Fluid Limits for Multiclass Many-Server Queues with General Reneging Distributions and Head-of-the-Line Scheduling

Author(s):  
Amber L. Puha ◽  
Amy R. Ward

We describe a fluid model with time-varying input that approximates a multiclass many-server queue with general reneging distribution and multiple customer classes (specifically, the multiclass G/GI/N+GI queue). The system dynamics depend on the policy, which is a rule for determining when to serve a given customer class. The class of admissible control policies are those that are head-of-the-line (HL) and nonanticipating. For a sequence of many-server queues operating under admissible HL control policies and satisfying some mild asymptotic conditions, we establish a tightness result for the sequence of fluid scaled queue state descriptors and associated processes and show that limit points of such sequences are fluid model solutions almost surely. The tightness result together with the characterization of distributional limit points as fluid model solutions almost surely provides a foundation for the analysis of particular HL control policies of interest. We leverage these results to analyze a set of admissible HL control policies that we introduce, called weighted random buffer selection (WRBS), and an associated WRBS fluid model that allows multiple classes to be partially served in the fluid limit (which is in contrast to previously analyzed static priority policies).

1973 ◽  
Vol 5 (01) ◽  
pp. 153-169 ◽  
Author(s):  
J. H. A. De Smit

Pollaczek's theory for the many server queue is generalized and extended. Pollaczek (1961) found the distribution of the actual waiting times in the model G/G/s as a solution of a set of integral equations. We give a somewhat more general set of integral equations from which the joint distribution of the actual waiting time and some other random variables may be found. With this joint distribution we can obtain distributions of a number of characteristic quantities, such as the virtual waiting time, the queue length, the number of busy servers, the busy period and the busy cycle. For a wide class of many server queues the formal expressions may lead to explicit results.


2014 ◽  
Vol 19 (6) ◽  
pp. 1294-1308 ◽  
Author(s):  
Nicola Acocella ◽  
Giovanni Di Bartolomeo ◽  
Patrizio Tirelli

This paper offers a reinterpretation of the Fed's time-varying implicit inflation target, based on two considerations. The first is that the need to alleviate the burden of distortionary taxation may justify the choice of a positive inflation rate. The second is based on compelling evidence that the degree of price and wage indexation falls with trend inflation. In fact, we find that a proper characterization of the joint evolution of fiscal variables and nominal rigidities has a strong impact on the Ramsey optimal policies, implying optimal inflation dynamics that are consistent with the observed evolution of U.S. trend inflation. By contrast, tax policies have been too lax, especially at the time of the controversial Bush tax cuts.


1972 ◽  
Vol 98 (2) ◽  
pp. 444-455
Author(s):  
Francis Clay McMichael ◽  
Frank C. Vigani
Keyword(s):  

1979 ◽  
Vol 57 (19) ◽  
pp. 2612-2616 ◽  
Author(s):  
Morris Wayman ◽  
Miranda G. S. Chua

Lignocellulosic residue remaining after autohydrolysis of extractive-free aspen wood meal at 195 °C for periods of time varying from 5 to 120 min followed by extraction with 90% dioxane was subjected to enzymatic hydrolysis to obtain residual lignin. Infrared studies indicated that in the early stages of autohydrolysis residual lignin resembles protolignin, but as autohydrolysis proceeds it changes to resemble more and more the extracted lignin. Residual lignin was found to be higher in carbon but lower in hydrogen and oxygen than aspen milled wood lignin. The methoxyl content was also lower than the reference lignin. From alkaline nitrobenzene oxidation, residual lignin is seen to become more condensed with increasing autohydrolysis time. The insolubility of residual lignin is attributed to the existence of strong bonds between this lignin and carbohydrate.


2019 ◽  
Vol 18 (11) ◽  
Author(s):  
G. C. Amaral ◽  
G. P. Temporão

Abstract Depolarization is one of the most important sources of error in a quantum communication link that can be introduced by the quantum channel. Even though standard quantum process tomography can, in theory, be applied to characterize this effect, in most real-world implementations depolarization cannot be distinguished from time-varying unitary transformations, especially when the timescales are much shorter than the detectors response time. In this paper, we introduce a method for distinguishing true depolarization from fast polarization rotations by employing Hong–Ou–Mandel interference. It is shown that the results are independent of the timing resolutions of the photodetectors.


2005 ◽  
Author(s):  
B.J. Cooke ◽  
J.L. Prince ◽  
Z.J. Staszak ◽  
D. Shope ◽  
W.J. Fahey

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