I am modeling the patient arrival rates during a mass casualty event and as we all know, they are time dependent and not constant. I am trying to use gamma distribution to model the arrival process. I am aware that gamma distribution is characterized by two parameters namely the shape and the scale parameter. Now during a disaster situation, the patients arriving to the hospital usually arrive in two waves, the first wave arrives within 5-30 minutes from the time the event occurs and the second wave after 30 mins may be. Following are my questions:
1. Relationship between the gamma parameters keeping in mind the arrival rate. How will the two parameters impact the arrival rate and pattern?
2. How can I find the gamma parameters that would give the above said delay times?
3. I want to model the arrival as gamma distribution over a time horizon with the time horizon divided into several small time intervals and within each of the small time intervals the arrival rate follows an exponential distribution. How do I model this in the simulation model designed by me. I need what way should I specify the same in the create block to which represents arrivals in my model.
> I am modeling the patient arrival rates during a mass casualty event > and as we all know, they are time dependent and not constant. I am > trying to use gamma distribution to model the arrival process. I am > aware that gamma distribution is characterized by two parameters > namely the shape and the scale parameter. Now during a disaster > situation, the patients arriving to the hospital usually arrive in two > waves, the first wave arrives within 5-30 minutes from the time the > event occurs and the second wave after 30 mins may be. Following are > my questions:
> 1. Relationship between the gamma parameters keeping in mind the > arrival rate. How will the two parameters impact the arrival rate and > pattern?
> 2. How can I find the gamma parameters that would give the above said > delay times?
> 3. I want to model the arrival as gamma distribution over a time > horizon with the time horizon divided into several small time > intervals and within each of the small time intervals the arrival rate > follows an exponential distribution. How do I model this in the > simulation model designed by me. I need what way should I specify the > same in the create block to which represents arrivals in my model.
> Thanks a lot. > Amita.
You are giving yourself a headache by using a Gamma distribution because you'll have a tough time explaining what the parameters mean to your customer. Better to select a 1 parameter distribution that has the approximate shape of the Gamma you have in mind. That should be good enough since you are only approximating arrivals.
For each arrival slug you have 2 random variables, the total number of patients and their arrival pattern. You could generate your patient count at sim start from 1 distribution and dump them into a queue. E.g. the number of total patients over the 25 minute period is N(1000, 250) or something.
Then you will need realizations of an arrival pdf as an order statistic to ping the patient queue and inject the patients into the system. So say the time dependent arrival pattern over 25 minutes is lognormally distributed (14, 11) or whatever. I'd have to think about this. But after you generate the n patients, you would generate n arrival times and then sort those. Then use the arrival times to ping the the patient queue.
Replay the same process for slug 2 with different parameters. This assumes of course that the # of patients and their arrival patterns are not correlated.
Without knowing what sim package you use, I can't tell you the actual mechanics of the model design.
> On Aug 4, 8:42 pm, Jiggy <joshiamit...@gmail.com> wrote:
> > Hello Everyone,
> > I am modeling the patient arrival rates during a mass casualty event > > and as we all know, they are time dependent and not constant. I am > > trying to use gamma distribution to model the arrival process. I am > > aware that gamma distribution is characterized by two parameters > > namely the shape and the scale parameter. Now during a disaster > > situation, the patients arriving to the hospital usually arrive in two > > waves, the first wave arrives within 5-30 minutes from the time the > > event occurs and the second wave after 30 mins may be. Following are > > my questions:
> > 1. Relationship between the gamma parameters keeping in mind the > > arrival rate. How will the two parameters impact the arrival rate and > > pattern?
> > 2. How can I find the gamma parameters that would give the above said > > delay times?
> > 3. I want to model the arrival as gamma distribution over a time > > horizon with the time horizon divided into several small time > > intervals and within each of the small time intervals the arrival rate > > follows an exponential distribution. How do I model this in the > > simulation model designed by me. I need what way should I specify the > > same in the create block to which represents arrivals in my model.
> > Thanks a lot. > > Amita.
> You are giving yourself a headache by using a Gamma distribution > because you'll have a tough time explaining what the parameters mean > to your customer. Better to select a 1 parameter distribution that > has the approximate shape of the Gamma you have in mind. That should > be good enough since you are only approximating arrivals.
