A busy period approach to some queueing games

2021 ◽  
Vol 97 (3-4) ◽  
pp. 261-277
Author(s):  
Moshe Haviv ◽  
Binyamin Oz
Keyword(s):  
2008 ◽  
Vol 36 (2) ◽  
pp. 98-100 ◽  
Author(s):  
Chaitanya Garikiparthi ◽  
Appie van de Liefvoort ◽  
Ken Mitchell

1986 ◽  
Vol 23 (1) ◽  
pp. 261-264 ◽  
Author(s):  
Saeed Ghahramani
Keyword(s):  

Conditions for finiteness of moments of the following quantities have been found: the duration of a busy period of an Μ /G/∞ system; the duration of a partial busy period of an M/G/C loss system, and the duration of a partial busy period of an M/G/C queue.


2006 ◽  
Vol 38 (01) ◽  
pp. 263-283 ◽  
Author(s):  
Nelson Antunes ◽  
Christine Fricker ◽  
Fabrice Guillemin ◽  
Philippe Robert

In this paper, motivated by the problem of the coexistence on transmission links of telecommunications networks of elastic and unresponsive traffic, we study the impact on the busy period of an M/M/1 queue of a small perturbation in the service rate. The perturbation depends upon an independent stationary process (X(t)) and is quantified by means of a parameter ε ≪ 1. We specifically compute the two first terms of the power series expansion in ε of the mean value of the busy period duration. This allows us to study the validity of the reduced service rate approximation, which consists in comparing the perturbed M/M/1 queue with the M/M/1 queue whose service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process (X(t)) play a key role.


1978 ◽  
Vol 29 (7) ◽  
pp. 707-708 ◽  
Author(s):  
B. H. Bissinger ◽  
V. N. Murty
Keyword(s):  

2004 ◽  
Vol 111 (2) ◽  
pp. 237-258 ◽  
Author(s):  
A. Baltrūnas ◽  
D.J. Daley ◽  
C. Klüppelberg

1862 ◽  
Vol 23 (1) ◽  
pp. 99-131 ◽  
Author(s):  
William Seller

It does not always happen that the memory of inquirers into nature, who have the merit or the fortune to strike first into a right path, is cherished as it deserves. This remark applies forcibly to the eminent person, whether regarded as a physiologist or as a physician, of whose life aud labours a brief memoir is now laid before the Society. The name of Robert Whytt was familiar to his contemporaries both at home and abroad. Increase of distance should hardly yet have dimmed its lustre. Yet, in proportion as the views which he initiated have expanded more and more in growing to maturity, the less and less is heard of their author. Biography—which never did Whytt great justice—begins already to put him aside. A few particulars of his life, with a catalogue of his works, have hitherto been common in books of that description, principally in those of Germany and France. In some newer French biographies his name has dropped out. But of a late Edinburgh Biographical Dictionary, extending to not a few volumes, while restricted to the lives of eminent Scotsmen, it will hardly obtain credit that an early luminary of the rising University, conspicuous among the European leaders of medical science during a busy period of the eighteenth century, should, amidst a cloud of mediocrity, be there sought for in vain.


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