Discrete vs. continuous

[Jim Hines]

Gene Bellinger writes: "Is there a set of criteria one can employ to determine whether a discrete or a continuous simulation is most appropriate?" Im not exactly sure what you mean by "discrete simulation". If you mean discrete event simulation, then I have the following rather inadequate thought: In a corporate setting, if people are interested in a very detailed problem, (like where to place machines on a shop floor, or perhaps exactly how to route a particular peice of paper through the organization -- I start thinking its discrete event. If I dont see any real feedback issues, again discrete event. If people are interested in the usual probelms of discrete event simulations (waiting times, length of ques (O.K., length of lines)), discrete event. And the contrary also holds: Continuous when there is a higher-level problem, obvious feedback). On the other hand, I have one or two potential clients who have considered asking me to work on what seems to me to be an obviously dynamic issue best captured continuously, only to learn that they are also considering asking a discrete-event firm to work on the same problem. So, I dont know. It sounds like you work in both fields, so you might be one of the few people with broad enough experience to answer the question. Jim Hines jimhines@interserv.com

["fred nickols"]

Jim Hines writes that hes not exactly sure what is meant by discrete vs continuous when applied to modeling. He then offers up a couple of possible examples. On my part, I have no idea at all what those terms mean when applied to modeling. My rudimentary grasp of those two terms manifests itself in something akin to the contrast between direct current or "DC" and alternating current or "AC." Digital and analog carry similar meanings, although Ill readily admit that neither of the two instances just given are necessarily exemplary. So, could Gene Bellinger, who originally posed the question, I believe, provide an example of each so were all on the same wavelength? Thanks. fred nickols fnickols@ets.org

[CrbnBlu@aol.com]

irt: fnickols@ets.org (fred nickols), Wed, Apr 24, 1996 5:16 AM EST Fred suggested that I describe the difference between discrete & continuous simulation, so heres an attempt. As I understand it, the fundamental difference between discrete and continuous has to do with how the simulation schedules its run. A discrete event simulation schedules from event to event and simply skips the time between events. A continuous simulation considers clock time or step time as the event which is scheduled so it moves from step time to step time. And the step time is generally small enough so the simulation appears continuous with regard to the longer term events happening within the model. It would seem the only way to do real continuous simulations would be with an analog machine, and this used to be done but it was most expensive. The digital computer, which is essentialy a discrete event machine, is made to mimic analog by using a small step time. Does this help? Gene Bellinger CrbnBlu@aol.com

["David N. Ford"]

To help clarify the differences between discrete and continuous modeling I see two ways in which models can be considered either discrete or continuous. 1. Time Handling: If the simulation slices time into evenly sized pieces and calculates the system conditions at teach timestep it is continuous. System dynamics uses this method. In contrast, if the simulation calculates the system conditions only when an event occurs which will change the condition of the system is can be called a discrete event or next event simulation. 2. System change: If the simulation assumes and models changes in parameter values as smooth over time then the change is continuous. In contrast if the simualtion models parameter changes with significant jumps in a single timestep than the change can be considered discrete. In this case system dynamics is continuous. This description agrees with Dr. Forrester suggestion for formulating models in Industrial Dynamics (pg. 64) "...we suggest that the system be treated, at least initially, on the basis of continuous flows and interactions of the variables. Discreteness of events is entirely compatible with the concept of information-feedback systems, but we must be on guard against unnecessarily cluttering our formulation with the detail of discrete events that only obscure the momentum and continuity exhibited by our industrial systems." Dr. Forrester expands this distinction and provides a good example. I believe that this is the basis of the common admonition to beginning modelers to avoid IF-THEN statements in equation formulation. I believe the current discussion is about the second meaning above and not the first. But SD models do not always have to be continuous. As suggested by Dr. Forrester, discrete events can be included in SD models but should not be the focus or initial basis for those models. In other words, include with caution and careful thought. In my own work I have found that beginning with an assumption of continuous change made the relatively few places where discrete event formulation were appropriate very clear. Dr. David Ford, Associate Professor System Dynamics Program Department of Information Science University of Bergen Bergen, Norway David.Ford@ifi.uib.no

