scholarly journals Time to Critical Condition in Emergency Services

2021 ◽  
Vol 26 (4) ◽  
pp. 70
Author(s):  
Pedro A. Pury
Keyword(s):  
Critical Condition ◽  
Emergency Services ◽  
Performance Indicator ◽  
First Passage Time ◽  
Analytical Formula ◽  
Practical Interest ◽  
Passage Time ◽  
Analytical Expression ◽  
Parallel Servers ◽  
Incoming Call

Providing uninterrupted response service is of paramount importance for emergency medical services, regardless of the operating scenario. Thus, reliable estimates of the time to the critical condition, under which there will be no available servers to respond to the next incoming call, become very useful measures of the system’s performance. In this contribution, we develop a key performance indicator by providing an explicit formula for the average time to the shortage condition. Our analytical expression for this average time is a function of the number of parallel servers and the inter-arrival and service times. We assume exponential distributions of times in our analytical expression, but for evaluating the mean first-passage time to the critical condition under more realistic scenarios, we validate our result through exhaustive simulations with lognormal service time distributions. For this task, we have implemented a simulator in R. Our results indicate that our analytical formula is an acceptable approximation under any situation of practical interest.

scholarly journals The Protein Hourglass: Exact First Passage Time Distributions for Protein Thresholds

2020 ◽  
Author(s):  
Krishna Rijal ◽  
Ashok Prasad ◽  
Dibyendu Das
Keyword(s):  
First Passage Time ◽  
Self Regulation ◽  
Threshold Value ◽  
Passage Time ◽  
First Passage Times ◽  
Lambda Phage ◽  
First Passage ◽  
Analytical Expression ◽  
Protein Levels ◽  
Passage Times

Protein thresholds have been shown to act as an ancient timekeeping device, such as in the time to lysis of E. coli infected with bacteriophage lambda. The time taken for protein levels to reach a particular threshold for the first time is defined as the first passage time of the protein synthesis system, which is a stochastic quantity. The first few moments of the distribution of first passage times were known earlier, but an analytical expression for the full distribution was not available. In this work, we derive an analytical expression for the first passage times for a long-lived protein. This expression allows us to calculate the full distribution not only for cases of no self-regulation, but also for both positive and negative self-regulation of the threshold protein. We show that the shape of the distribution matches previous experimental data on lambda-phage lysis time distributions. We also provide analytical expressions for the FPT distribution with non-zero degradation in Laplace space. Furthermore, we study the noise in the precision of the first passage times described by coefficient of variation (CV) of the distribution as a function of the protein threshold value. We show that under conditions of positive self-regulation, the CV declines monotonically with increasing protein threshold, while under conditions of linear negative self-regulation, there is an optimal protein threshold that minimizes the noise in the first passage times.

FIRST-ORDER NETWORK COHERENCE AND EIGENTIME IDENTITY ON THE WEIGHTED CAYLEY NETWORKS

Fractals ◽  
2017 ◽  
Vol 25 (05) ◽  
pp. 1750049 ◽  
Author(s):  
MEIFENG DAI ◽  
XIAOQIAN WANG ◽  
YUE ZONG ◽  
JIAHUI ZOU ◽  
YUFEI CHEN ◽  
...  
Keyword(s):  
First Passage Time ◽  
Analytical Formula ◽  
Passage Time ◽  
Small Degree ◽  
Network Size ◽  
Mean First Passage Time ◽  
Weight Factor ◽  
First Passage ◽  
First Order ◽  
Definition Of

In this paper, we first study the first-order network coherence, characterized by the entire mean first-passage time (EMFPT) for weight-dependent walk, on the weighted Cayley networks with the weight factor. The analytical formula of the EMFPT is obtained by the definition of the EMFPT. The obtained results show that the scalings of first-order coherence with network size obey four laws along with the range of the weight factor. Then, we study eigentime identity quantifying as the sum of reciprocals of all nonzero normalized Laplacian eigenvalues on the weighted Cayley networks with the weight factor. We show that all their eigenvalues can be obtained by calculating the roots of several small-degree polynomials defined recursively. The obtained results show that the scalings of the eigentime identity on the weighted Cayley networks obey two laws along with the range of the weight factor.

scholarly journals On the Probabilities of Correlated Defaults: a First Passage Time Approach

2008 ◽  
Vol 13 (1) ◽  
pp. 117-133 ◽  
Author(s):  
M. Valužis
Keyword(s):  
Brownian Motion ◽  
Credit Risk ◽  
First Passage Time ◽  
Joint Probability ◽  
Passage Time ◽  
Geometric Brownian Motion ◽  
First Passage ◽  
Analytical Expression ◽  
Exact Analytical Expression ◽  
Correlated Defaults

This article investigates the joint probability of correlated defaults in the first passage time approach of credit risk subject to condition that the underlying firms’ assets values and the default boundaries follow geometric Brownian motion processes. The exact analytical expression of joint probability of two correlated defaults in the case of stochastic default boundaries is presented. Also, some properties of this solution are provided.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap
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