MONOTONICITY AND CONVEXITY OF SOME FUNCTIONS ASSOCIATED WITH DENUMERABLE MARKOV CHAINS AND THEIR APPLICATIONS TO QUEUING SYSTEMS
2005 ◽
Vol 20
(1)
◽
pp. 67-86
◽
Keyword(s):
Motivated by various applications in queuing theory, this article is devoted to the monotonicity and convexity of some functions associated with discrete-time or continuous-time denumerable Markov chains. For the discrete-time case, conditions for the monotonicity and convexity of the functions are obtained by using the properties of stochastic dominance and monotone matrix. For the continuous-time case, by using the uniformization technique, similar results are obtained. As an application, the results are applied to analyze the monotonicity and convexity of functions associated with the queue length of some queuing systems.
Keyword(s):
2007 ◽
Vol 39
(02)
◽
pp. 360-384
◽
Keyword(s):
Keyword(s):
1992 ◽
Vol 29
(04)
◽
pp. 838-849
◽
2006 ◽
Vol 43
(04)
◽
pp. 1044-1052
◽
Keyword(s):
Keyword(s):
1998 ◽
Vol 7
(4)
◽
pp. 397-401
◽
Keyword(s):
2013 ◽
Vol 50
(4)
◽
pp. 943-959
◽