Discrete rate simulation

What is discrete rate simulation?

Discrete rate simulation (DRS) is a form of discrete event simulation in which the thing that flows through the model is a rate, not a stream of individual items. A filler runs at a rate. A conveyor carries a rate. A tank fills at the difference between the rate coming in and the rate going out.

The model only does work when a rate changes. A machine breaks down, a buffer fills, a tank runs dry, a changeover starts, a shift ends. At each of those moments the model works out the new rate for every connected piece of equipment and then calculates when the next change will happen. Between events, nothing needs to be computed, because the flows are known.

Andy Siprelle created the method in 1990 under the name bulk flow simulation. It was later renamed discrete rate simulation, and discrete rate libraries or extensions are now part of all the major commercial simulation packages, including ExtendSim, AnyLogic and Siemens Plant Simulation.

Why rates instead of items?

Take a packaging line that fills product at high speed. A conventional discrete event model treats each container as its own item. Every container is created, moved, queued, filled, capped, labeled and packed, and each of those steps is an event the computer must schedule and process. The event count grows with every container the line makes.

Most of those events tell you nothing new. While the line is running smoothly, container 40,001 behaves exactly like container 40,000. What matters is when that smooth running stops, and how far the effect spreads up and down the line.

A rate model skips the repetition. For a high-speed system it can cut the events in a stretch of simulation from 40,000 steps to 2. That speed changes how the model gets used. You can run many replications, test many scenarios and check the model against history, in the time a conventional model takes to run a handful of cases.

Discrete rate vs. discrete event vs. continuous

The three approaches sit on a scale from fine detail to broad flow. The Fraunhofer Institute describes discrete rate as mesoscopic simulation, between microscopic item-by-item discrete event models and continuous models of flows.

	Discrete event	Discrete rate	Continuous
What flows	Individual items, each with its own attributes	Rates of flow between pieces of equipment and storage	Quantities that change smoothly over time
When the model calculates	Every time an item moves or changes state	Only when a rate changes: a stop, start, full or empty	At every small time step
Best fit	Assembly, job shops, routing, items with individual identity	High-speed packaging, food and bulk lines, tanks, conveyors, make-store-pack plants	Chemical reactions, heat transfer, process control
Run speed on a high-volume line	Slow, because event counts grow with volume	Fast, because events grow with changes, not volume	Depends on the time step
Watch out for	Run times that make experiments impractical	Questions that depend on one specific item	Discrete stops and changeovers are awkward to represent

None of these is better in general. A model of vehicle routing or an assembly plant where every unit carries its own options belongs in discrete event. A model of a line moving hundreds of containers a minute through accumulation conveyors belongs in discrete rate. Many real plants need both, and a good discrete rate tool will let you mix them: rate flow on the high-speed packing line, individual items for the pallets that come off the end.

Where discrete rate wins

High-speed consumer packaged goods lines

Filling, capping, labeling, case packing and palletizing lines run fast and stop often. Short stops matter because they add up, and because accumulation between machines decides whether a stop stays local or takes the whole line down. A rate model captures each stop and each buffer precisely without paying for every container.

Bulk flow

Powder, grain, liquid and other bulk material has no natural "item" at all. Forcing it into items means inventing a lot size and living with the error. A rate model handles it as it really is. Our first published model, in 1995, was a bulk manufacturing system.

Tanks, bins and silos

In-process storage fills and drains at the difference between two rates. A rate model knows exactly when a bin will fill or empty, so it can show when an upstream process will block, when a packer will starve, and what the storage is worth.

Conveyors and accumulation

Conveyors both move product and store it. Discrete rate models treat accumulation as the buffer it is, which is usually the question: how much conveyor, and where?

Make-store-pack plants and moving bottlenecks

When a making process feeds storage that feeds packing lines of different speeds, the bottleneck can move with the product mix. We call this the "slurp rate" problem: depending on the package size, the packing lines draw down in-process storage too fast or too slowly. Rate models are well suited to testing scheduling rules against it. In one coffee plant, a quality change inserted a new step between roasting and grinding, and the planning system could no longer build schedules that held up. A discrete rate model let the team conceive, test and verify a new scheduling algorithm that held up across demand scenarios.

Supply chains

The same idea scales up. Product moving between plants, warehouses and customers can be modeled as flows, which is why months of supply chain operation can run in minutes.