> For each arrival slug you have 2 random variables, the total number of > patients and their arrival pattern. You could generate your patient > count at sim start from 1 distribution and dump them into a queue. > E.g. the number of total patients over the 25 minute period is N(1000, > 250) or something.
> Then you will need realizations of an arrival pdf as an order > statistic to ping the patient queue and inject the patients into the > system. So say the time dependent arrival pattern over 25 minutes is > lognormally distributed (14, 11) or whatever. I'd have to think about > this. But after you generate the n patients, you would generate n > arrival times and then sort those. Then use the arrival times to ping > the the patient queue.
> Replay the same process for slug 2 with different parameters. This > assumes of course that the # of patients and their arrival patterns > are not correlated.
> Without knowing what sim package you use, I can't tell you the actual > mechanics of the model design.
> SteveM
Thank you so much for your reply....I am using ARENA 10.0 to model this....it would be great if you can explain me to do this giving an example... :) . Shall wait for your nxt reply.
> > On Aug 4, 8:42 pm, Jiggy <joshiamit...@gmail.com> wrote:
> > > Hello Everyone,
> > > I am modeling the patient arrival rates during a mass casualty event > > > and as we all know, they are time dependent and not constant. I am > > > trying to use gamma distribution to model the arrival process. I am > > > aware that gamma distribution is characterized by two parameters > > > namely the shape and the scale parameter. Now during a disaster > > > situation, the patients arriving to the hospital usually arrive in two > > > waves, the first wave arrives within 5-30 minutes from the time the > > > event occurs and the second wave after 30 mins may be. Following are > > > my questions:
> > > 1. Relationship between the gamma parameters keeping in mind the > > > arrival rate. How will the two parameters impact the arrival rate and > > > pattern?
> > > 2. How can I find the gamma parameters that would give the above said > > > delay times?
> > > 3. I want to model the arrival as gamma distribution over a time > > > horizon with the time horizon divided into several small time > > > intervals and within each of the small time intervals the arrival rate > > > follows an exponential distribution. How do I model this in the > > > simulation model designed by me. I need what way should I specify the > > > same in the create block to which represents arrivals in my model.
> > > Thanks a lot. > > > Amita.
> > You are giving yourself a headache by using a Gamma distribution > > because you'll have a tough time explaining what the parameters mean > > to your customer. Better to select a 1 parameter distribution that > > has the approximate shape of the Gamma you have in mind. That should > > be good enough since you are only approximating arrivals.
> > For each arrival slug you have 2 random variables, the total number of > > patients and their arrival pattern. You could generate your patient > > count at sim start from 1 distribution and dump them into a queue. > > E.g. the number of total patients over the 25 minute period is N(1000, > > 250) or something.
> > Then you will need realizations of an arrival pdf as an order > > statistic to ping the patient queue and inject the patients into the > > system. So say the time dependent arrival pattern over 25 minutes is > > lognormally distributed (14, 11) or whatever. I'd have to think about > > this. But after you generate the n patients, you would generate n > > arrival times and then sort those. Then use the arrival times to ping > > the the patient queue.
> > Replay the same process for slug 2 with different parameters. This > > assumes of course that the # of patients and their arrival patterns > > are not correlated.
> > Without knowing what sim package you use, I can't tell you the actual > > mechanics of the model design.
> > SteveM
> Thank you so much for your reply....I am using ARENA 10.0 to model > this....it would be great if you can explain me to do this giving an > example... :) . Shall wait for your nxt reply.
Sorry. Can't help you there. I use Extend not Arena.
> > > On Aug 4, 8:42 pm, Jiggy <joshiamit...@gmail.com> wrote:
> > > > Hello Everyone,
> > > > I am modeling the patient arrival rates during a mass casualty event > > > > and as we all know, they are time dependent and not constant. I am > > > > trying to use gamma distribution to model the arrival process. I am > > > > aware that gamma distribution is characterized by two parameters > > > > namely the shape and the scale parameter. Now during a disaster > > > > situation, the patients arriving to the hospital usually arrive in two > > > > waves, the first wave arrives within 5-30 minutes from the time the > > > > event occurs and the second wave after 30 mins may be. Following are > > > > my questions:
> > > > 1. Relationship between the gamma parameters keeping in mind the > > > > arrival rate. How will the two parameters impact the arrival rate and > > > > pattern?
