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PROFESSOR: All right, so today we're returning to simulations. And I'm going to do at first, a little bit more abstractly, and then come back to some details. So they're different ways to classify simulation models. The first is whether it's stochastic or deterministic. And the difference here is in a deterministic simulation, you should get the same result every time you run it. And there's a lot of uses we'll see for deterministic simulations. And then there's stochastic simulations, where the answer will differ from run to run because there's an element of randomness in it. So here if you run it again and again you get the same outcome every time, here you may not. So, for example, the problem set that's due today — is that a stochastic or deterministic simulation? Somebody? Stochastic, exactly. And that's what we're going to focus on in this class, because one of the interesting questions we'll see about stochastic simulations is, how often do have to run them before you believe the answer? And that turns out to be a very important issue. You run it once, you get an answer, you can't take it to the bank. Because the next time you run it, you may get a completely different answer. So that will get us a little bit into the whole issue of statistical analysis.

Another interesting dichotomy is static vs dynamic. We'll look at both, but will spend more time on dynamic models. So the issue — it's not my phone. If it's your mother, you could feel free to take it, otherwise — OK, no problem. Inevitable. In a dynamic situation, time plays a role. And you look at how things evolve over time. In a static simulation, there is no issue with time. We'll be looking at both, but most of the time we'll be focusing on dynamic ones. So an example of this kind of thing would be a queuing network model. This is one of the most popular and important kinds of dynamic simulations. Where you try and look at how queues, a fancy word for lines, evolve over time. So for example, people who are trying to decide how many lanes should be in a highway, or how far apart the exits should be, or what should the ratio of Fast Lane tolls to manually staffed tolls should be. All use queuing networks to try and answer that question. And we'll look at some examples of these later because they are very important. Particularly for things related to scheduling and planning.

A third dichotomy is discrete vs continuous. Imagine, for example, trying to analyze the flow of traffic along the highway. One way to do it, is to try and have a simulation which models each vehicle. That would be a discrete simulation, because you've got different parts. Alternatively, you might decide to treat traffic as a flow, kind of like water flowing through things, where changes in the flow can be described by differential equations. That would lead to a continuous model. Another example is, a lot of effort has gone into analyzing the way blood flows through the human body. You can try and model it discretely, where you take each red blood cell, each white blood cell, and look at how they move, or simulate how they move.

PROFESSOR: All right, so today we're returning to simulations. And I'm going to do at first, a little bit more abstractly, and then come back to some details. So they're different ways to classify simulation models. The first is whether it's stochastic or deterministic. And the difference here is in a deterministic simulation, you should get the same result every time you run it. And there's a lot of uses we'll see for deterministic simulations. And then there's stochastic simulations, where the answer will differ from run to run because there's an element of randomness in it. So here if you run it again and again you get the same outcome every time, here you may not. So, for example, the problem set that's due today — is that a stochastic or deterministic simulation? Somebody? Stochastic, exactly. And that's what we're going to focus on in this class, because one of the interesting questions we'll see about stochastic simulations is, how often do have to run them before you believe the answer? And that turns out to be a very important issue. You run it once, you get an answer, you can't take it to the bank. Because the next time you run it, you may get a completely different answer. So that will get us a little bit into the whole issue of statistical analysis.

Another interesting dichotomy is static vs dynamic. We'll look at both, but will spend more time on dynamic models. So the issue — it's not my phone. If it's your mother, you could feel free to take it, otherwise — OK, no problem. Inevitable. In a dynamic situation, time plays a role. And you look at how things evolve over time. In a static simulation, there is no issue with time. We'll be looking at both, but most of the time we'll be focusing on dynamic ones. So an example of this kind of thing would be a queuing network model. This is one of the most popular and important kinds of dynamic simulations. Where you try and look at how queues, a fancy word for lines, evolve over time. So for example, people who are trying to decide how many lanes should be in a highway, or how far apart the exits should be, or what should the ratio of Fast Lane tolls to manually staffed tolls should be. All use queuing networks to try and answer that question. And we'll look at some examples of these later because they are very important. Particularly for things related to scheduling and planning.

A third dichotomy is discrete vs continuous. Imagine, for example, trying to analyze the flow of traffic along the highway. One way to do it, is to try and have a simulation which models each vehicle. That would be a discrete simulation, because you've got different parts. Alternatively, you might decide to treat traffic as a flow, kind of like water flowing through things, where changes in the flow can be described by differential equations. That would lead to a continuous model. Another example is, a lot of effort has gone into analyzing the way blood flows through the human body. You can try and model it discretely, where you take each red blood cell, each white blood cell, and look at how they move, or simulate how they move.

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