# ChiAha Discrete Rate Simulation

Discrete Rate Simulation (DRS) is a direct way to understand production flow/reliability problems, such as those found in mixed continuous/batch or high-speed/high-volume production. Its worldview is a natural fit for the way continuous production works, where we are concerned with machines’ rates and the flow of material that:

is of a bulk or aggregate nature, or

moves so fast that it can rewardingly be modeled as homogeneous flow

DRS can be considered a variant of Discrete Event Simulation (DES), and a "missing link" that gives the modeler the option to represent material, or "what flows", not as distinct entities, but as homogenous quantities, and to describe its flow using rates.

The DRS worldview provides a very accurate fit to a great many manufacturing problems, in which we are concerned with *performance* (i.e., throughput, availability, OEE), and not the detail of unit operations. Due to its simple worldview, DRS also provides quick insight into many non-manufacturing flow problems as well. Because of this, instead of using the term "material" to describe what flows, we sometimes revert to using the word "stuff".

[DRS] represents a general breakthrough in the way that

materialis represented in simulation models. For representing high-volume or highspeed production (e.g., processing or packaging), or where there is the ability to view material flow in terms of rates (e.g., cash flow, document processing, facilities planning), the discrete rate flow blocks are a natural fit. This is a class of problem where the standard technique in discrete event modeling is aggregation, which results in inaccurate and slow models (Sturrock and Drake, 1996) (Also Siprelle, 1995). An example application of Flow blocks is in simulating the flow of materials through complete cereal plants, from batch and continuous processing operations through high-speed packaging lines.

### The Role of Production Flow Graphs in Modeling

Production modeling software enables modelers to compose production flow graphs comprised of graphical nodes to represent the conceptual "pieces" through which material flows in a production process, and critically, where the material can *reside*. Nodes are used to define the possible routes, and the requisite resources (e.g., machines) or available spaces (e.g. a space for WIP to reside over time) that the material, or "what flows" will occupy.

This emphasis on where material can flow and reside is essential to understanding of production simulation, and the customary built-in behavior of *blocking* and *starving*. In the fast food industry, for example, much study has been made on how many vehicles can fit in a drive-thru lane between the ordering kiosk and the pickup window. To model that, a modeler uses a node representing a Queue with a capacity equal to the number of vehicle spaces. When in the simulation run, the Queue becomes full, it represents the condition where all spaces are occupied, meaning nobody can order. Therefore, customers upstream from the ordering kiosk become *blocked* from proceeding to the ordering kiosk. Conversely, if nobody is in line to order, the ordering kiosk becomes *starved.*

Whether material is represented by discrete items or as DRS homogenous flows, its movement is dependent on where the material resides, and whether there is availability to accept it downstream from where it resides.

### DRS Compared with Discrete Event Simulation (DES)

Just as in DES, DRS leverages a clock, so that time can "hop" over a sequence of (typically, but not always, unevenly spaced) events.

Thus the number of events are reduced, resulting in *time compression*, which is essential in quickly answering strategic questions of interest in production processes. DES reduces the number of events over a continuous model, and DRS reduces them drastically even more, resulting in a model with a very fast execution speed. The graph below depicts a model of a system of a Fast-Slow draining bucket, using 3 different techniques: Continuous (in red), Discrete Event (in blue), and Discrete Rate (in **black**). You can see that the black line encounters only a handful of events in the course of the simulation run. The continuous model has the greatest number of steps.

### DRS Contrasted with DES

In contrast with DES, DRS represents material not as distinct items, but as homogenous flow.

Whilst a DES assumes no change in the system between consecutive events, a DRS assumes that material flows at a constant *effective rate *between consecutive events, so that a Buffer can change level in linear fashion between consecutive events.

Events are posted when DRS Buffers (or Conveyors) anticipate reaching empty, full or set levels of accumulation. This is in contrast to a typical DES, where events are posted when item delays are completed, or when items move from one residence node (e.g. a Queue or a Machine) to another.

DRS events can be posted tentatively; i.e., they can be

*cancelled*when an effective rate changes; e.g., due to a start or stop event resulting in a change in relative effective rate for a buffer.A DRS simulation conveys potential rate information between nodes, accounts for accumulated material, and facilitates blocking and starving behavior throughout all branches of the production graph.

When DRS Buffers (or Conveyors) reach full or empty, blocking or starving behavior is emulated via the recalculation of

*effective rates*. This step leverages a Max Flow algorithm.

### Areas of application

There are many areas in which the worldview of DRS has been applied:

High speed/volume production lines

Pulp and paper processing

Oil and gas

Traffic

DRS has matured and evolved over the past 3 decades. DRS has been researched, and attached to another term, mesoscopic simulation, which evokes the idea of playing with less detail, while also requiring much less effort, resulting in a sweet spot.

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