Tail behaviour of a finite/infinitecapacity priority queue
 Author
 Thomas Demoor (UGent) , Joris Walraevens (UGent) , Dieter Fiems (UGent) and Herwig Bruneel (UGent)
 Organization
 Abstract
 Priority queues have been studied extensively throughout the last few decades. One of the main performance measures of interest is the loss probability, caused by the evident finiteness of queues. From analytical point of view, finitecapacity queues are more complex to study than queues with infinite capacity. Therefore, the most common approach for studying the loss probability is to analyze the tail behaviour of the corresponding infinitecapacity system. From this behaviour, the loss probability of the finitecapacity system can be approximated. However, this approximation can be rather inaccurate. Consider a system with two priority classes where the lowpriority queue has infinite capacity but the highpriority queue can only accommodate N packets. In the system where both queues have infinite capacity, the tail behaviour of the queue content of the lowpriority class can be geometric or nongeometric, dependent on whether the dominant singularity of the respective generating function is a pole or a branch point. However, in the system with a finite highpriority queue the tail is always geometric, even when N is large. Investigating this discrepancy is the topic of our contribution. In the finite system, the lowpriority queue content can be expressed by a matrix equation. These matrices contain (partial) generating functions. Finding the poles corresponds to solving a nonlinear eigenvalue problem. However, finding all poles is infeasible for larger N. Therefore, a numerical method is used to obtain the poles in a certain region (around the dominant pole).
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU1255985
 Chicago
 Demoor, Thomas, Joris Walraevens, Dieter Fiems, and Herwig Bruneel. 2010. “Tail Behaviour of a Finite/infinitecapacity Priority Queue.” In Queueing Theory, 3rd Madrid Conference, Booklet of Abstracts, 31–32.
 APA
 Demoor, Thomas, Walraevens, J., Fiems, D., & Bruneel, H. (2010). Tail behaviour of a finite/infinitecapacity priority queue. Queueing Theory, 3rd Madrid conference, Booklet of abstracts (pp. 31–32). Presented at the 3rd Madrid conference on Queueing Theory (MCQT ’10).
 Vancouver
 1.Demoor T, Walraevens J, Fiems D, Bruneel H. Tail behaviour of a finite/infinitecapacity priority queue. Queueing Theory, 3rd Madrid conference, Booklet of abstracts. 2010. p. 31–2.
 MLA
 Demoor, Thomas, Joris Walraevens, Dieter Fiems, et al. “Tail Behaviour of a Finite/infinitecapacity Priority Queue.” Queueing Theory, 3rd Madrid Conference, Booklet of Abstracts. 2010. 31–32. Print.
@inproceedings{1255985, abstract = {Priority queues have been studied extensively throughout the last few decades. One of the main performance measures of interest is the loss probability, caused by the evident finiteness of queues. From analytical point of view, finitecapacity queues are more complex to study than queues with infinite capacity. Therefore, the most common approach for studying the loss probability is to analyze the tail behaviour of the corresponding infinitecapacity system. From this behaviour, the loss probability of the finitecapacity system can be approximated. However, this approximation can be rather inaccurate. Consider a system with two priority classes where the lowpriority queue has infinite capacity but the highpriority queue can only accommodate N packets. In the system where both queues have infinite capacity, the tail behaviour of the queue content of the lowpriority class can be geometric or nongeometric, dependent on whether the dominant singularity of the respective generating function is a pole or a branch point. However, in the system with a finite highpriority queue the tail is always geometric, even when N is large. Investigating this discrepancy is the topic of our contribution. In the finite system, the lowpriority queue content can be expressed by a matrix equation. These matrices contain (partial) generating functions. Finding the poles corresponds to solving a nonlinear eigenvalue problem. However, finding all poles is infeasible for larger N. Therefore, a numerical method is used to obtain the poles in a certain region (around the dominant pole).}, author = {Demoor, Thomas and Walraevens, Joris and Fiems, Dieter and Bruneel, Herwig}, booktitle = {Queueing Theory, 3rd Madrid conference, Booklet of abstracts}, language = {eng}, location = {Toledo, Spain}, pages = {3132}, title = {Tail behaviour of a finite/infinitecapacity priority queue}, year = {2010}, }