> > > > 2. How can I find the gamma parameters that would give the above said > > > > delay times?
> > > > 3. I want to model the arrival as gamma distribution over a time > > > > horizon with the time horizon divided into several small time > > > > intervals and within each of the small time intervals the arrival rate > > > > follows an exponential distribution. How do I model this in the > > > > simulation model designed by me. I need what way should I specify the > > > > same in the create block to which represents arrivals in my model.
> > > > Thanks a lot. > > > > Amita.
> > > You are giving yourself a headache by using a Gamma distribution > > > because you'll have a tough time explaining what the parameters mean > > > to your customer. Better to select a 1 parameter distribution that > > > has the approximate shape of the Gamma you have in mind. That should > > > be good enough since you are only approximating arrivals.
> > > For each arrival slug you have 2 random variables, the total number of > > > patients and their arrival pattern. You could generate your patient > > > count at sim start from 1 distribution and dump them into a queue. > > > E.g. the number of total patients over the 25 minute period is N(1000, > > > 250) or something.
> > > Then you will need realizations of an arrival pdf as an order > > > statistic to ping the patient queue and inject the patients into the > > > system. So say the time dependent arrival pattern over 25 minutes is > > > lognormally distributed (14, 11) or whatever. I'd have to think about > > > this. But after you generate the n patients, you would generate n > > > arrival times and then sort those. Then use the arrival times to ping > > > the the patient queue.
> > > Replay the same process for slug 2 with different parameters. This > > > assumes of course that the # of patients and their arrival patterns > > > are not correlated.
> > > Without knowing what sim package you use, I can't tell you the actual > > > mechanics of the model design.
> > > SteveM
> > Thank you so much for your reply....I am using ARENA 10.0 to model > > this....it would be great if you can explain me to do this giving an > > example... :) . Shall wait for your nxt reply.
> Sorry. Can't help you there. I use Extend not Arena.
> Good Luck,
> SteveM
Hey no problem. Thanks a lot for your reply though :)
> I am modeling the patient arrival rates during a mass casualty event > and as we all know, they are time dependent and not constant. I am > trying to use gamma distribution to model the arrival process. I am > aware that gamma distribution is characterized by two parameters > namely the shape and the scale parameter. Now during a disaster > situation, the patients arriving to the hospital usually arrive in two > waves, the first wave arrives within 5-30 minutes from the time the > event occurs and the second wave after 30 mins may be. Following are > my questions:
> 1. Relationship between the gamma parameters keeping in mind the > arrival rate. How will the two parameters impact the arrival rate and > pattern?
> 2. How can I find the gamma parameters that would give the above said > delay times?
> 3. I want to model the arrival as gamma distribution over a time > horizon with the time horizon divided into several small time > intervals and within each of the small time intervals the arrival rate > follows an exponential distribution. How do I model this in the > simulation model designed by me. I need what way should I specify the > same in the create block to which represents arrivals in my model.
> Thanks a lot. > Amita.
I agree with sbma...@gmail.com; do you really have a strong reason to use the gamma?...
I think it is the a similar idea to sbma...@gmail.com's, but I believe you should separate the number of patients from their arrival times. I also understand the two arrival waves are independent, so you can just do the same thing twice starting at different times.
My fisrt idea would look something like building a histogram backwards. First, generate the total number of patients that will arrive in, say, the first wave (repeat for the second) and how long this wave will last. Then divide the lenght of the wave in as many intervals as you see fit (you can randomise this amount if you like). The next step is to take the area under the distribution you are using in each interval (sorry I can't help you with choosing the gamma parametres... – but see below) and multiply it by the total number of arrivals; this will give you the number of arrivals in each interval. I have absolutely no idea how to do this in Arena and even if it can be done, you'll have to mind the rounding problems (unless you can have fractional patients arriving – pardon the dark humour ¦¬) ). With the number of arrivals of each interval, you can use the Exponential distribution (as you propoused) to find the intervals; this should be straight foward now.
HTH and tell me if you need clarification, I'm in a bit of a hurry right now,
DB Fuller
PS: Just checked a software I have here; if you can tell me explicitly three things: mean, std. deviation and skewness, I can tell you alpha and beta for the gamma distribution.