["fred nickols"]

Genes description of discrete vs continuous helps me understand what is being discussed. It also reminds me of the transition period in the Navy when we were shifting from analog to digital computers as the heart of our gun fire and missile systems. When the digital computers first came along, in the mid 1960s, we could use them to position missile launchers but we couldnt use them to control gun mounts. The reason was that you simply pointed the missile launcher in the general direction of the target and fired; you didnt have to track it because the missile either "rode" a beam or "homed in" using its own tracking system. The gun mount had to be in continuous motion as the fire control director tracked the target. The compute times for the digital computers back then were slow enough that incremental calculations, no matter how smooth you tried to make them, still had the undesirable effect of literally "jerking around" the gun mount. At 10 tons or so, and still manned in those days, a gun mount was something you didnt want to jerk around. Thanks for the explanation, Gene... fred nickols fnickols@ets.org

[Jim Hines]

Gene Bellinger in SD0046 briefly and lucidly contrasted discrete-event with continuous-time modeling. Gene, would you also agree that: All modeling approaches need to simplify. One of the key approaches in system dynamics modeling is to aggregate separate "elements" together (e.g. aggregate people into a workforce). What makes this approach workable is the key distinction between stocks and flows. In discrete-event modeling the simplification is that elements are not active all the time. This simplification is what allows the clock in these kinds of models to jump from one event to the next; nothing happens in between. The plus for system dynamics modelers is that we can more easily represent the fact that things are continually changing and influencing eachother. I think this probably helps with the representation of feedback. The plus for discrete-event modelers is that "they" can represent individual elements more easily. This helps with the representation of diversity within a population. Perhaps I should have used "continuous-time" modeling in place of "system dynamics" modeling? Jim Hines jimhines@interserv.com

[CrbnBlu@aol.com]

irt: david.ford@ifi.uib.no (David N. Ford), Thu, Apr 25, 1996 5:35 AM EST Your description of discrete & continuous from a Time Handling and System Change perspective adds a dimension I had not considered. My initial question was posed from a Time Handling perspective, and now I perceieve it as being relevant also from the System Change perspective. I will have to ponder this a while. thanks, Gene Bellinger CrbnBlu@aol.com

[CrbnBlu@aol.com]

irt: jimhines@interserv.com (Jim Hines), Thu, Apr 25, 1996 7:43 PM EST Yes, I would agree that all modeling needs to simplify. I continue to take, or use, the definition of a model as, "A simplification of reality intended to promote understanding." And I agree with your contrast between the pluses for discrete-event modeling and system dyanmics modeling. The point that continues to confuse me is when when I misinterpret the character of the environment with the character of the understanding desired. And Im trying to understand a way to stop doing this because it gets me in a real bind, meaing all the modeling work doesnt promote the understanding desired. I just posted a message that should be in todays set of messages that I thought I posted yesterday, but sent to the wrong address. This should add some clarification as to whats confusing me. thanks, Gene Bellinger CrbnBlu@aol.com

["Joel Rahn"]

On Thu, 25 Apr 1996 10:59:13 +0000, Jim Hines <jimhines@interserv.com> wrote: > >The plus for system dynamics modelers is that we can more easily >represent the fact that things are continually changing and >influencing eachother. I think this probably helps with the >representation of feedback. > My colleagues and many students (I am in an OR-Decision Sciences department) have a lot of trouble with the "continually changing" aspect of SD. They see things in terms of discrete decisions. I have always found it interesting that SD clearly emphasises the distinction between material and information flows and the sources of decisions, whereas no discrete simulation approach or package (that I am aware of) deals explicitly with either of these as part of model conceptualisation. On the topic, the four-point check mentioned by Gene(? - sorry if the credit is misplaced; my e-mail is so deficient I cant check it right now) sums up the criteria for deciding which approach to use pretty well. I tell my students that if they have to know what each item in a system is doing at any time, use a discrete, stochastic simulation; if they need only to deal with the overall flow of items, a continuous (SD) or fixed-time-advance (time-series) approach is best, and if they need to deal with the overall flow of items and decisions, SD is best. R. Joel Rahn Dipartement OSD Faculti des sciences de ladministration Universiti Laval Ste-Foy, Quibec G1K 7P4 CANADA til.: 418 656 7163 fax: 418 656 2624 e-mail: Joel.Rahn@fsa.ulaval.ca

