient rejection intensity and the stationary rejection rate. Sample numerical calculations are provided for illustration. They include various settings of the level of dependence between jobs, job rejection probabilities, and system load, as well as their impact on the departure and rejection processes.
Source: Entropy
DOI: 10.3390/e28010093
Author: Andrzej Chydzinski
Institution: Silesian University of Technology
Language: English
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: Narodowym Centrum Nauki
Award: G7992607525
OpenAlex ID: W7123945260