> On 4 ago, 21:42, Jiggy <joshiamit...@gmail.com> wrote:
> > Hello Everyone,
> > I am modeling the patient arrival rates during a mass casualty event > > and as we all know, they are time dependent and not constant. I am > > trying to use gamma distribution to model the arrival process. I am > > aware that gamma distribution is characterized by two parameters > > namely the shape and the scale parameter. Now during a disaster > > situation, the patients arriving to the hospital usually arrive in two > > waves, the first wave arrives within 5-30 minutes from the time the > > event occurs and the second wave after 30 mins may be. Following are > > my questions:
> > 1. Relationship between the gamma parameters keeping in mind the > > arrival rate. How will the two parameters impact the arrival rate and > > pattern?
> > 2. How can I find the gamma parameters that would give the above said > > delay times?
> > 3. I want to model the arrival as gamma distribution over a time > > horizon with the time horizon divided into several small time > > intervals and within each of the small time intervals the arrival rate > > follows an exponential distribution. How do I model this in the > > simulation model designed by me. I need what way should I specify the > > same in the create block to which represents arrivals in my model.
> > Thanks a lot. > > Amita.
> I agree with sbma...@gmail.com; do you really have a strong reason to > use the gamma?...
> I think it is the a similar idea to sbma...@gmail.com's, but I believe > you should separate the number of patients from their arrival times. I > also understand the two arrival waves are independent, so you can just > do the same thing twice starting at different times.
> My fisrt idea would look something like building a histogram > backwards. First, generate the total number of patients that will > arrive in, say, the first wave (repeat for the second) and how long > this wave will last. Then divide the lenght of the wave in as many > intervals as you see fit (you can randomise this amount if you like). > The next step is to take the area under the distribution you are using > in each interval (sorry I can't help you with choosing the gamma > parametres... – but see below) and multiply it by the total number of > arrivals; this will give you the number of arrivals in each interval. > I have absolutely no idea how to do this in Arena and even if it can > be done, you'll have to mind the rounding problems (unless you can > have fractional patients arriving – pardon the dark humour ¦¬) ). With > the number of arrivals of each interval, you can use the Exponential > distribution (as you propoused) to find the intervals; this should be > straight foward now.
> HTH and tell me if you need clarification, I'm in a bit of a hurry > right now,
> DB Fuller
> PS: Just checked a software I have here; if you can tell me explicitly > three things: mean, std. deviation and skewness, I can tell you alpha > and beta for the gamma distribution.
Thanks for the reply, I am using Gamma distribution as it gives flexibility for choosing the shape of the distribution and also it is found to be used commonly to model the non homogeneous poisson process. The arrivals are going to be exponential in nature with a mean lamda. but lamda follows a gamma distribution with parameters alpha and beta...so my experiment is going to be that I will allow 400 victims in the system, and try to perform an analysis by changing the arrival pattern and see which of the arrivals are sensitive on the system performance..so in this case, the number of victims is fixed, the rate at which I inject them (as steve mentioned) is what I need to analyze. It would be great if you can make me understand this by giving an hypothetical example. Also, you said that if I give you mean , std deviation and Skewness, you can tell me gamma parameters, but unfortunately I do not have data to obtain teh same.
> On Aug 6, 7:10 am, DB Fuller <fulle...@gmail.com> wrote:
> > On 4 ago, 21:42, Jiggy <joshiamit...@gmail.com> wrote:
> > > Hello Everyone,
> > > I am modeling the patient arrival rates during a mass casualty event > > > and as we all know, they are time dependent and not constant. I am > > > trying to use gamma distribution to model the arrival process. I am > > > aware that gamma distribution is characterized by two parameters > > > namely the shape and the scale parameter. Now during a disaster > > > situation, the patients arriving to the hospital usually arrive in two > > > waves, the first wave arrives within 5-30 minutes from the time the > > > event occurs and the second wave after 30 mins may be. Following are > > > my questions:
> > > 1. Relationship between the gamma parameters keeping in mind the > > > arrival rate. How will the two parameters impact the arrival rate and > > > pattern?
