Title 



Commuting Matrices in the Queue Length and Sojourn Time Analysis of MAP/MAP/1 Queues
 
Author 



 
Abstract 



Queues with Markovian arrival and service processes, i.e., MAP/MAP/1 queues, have been useful in the analysis of computer and communication systems and different representations for their stationary sojourn time and queue length distribution have been derived. More specifically, the class of MAP/MAP/1 queues lies at the intersection of the class of QBD queues and the class of semiMarkovian queues. While QBD queues have a matrix exponential representation for their queue length and sojourn time distribution of order N and N2, respectively, where N is the size of the background continuous time Markov chain, the reverse is true for a semiMarkovian queue. As the class of MAP/MAP/1 queues lies at the intersection, both the queue length and sojourn time distribution of a MAP/MAP/1 queue has an order N matrix exponential representation. The aim of this article is to understand why the order N2 distributions of the sojourn time of a QBD queue and the queue length of a semiMarkovian queue can be reduced to an order N distribution in the specific case of a MAP/MAP/1 queue. We show that the key observation exists in establishing the commutativity of some fundamental matrices involved in the analysis of the MAP/MAP/1 queue.   
Language 



English
 
Source (journal) 



Stochastic models.  New York, N.Y.  
Publication 



New York, N.Y. : 2014
 
ISSN 



15326349
 
Volume/pages 



30:4(2014), p. 554575
 
ISI 



000344371600007
 
Full text (Publisher's DOI) 


  
