scholarly journals Fluid and Diffusion Approximations of a Two-Station Mixed Queueing Network

1995 ◽  
Vol 20 (2) ◽  
pp. 321-354 ◽  
Author(s):  
Viên Nguyen
Keyword(s):  
Queueing Network ◽  
Diffusion Approximations ◽  
And Diffusion

scholarly journals A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

2018 ◽  
Vol 123 (2) ◽  
pp. 289-312 ◽  
Author(s):  
Pavel Mozgunov ◽  
Marco Beccuti ◽  
Andras Horvath ◽  
Thomas Jaki ◽  
Roberta Sirovich ◽  
...  
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Reaction Networks ◽  
Diffusion Approximations ◽  
And Diffusion

scholarly journals Heavy-Traffic Limits for a Many-Server Queueing Network with Switchover

2013 ◽  
Vol 45 (3) ◽  
pp. 645-672 ◽  
Author(s):  
Guodong Pang ◽  
David D. Yao
Keyword(s):  
Load Balancing ◽  
Differential Equations ◽  
Piecewise Linear ◽  
Heavy Traffic ◽  
Queueing Network ◽  
State Dependent ◽  
Diffusion Limits ◽  
Qed Regime ◽  
The Many ◽  
And Diffusion

We study a multiclass Markovian queueing network with switchover across a set of many-server stations. New arrivals to each station follow a nonstationary Poisson process. Each job waiting in queue may, after some exponentially distributed patience time, switch over to another station or leave the network following a probabilistic and state-dependent mechanism. We analyze the performance of such networks under the many-server heavy-traffic limiting regimes, including the critically loaded quality-and-efficiency-driven (QED) regime, and the overloaded efficiency-driven (ED) regime. We also study the limits corresponding to mixing the underloaded quality-driven (QD) regime with the QED and ED regimes. We establish fluid and diffusion limits of the queue-length processes in all regimes. The fluid limits are characterized by ordinary differential equations. The diffusion limits are characterized by stochastic differential equations, with a piecewise-linear drift term and a constant (QED) or time-varying (ED) covariance matrix. We investigate the load balancing effect of switchover in the mixed regimes, demonstrating the migration of workload from overloaded stations to underloaded stations and quantifying the load balancing impact of switchover probabilities.

scholarly journals Generalized Lemaítre–Tolman–Bondi spacetime under the influence of electric charge and Palatini f(R) gravity

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
M. Z. Bhatti ◽  
Z. Yousaf ◽  
F. Hussain
Keyword(s):  
Electromagnetic Field ◽  
Evolution Equations ◽  
Mass Function ◽  
Diffusion Approximations ◽  
Riemann Curvature ◽  
Field Equations ◽  
Riemann Curvature Tensor ◽  
Inhomogeneous Universe ◽  
Dust Fluid ◽  
And Diffusion

AbstractThe objective of this article is to investigate the effects of electromagnetic field on the generalization of Lemaître–Tolman–Bondi (LTB) spacetime by keeping in view the Palatini f(R) gravity and dissipative dust fluid. For performing this analysis, we followed the strategy deployed by Herrera et al. (Phys Rev D 82(2):024021, 2010). We have explored the modified field equations along with kinematical quantities and mass function and constructed the evolution equations to study the dynamics of inhomogeneous universe along with Raychauduary and Ellis equations. We have developed the relation for Palatini f(R) scalar functions by splitting the Riemann curvature tensor orthogonally and associated them with metric coefficients using modified field equations. We have formulated these scalar functions for LTB and its generalized version, i.e., GLTB under the influence of charge. The properties of GLTB spacetime are consistent with those of the LTB geometry and the scalar functions found in both cases are comparable in the presence of charge and Palatini f(R) curvature terms. The symmetric properties of generalized LTB spacetime are also studied using streaming out and diffusion approximations.

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