> > > 2. How can I find the gamma parameters that would give the above said > > > delay times?
> > > 3. I want to model the arrival as gamma distribution over a time > > > horizon with the time horizon divided into several small time > > > intervals and within each of the small time intervals the arrival rate > > > follows an exponential distribution. How do I model this in the > > > simulation model designed by me. I need what way should I specify the > > > same in the create block to which represents arrivals in my model.
> > > Thanks a lot. > > > Amita.
> > I agree with sbma...@gmail.com; do you really have a strong reason to > > use the gamma?...
> > I think it is the a similar idea to sbma...@gmail.com's, but I believe > > you should separate the number of patients from their arrival times. I > > also understand the two arrival waves are independent, so you can just > > do the same thing twice starting at different times.
> > My fisrt idea would look something like building a histogram > > backwards. First, generate the total number of patients that will > > arrive in, say, the first wave (repeat for the second) and how long > > this wave will last. Then divide the lenght of the wave in as many > > intervals as you see fit (you can randomise this amount if you like). > > The next step is to take the area under the distribution you are using > > in each interval (sorry I can't help you with choosing the gamma > > parametres... – but see below) and multiply it by the total number of > > arrivals; this will give you the number of arrivals in each interval. > > I have absolutely no idea how to do this in Arena and even if it can > > be done, you'll have to mind the rounding problems (unless you can > > have fractional patients arriving – pardon the dark humour ¦¬) ). With > > the number of arrivals of each interval, you can use the Exponential > > distribution (as you propoused) to find the intervals; this should be > > straight foward now.
> > HTH and tell me if you need clarification, I'm in a bit of a hurry > > right now,
> > DB Fuller
> > PS: Just checked a software I have here; if you can tell me explicitly > > three things: mean, std. deviation and skewness, I can tell you alpha > > and beta for the gamma distribution.
> Thanks for the reply, I am using Gamma distribution as it gives > flexibility for choosing the shape of the distribution and also it is > found to be used commonly to model the non homogeneous poisson > process. The arrivals are going to be exponential in nature with a > mean lamda. but lamda follows a gamma distribution with parameters > alpha and beta...so my experiment is going to be that I will allow 400 > victims in the system, and try to perform an analysis by changing the > arrival pattern and see which of the arrivals are sensitive on the > system performance..so in this case, the number of victims is fixed, > the rate at which I inject them (as steve mentioned) is what I need to > analyze. It would be great if you can make me understand this by > giving an hypothetical example. Also, you said that if I give you > mean , std deviation and Skewness, you can tell me gamma parameters, > but unfortunately I do not have data to obtain teh same.
> Thanks. > Amita.
I need to know how the arrival rate, shape parameter and scale parameter are related and how do i specify it as an expression in create block. I was thinking that it should be specified as EXPO (GAMMA (shape, scale)).I want to know, depending upon the arrival rate that I decided, can I get the values of shape and scale???
> On Aug 6, 5:09 pm, Jiggy <joshiamit...@gmail.com> wrote:
> > On Aug 6, 7:10 am, DB Fuller <fulle...@gmail.com> wrote:
> > > On 4 ago, 21:42, Jiggy <joshiamit...@gmail.com> wrote:
> > > > Hello Everyone,
> > > > I am modeling the patient arrival rates during a mass casualty event > > > > and as we all know, they are time dependent and not constant. I am > > > > trying to use gamma distribution to model the arrival process. I am > > > > aware that gamma distribution is characterized by two parameters > > > > namely the shape and the scale parameter. Now during a disaster > > > > situation, the patients arriving to the hospital usually arrive in two > > > > waves, the first wave arrives within 5-30 minutes from the time the > > > > event occurs and the second wave after 30 mins may be. Following are > > > > my questions:
> > > > 1. Relationship between the gamma parameters keeping in mind the > > > > arrival rate. How will the two parameters impact the arrival rate and > > > > pattern?
> > > > 2. How can I find the gamma parameters that would give the above said > > > > delay times?
> > > > 3. I want to model the arrival as gamma distribution over a time > > > > horizon with the time horizon divided into several small time > > > > intervals and within each of the small time intervals the arrival rate > > > > follows an exponential distribution. How do I model this in the > > > > simulation model designed by me. I need what way should I specify the &
