Coxian distribution

2011 ◽  
Keyword(s):  
Coxian Distribution

scholarly journals Some results on optimal stopping under phase-type distributed implementation delay

2020 ◽  
Vol 91 (3) ◽  
pp. 559-583
Author(s):  
Jukka Lempa
Keyword(s):  
General Result ◽  
Optimal Stopping ◽  
Waiting Period ◽  
Coxian Distribution ◽  
Diffusion Dynamics ◽  
Phase Type ◽  
Distributed Implementation ◽  
Implementation Delay ◽  
Scalar Diffusion ◽  
Strong Markov

AbstractWe study optimal stopping of strong Markov processes under random implementation delay. By random implementation delay we mean the following: the payoff is not realised immediately when the process is stopped but rather after a random waiting period. The distribution of the random waiting period is assumed to be phase-type. We prove first a general result on the solvability of the problem. Then we study the case of Coxian distribution both in general and with scalar diffusion dynamics in more detail. The study is concluded with two explicit examples.

Modelling a Bathtub-Shaped Failure Rate by a Coxian Distribution

2016 ◽  
Vol 65 (2) ◽  
pp. 878-885 ◽  
Author(s):  
Qihong Duan ◽  
Junrong Liu
Keyword(s):  
Failure Rate ◽  
Coxian Distribution

scholarly journals Global stability of an SEIR epidemic model where empirical distribution of incubation period is approximated by Coxian distribution

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Sungchan Kim ◽  
Jong Hyuk Byun ◽  
Il Hyo Jung
Keyword(s):  
Global Stability ◽  
Incubation Period ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Empirical Distribution ◽  
Global Dynamics ◽  
Seir Model ◽  
Coxian Distribution ◽  
Using Data

AbstractIn this work, we have developed a Coxian-distributed SEIR model when incorporating an empirical incubation period. We show that the global dynamics are completely determined by a basic reproduction number. An application of the Coxian-distributed SEIR model using data of an empirical incubation period is explored. The model may be useful for resolving the realistic intrinsic parts in classical epidemic models since Coxian distribution approximately converges to any distribution.

Approximation of probability distribution functions by Coxian distribution to evaluate multimedia systems

2004 ◽  
Vol 35 (2) ◽  
pp. 16-24 ◽  
Author(s):  
Yukie Sasaki ◽  
Hiroei Imai ◽  
Masahiro Tsunoyama ◽  
Ikuo Ishii
Keyword(s):  
Probability Distribution ◽  
Distribution Functions ◽  
Multimedia Systems ◽  
Probability Distribution Functions ◽  
Coxian Distribution

scholarly journals On the value function of the M/Cox(r)/1 queue

2006 ◽  
Vol 43 (2) ◽  
pp. 363-376 ◽  
Author(s):  
Sandjai Bhulai
Keyword(s):  
Value Function ◽  
Queueing Systems ◽  
Single Step ◽  
Closed Form Expression ◽  
Single Server ◽  
Form Expression ◽  
Coxian Distribution ◽  
Optimal Value ◽  
Service Times ◽  
The Value Function

We consider a single-server queueing system at which customers arrive according to a Poisson process. The service times of the customers are independent and follow a Coxian distribution of order r. The system is subject to costs per unit time for holding a customer in the system. We give a closed-form expression for the average cost and the corresponding value function. The result can be used to derive nearly optimal policies in controlled queueing systems in which the service times are not necessarily Markovian, by performing a single step of policy iteration. We illustrate this in the model where a controller has to route to several single-server queues. Numerical experiments show that the improved policy has a close-to-optimal value.

scholarly journals On the value function of the M/Cox(r)/1 queue

2006 ◽  
Vol 43 (02) ◽  
pp. 363-376
Author(s):  
Sandjai Bhulai
Keyword(s):  
Value Function ◽  
Queueing Systems ◽  
Single Step ◽  
Closed Form Expression ◽  
Single Server ◽  
Form Expression ◽  
Coxian Distribution ◽  
Optimal Value ◽  
Service Times ◽  
The Value Function

We consider a single-server queueing system at which customers arrive according to a Poisson process. The service times of the customers are independent and follow a Coxian distribution of order r. The system is subject to costs per unit time for holding a customer in the system. We give a closed-form expression for the average cost and the corresponding value function. The result can be used to derive nearly optimal policies in controlled queueing systems in which the service times are not necessarily Markovian, by performing a single step of policy iteration. We illustrate this in the model where a controller has to route to several single-server queues. Numerical experiments show that the improved policy has a close-to-optimal value.

On the Three-Moment Approximation of a General Distribution by a Coxian Distribution

1988 ◽  
Vol 2 (2) ◽  
pp. 257-261 ◽  
Author(s):  
M. C. Van Der Heijden
Keyword(s):  
Coefficient Of Variation ◽  
Random Variable ◽  
Upper Bounds ◽  
General Distribution ◽  
Positive Random Variable ◽  
Lower And Upper Bounds ◽  
The Third ◽  
Coxian Distribution ◽  
Moment Approximation ◽  
Third Moment

The Coxian-2 distribution is a very useful distribution for queuing and reliability analysis. It is important to know when a general probability distribution can be approximated by a Coxian-2 distribution by fitting the first three moments. For a positive random variable with a squared coefficient of variation larger than 1, a lower bound on its third moment is known for which a three-moment fit exists. To complete the figure, in this note lower and upper bounds on the third moment are derived when the squared coefficient of variation is between 0.5 and 1. Also, we characterize the C2-distributions that correspond to these bounds.

Sign in / Sign up

Export Citation Format

Share Document