Upper Bounds on Performance Measures of Heterogeneous MMc Queues
Joint Authors
Yehia, H. C.
Kerbache, Laoucine
Pedrosa, L. A. C.
Alves, F. S. Q.
Cruz, F. R. B.
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-07-06
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
In many real-life queueing systems, the servers are often heterogeneous, namely they work at different rates.
This paper provides a simple method to compute tight upper bounds on two important performance measures of single-class heterogeneous multi-server Markovian queueing systems, namely the average number in queue and the average waiting time in queue.
This method is based on an expansion of the state space that is followed by an approximate reduction of the state space, only considering the most probable states.
In most cases tested, we were able to approximate the actual behavior of the system with smaller errors than those obtained from traditional homogeneous multiserver Markovian queues, as shown by GPSS simulations.
In addition, we have correlated the quality of the approximation with the degree of heterogeneity of the system, which was evaluated using its Gini index.
Finally, we have shown that the bounds are robust and still useful, even considering quite different allocation strategies.
A large number of simulation results show the accuracy of the proposed method that is better than that of classical homogeneous multiserver Markovian formulae in many situations.
American Psychological Association (APA)
Alves, F. S. Q.& Yehia, H. C.& Pedrosa, L. A. C.& Cruz, F. R. B.& Kerbache, Laoucine. 2011. Upper Bounds on Performance Measures of Heterogeneous MMc Queues. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-18.
https://search.emarefa.net/detail/BIM-491761
Modern Language Association (MLA)
Alves, F. S. Q.…[et al.]. Upper Bounds on Performance Measures of Heterogeneous MMc Queues. Mathematical Problems in Engineering No. 2011 (2011), pp.1-18.
https://search.emarefa.net/detail/BIM-491761
American Medical Association (AMA)
Alves, F. S. Q.& Yehia, H. C.& Pedrosa, L. A. C.& Cruz, F. R. B.& Kerbache, Laoucine. Upper Bounds on Performance Measures of Heterogeneous MMc Queues. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-18.
https://search.emarefa.net/detail/BIM-491761
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-491761