[jimhines@interserv.com]

"The point that continues to confuse me is when when I misinterpret the character of the environment with the character of the understanding desired." You may be trying to express what confuses you, but your statement is clarifying for me: What determines the choice of SD vs. Discrete Event is the character of the understanding desired. Now, we need to get a little sharper on the character of the understanding that Discrete Event modeling produces. I said earlier that it has to do with variability within a population of entities. Im not sure about that, because people sometimes give results of discrete event simulations sometimes as just the mean (I think). So ... suggestions? Jim Hines jimhines@interserv.com

[jimhines@interserv.com]

On Fri, 26 Apr 96, "Joel Rahn" <rahnj@fsa.ulaval.ca> wrote in SD0069: I tell >my students that if they have to know what each item in a system is doing >at any time, use a discrete, stochastic simulation; if they need only to >deal with the overall flow of items, a continuous (SD) or >fixed-time-advance (time-series) approach is best, and if they need to deal >with the overall flow of items and decisions, SD is best. Joel: two questions 1) What is "fixed-time-advance" approach? 2) What about feedback as a criterion? When your students want to investigate feedback, does it matter whether they go SD or discrete? Jim Hines jimhines@interserv.com

["Joel Rahn"]

On Sun, 28 Apr 1996 20:03:33 -0700, jimhines@interserv.com <jimhines@interserv.com> wrote: >Joel: two questions >1) What is "fixed-time-advance" approach? It is the discrete time step approach beloved of econometricians and time series mavens. Their observable variables are generally aggregates or averages over a time period. >2) What about feedback as a criterion? When your students want to investigate >feedback, does it matter whether they go SD or discrete? Yes indeed. I should have added in the last sentence "...and decisions and feedback, SD is best". I guess I have internalized the idea that if you have flows of decisions, you generally have feedback (otherwise you are modeling irrational decision-making)... Hmmm, maybe that is why there are so few models of political processes, or why we usually dont deal with decision processes having a large component of irrationality. Why do I feel I have just stepped in a cow-pie of gargantuan dimension? R. Joel Rahn Dipartement OSD Faculti des sciences de ladministration Universiti Laval Ste-Foy, Quibec G1K 7P4 CANADA til.: 418 656 7163 fax: 418 656 2624 e-mail: Joel.Rahn@fsa.ulaval.ca

["Joel Rahn"]

On Sun, 28 Apr 1996 18:55:42 -0700, jimhines@interserv.com <jimhines@interserv.com> wrote: >for me: What determines the choice of SD vs. Discrete Event is the >character of the understanding desired.... So ... suggestions? Yes, the results of discrete event simulations are sometimes given as the means of various measures of performance (queue lengths, time in system, utilization percentages) but a complete study should also report estimated confidence intervals for these measures and control for correlation and confounding effects. The important variability in discrete-event simulations is the variability in time between successive events (between arrivals, service starts and finishes) since it is this variability that explains the creation of queues, as well as their variability, and thus explains the variability of time-in-system and in utilization rates. Other variability may be important (type of product to be produced, service priorities, alternate routings through the system) but without the time-interval variability, you could just do a Monte Carlo evaluation of the distribution function of a performance measure (using something like @RISK, for example), no simulation (as understood here, involving change of state over time) would be required. R. Joel Rahn Dipartement OSD Faculti des sciences de ladministration Universiti Laval Ste-Foy, Quibec G1K 7P4 CANADA til.: 418 656 7163 fax: 418 656 2624 e-mail: Joel.Rahn@fsa.ulaval.ca

