MM1 simulation in Excel

[@khalidisa1190]

Where did u get the value of lambda n mu?

[@dralbertomarquez]

This is just an example. I decided on those parameters just because. No particular reason. The model is not representing any particular real-life situation. It is just a demonstration of how discrete event simulation works.

[@vmehdi]

Hi. If lambda > mu, then the waiting time increases constantly. Am I right? So what should we change to show the Little's Law?

[@dralbertomarquez]

I do not understand your question. Your question sounds to me like "Since the salsa needs tomatoes, why the keys are in the drawer?"

[@akhilmnair9155]

Sir. I have a small dought. Why we used both exponential distributions as in M/M/1 model arrival follows Poisson distribution

[@dralbertomarquez]

The exponential distribution and the Poisson distribution are 2 sides of the same phenomena. In nature there are certain processes that are memoryless or we prefer to model as memoryless. In the case of queueing theory, a memoryless process of arrival would mean the current arrival does not depend on how much time has passed since the previous arrival. Similarly, a memoryless process time will not depend on when the previous process has concluded. That means the time between arrivals is exponential (the exponential distribution is the only distribution with memoryless property) and the processing time is exponential too. We prefer to use exponential distributions in the introductory queueing models to keep the variable time out of the equations. In other words, the computation of the solutions for the M/M/1 produces relatively simple (mathematically tractable) solutions if we use a memoryless probability distribution. So if you measure the probability of how much time has elapsed between client arrivals as an exponential distribution, you could compute the probability of having exactly zero arrivals, one arrival, two arrivals, etc. using that exponential distribution. However, that would involve several computations and the convolution of the probabilities. Instead of doing that, when a process has the time separating events being exponentially distributed, the probability of the counting process of the events for a given amount of time can be computed using a Poisson distribution. So if you want to estimate the probability of the number of events use Poisson. If you want to compute the probability of how much time is between such events in the process, use exponential distribution.

[@guscilikhendi8712]

@@dralbertomarquez can we apply for M/G/1 ? I am new to this subject, Sorry for the silly question.

[@dralbertomarquez]

Yes, you would have to know which distribution to use in for the processing time, other than exponential distribution.

[@duyhai2508]

Really appreciate this video, but how about the M/M/2 stimulation, how can we run that

[@dralbertomarquez]

I don't know. I have not thought about it. May be with a counter, of available servers.

[@yufandu815]

Sir, how to simulate if lamda is not constant(nonhomogeneous poisson process)?

[@dralbertomarquez]

You can change the parameter dynamically in the simulation. So in principle you could have an exponential likelyhood of time between arrivals, that changes the lamba over time.

[@berfingulmus3321]

Hi professor ı have question about this example, ı have similar homework and ı have to find a number of waiting customer in the queue. Can someone help me to find waiting people numbers in the queue?

[@dralbertomarquez]

The number in queue is a time-based statistics. Here is a video on how to do it: kzbin.info/www/bejne/gpXVdoylnrOZjLM

[@centreforuniversity-indust9506]

can i know how the data spread for this project?

[@dralbertomarquez]

I think your English needs some polishing maybe? I am not clear what your question is.

[@guscilikhendi8712]

can we apply for M/G/1 ? I am new to this subject, Sorry for the silly question.

[@dralbertomarquez]

Yes. The selection of the transformation is based on an exponential distribution. You can in principle use any distribution for the time it takes to be served (G) in the M/G/1. You just need to generate random service times that follow your desired G distribution.

[@mohamedeljattari2821]

Hi, sir. Is it possible to download this excel file?

[@dralbertomarquez]

You can build it in 10 minutes. Why would you want to download it when the value is in the making?

[@wecarebybitsnbytes8506]

The waiting time is in minutes or hours?

[@dralbertomarquez]

It doesn't really matter. If the interarrival time is minutes, waiting times will be minutes. If interarrival time is hours, then waiting time will be hours. You are just adding time in the units you are manipulating.

[@sshirr]

you're a boss

[@dralbertomarquez]

Thank you