Generalized state-dependent Erlangian queues: Speculations about calculating measures of effectiveness

1975 ◽  
Vol 12 (02) ◽  
pp. 358-363 ◽  
Author(s):  
B. W. Conolly
Keyword(s):  
Renewal Theory ◽  
Time Dependent ◽  
State Dependent ◽  
Measures Of Effectiveness ◽  
Generalized State

The provision of easily calculable measures of effectiveness for generalised Erlang queues (state-dependent parameters λn and μn of arrival and of service) motivates speculation about the applicability of renewal theory. The application envisaged is justified by known results for certain models and its extension to an operationally more promising system is proposed. Use of the formula ‘L = λW' with ‘effective’ λ calculated by foregoing methods is likewise shown to be justified by known results for certain models and hence its wider applicability is conjectured. Mechanisms are discussed which may provide improved models, and investigation is made of choices of λn and μn which may lead to time dependent solutions having a prescribed form. The example of panic buying is considered as an example.

Generalized state-dependent Erlangian queues: Speculations about calculating measures of effectiveness

1975 ◽  
Vol 12 (2) ◽  
pp. 358-363 ◽  
Author(s):  
B. W. Conolly
Keyword(s):  
Renewal Theory ◽  
Time Dependent ◽  
State Dependent ◽  
Measures Of Effectiveness ◽  
Generalized State

The provision of easily calculable measures of effectiveness for generalised Erlang queues (state-dependent parameters λn and μn of arrival and of service) motivates speculation about the applicability of renewal theory. The application envisaged is justified by known results for certain models and its extension to an operationally more promising system is proposed. Use of the formula ‘L = λW' with ‘effective’ λ calculated by foregoing methods is likewise shown to be justified by known results for certain models and hence its wider applicability is conjectured. Mechanisms are discussed which may provide improved models, and investigation is made of choices of λn and μn which may lead to time dependent solutions having a prescribed form. The example of panic buying is considered as an example.

A state-dependent lifetime process of individuals subject to external perturbations

1980 ◽  
Vol 17 (04) ◽  
pp. 922-938
Author(s):  
Wolfgang Mergenthaler
Keyword(s):  
Ionizing Radiation ◽  
State Space ◽  
Lifetime Distribution ◽  
The State ◽  
Time Dependent ◽  
Biological Cell ◽  
Regeneration Time ◽  
External Perturbations ◽  
State Dependent ◽  
The Mean

We consider an individual which ultimately dies or divides, and whose state is subject to drift and jumps caused by external perturbations. The mortality and division rates being state-dependent, the present paper deals with the time-dependent distribution of the individual's position in the state-space and with its lifetime distribution. The results are applied to a model of a biological cell which is exposed to ionizing radiation. Under certain conditions on the parameters of the type of perturbation one can show that the division probability decreases and the mean regeneration time increases with increasing frequency and ‘effect' of the perturbations.

scholarly journals Earthquake simulations with time-dependent nucleation and long-range interactions

1995 ◽  
Vol 2 (3/4) ◽  
pp. 109-120 ◽  
Author(s):  
J. H. Dieterich
Keyword(s):  
Long Range ◽  
Approximate Solutions ◽  
Time Dependent ◽  
Earthquake Activity ◽  
Fault Surface ◽  
Elastic Interactions ◽  
State Dependent ◽  
Aftershock Sequences ◽  
Earthquake Nucleation ◽  
Earthquake Simulations

Abstract. A model for rapid simulation of earthquake sequences is introduced which incorporates long-range elastic interactions among fault elements and time-dependent earthquake nucleation inferred from experimentally derived rate- and state-dependent fault constitutive properties. The model consists of a planar two-dimensional fault surface which is periodic in both the x- and y-directions. Elastic interactions among fault elements are represented by an array of elastic dislocations. Approximate solutions for earthquake nucleation and dynamics of earthquake slip are introduced which permit computations to proceed in steps that are determined by the transitions from one sliding state to the next. The transition-driven time stepping and avoidance of systems of simultaneous equations permit rapid simulation of large sequences of earthquake events on computers of modest capacity, while preserving characteristics of the nucleation and rupture propagation processes evident in more detailed models. Earthquakes simulated with this model reproduce many of the observed spatial and temporal characteristics of clustering phenomena including foreshock and aftershock sequences. Clustering arises because the time dependence of the nucleation process is highly sensitive to stress perturbations caused by nearby earthquakes. Rate of earthquake activity following a prior earthquake decays according to Omori's aftershock decay law and falls off with distance.

scholarly journals State-independent Block of BK Channels by an Intracellular Quaternary Ammonium

2006 ◽  
Vol 128 (3) ◽  
pp. 347-364 ◽  
Author(s):  
Christina M. Wilkens ◽  
Richard W. Aldrich
Keyword(s):  
Steady State ◽  
Quaternary Ammonium ◽  
Bk Channels ◽  
Bk Channel ◽  
Fold Change ◽  
Time Dependent ◽  
Kinetic Measurements ◽  
State Dependent ◽  
Channel Opening ◽  
High Concentrations

Intracellular blockade by quaternary ammonium (QA) molecules of many potassium channels is state dependent, where the requirement for channel opening is evidenced by a time-dependent component of block in the macroscopic record. Whether this is the case for Ca2+- and voltage-activated potassium (BK) channels, however, remains unclear. Previous work (Li, W., and R.W. Aldrich. 2004. J. Gen. Physiol. 124:43–57) tentatively proposed a state-dependent, trapping model, but left open the possibility of state-independent block. Here, we found BK channel blockade by a novel QA derivative, bbTBA, was time dependent, raising the possibility of state-dependent, open channel block. Alternatively, the observed voltage dependence of block could be sufficient to explain time-dependent block. We have used steady-state and kinetic measurements of bbTBA blockade in order to discriminate between these two possibilities. bbTBA did not significantly slow deactivation kinetics at potentials between −200 and −100 mV, suggesting that channels can close unhindered by bound bbTBA. We further find no evidence that bbTBA is trapped inside BK channels after closing. Measurements of steady state fractional block at +40 mV revealed a 1.3-fold change in apparent affinity for a 33-fold change in Po, in striking contrast to the 31-fold change predicted by state-dependent block. Finally, the appearance of a third kinetic component of bbTBA blockade at high concentrations is incompatible with state-dependent block. Our results suggest that access of intracellular bbTBA to the BK channel cavity is not strictly gated by channel opening and closing, and imply that the permeation gate for BK channels may not be intracellular.

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