[CrbnBlu@aol.com]

irt: jimhines@interserv.com, Mon, Apr 29, 1996 5:31 AM EST Jim made the comment, "What determines the choice of SD vs. Discrete Event is the character of the understanding desired," and although I think this has passed by several times, finally it caught me. I have continued to perceive my confusion in terms of implementation, and as such I continued to search for an understanding in the wrong place. My repeated implementation difficulties have been the result of not having a clear distinction of the character of understanding desired. I guess as Covey said in "The 7 Habits," "begin with the end in mind," yet "the end" is not the implementation and simulation but "the understanding." So I guess Im now at the point of asking what is the different character of understanding provided by discrete and continuous considerations of a particular situation? The current thought, which Im not quite comfortable with yet is that I would look to a continuous perspective to provide insight into the transition of one or more variables over time. I would then look to a discrete perspective to provide me with an insight as to possible distribution of values for one or more values at some point in time. So I now see one as providing variable transitions while the other provides value probablilities (developed over multiple runs). Gene Bellinger CrbnBlu@aol.com

[William Steinhurst]

IRT: CrbnBlu@aol.com Wed, 24 Apr 1996 > > It would seem the only way to do real continuous simulations would be with an > analog machine, and this used to be done but it was most expensive. The > digital computer, which is essentialy a discrete event machine, is made to > mimic analog by using a small step time. The Euler method used in DYNAMO, etc., is a discrete numerical solution method that is applied to continuous differential equations. In other words the model is continuous in time and "simulating" it digitally means finding a solution to the continuous problem using discrete numerical methods. I hope this is not a nit pick, but I feel there is an important difference between a numerical approximation to a continuous solution and the simulation of a discrete model. BTW there is now a third method in principle: symbolic math programs (Mathematica, Maple, etc.) can solve *some* systems of ODEs that would be beyond any pencil and paper work. Has anyone tried them on classic SD problems? William Steinhurst wsteinhu@psd.state.vt.us

["CDH"]

Hi group and Raymond. My name is Rainer Uwe Bode and I work in Brazil at a consulting firm. I do SD modeling since 1996. I have been accompanying this discussion for the last two weeks, and I must say that in case I had some certainties before, they are all gone now. Raymond says: If a process converts a single object at a time, > it is a discrete-event process. If the process works on a continuous > stream, it is a continuous process. If a system is composed of one or more > discrete-event processes, it must be a discrete-event system. If a system > is composed of one or more continuous processes, it must be a continuous > system. So, if you have pieces on an assembly line, lets say bars of steal, managing one at a time, you willl have, accordingly, discrete time events. But, if you convert all the bars into weight and process them at tons/ hour, you will have a continuous process in continuous time. So, the same event can be addressed and modeled in two different ways. Then, the problem is not the one-at-a-time, since you can convert almost all intire units into averaged pieces processed continuously, like envelopes. The problem in deciding what method to use seems more to be one of deciding wether you want to accompany the variations of a stream of items, or if you want to accompany a single object from start to finish. So, if you want to see, in a set of bars, bar 37 travel through the system, you would want to use a discrete-event-modeling. If tou prefer to analyse the journey of the bundle of bars, the bottlenecks and the supply-chain, SD would be more than adequate. Still, the specs of the flow of time seem to be of minor importance when comparing dicrete and SD modeling: to me, the basic criterium for choice seems to be the necessity of considering the more complex phenomena, like feedbacks and non-linearities. To me, with SD ou are able to address a lot more broader spectrum of problems, whereas discrete-event-modeling seems to be useful in a more limited order. Rainer Uwe Bode CDH- Recife cdeh@hotlink.com.br