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Ross‐Type Conjectures on Monotonicity of Queues
Author(s) -
Miyoshi Naoto,
Rolski Tomasz
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00318.x
Subject(s) - citation , queue , monotonic function , type (biology) , mathematical economics , mathematics , operations research , mathematical sciences , computer science , library science , statistics , programming language , mathematical analysis , ecology , biology
In his seminal paper from 1978, Ross set up a few conjectures which formalize a common belief that more variable arrival processes lead to worse performance in queueing systems. We study these types of problems for Cox/GI/1/∞, Cox/GI/∞/∞, and Cox/GI/1/0 systems. Assumptions are stated in terms of ≤idcx-regularity. For example, in the class of stationary Markov processes, the regularity property holds under a doubly stochastic monotonicity assumption. A special case is a result of Daley (1968) on the decreasing covariance function for stochastically monotone stationary Markov processes.