The Lineage of Discrete Rate Simulation
Five Decades, from SLAM to Today

Discrete rate simulation grew out of work that runs from Pritsker’s combined discrete-continuous modeling in 1979, through Andrew Siprelle’s bulk flow blocks, to the linear-programming engines of the late 2000s and the engine ReliaSim runs today. Here is what each era contributed and what carried forward, with the sources.

Era 1: Pritsker’s SLAM (1979–1983)

SLAM, the language

A. Alan B. Pritsker and Claude Dennis Pegden introduced the Simulation Language for Alternative Modeling (SLAM) in 1979 with the textbook Introduction to Simulation and SLAM. SLAM brought three kinds of modeling that had needed separate tools into one language: network modeling, discrete event simulation and continuous simulation. Pritsker called the combination combined discrete-continuous simulation.

Earlier languages such as GPSS, SIMSCRIPT, CSL and CSMP were usually committed to one approach. SLAM let one model use whichever approach fit each part of the system.

The Valdez Tanker example

The best-known SLAM teaching example became the Valdez Tanker problem. The standard published version, Koelling and Remy (1983), describes an oil export system: continuous pipeline flow fills a storage tank, and tankers arrive one at a time to load. Oil flow is continuous; tanker arrivals are discrete events.

Koelling and Remy published exact parameters: tanker capacity of 330,000 barrels, a load rate of 45,875 barrels a day, a triangular interarrival distribution. Specific numbers make a model reproducible, and that habit still anchors the work.

What carried forward: the combined framework, the Valdez Tanker as the standard example of mixing discrete and continuous behavior, and publishing exact parameters with every model.

Era 1.5: Andrew Siprelle’s bulk flow blocks (1998)

From paper to product

Andrew Siprelle created the method in 1990, originally as bulk flow simulation. His 1995 Winter Simulation Conference paper with David Parsons put it in the academic record, and the 1997 follow-up with Richard Phelps, Simulation of Bulk Flow and High Speed Operations, extended it. The history page covers those years.

By 1998 Siprelle’s company, Simulation Dynamics, Inc., shipped SDI Industry, a commercial product built around bulk flow modeling. Damiron and Nastasi’s 2008 paper cites that work as the “ground-breaking technology” their linear-programming approach built on.

Bulk flow blocks: separate item-to-flow and flow-to-item

SDI Industry introduced what are now called the three primitives: rate-limiting constraints, level-accumulating buffers and random interrupts. It added two blocks for moving between item-based and rate-based parts of a model:

• Item-to-flow: items entering a rate-based region become flow, and each item’s quantity adds to a buffer’s level.
• Flow-to-item: flow leaves the rate region as discrete items, and the buffer’s level drains into each item.

Siprelle kept these as two separate blocks, because items becoming flow and flow becoming items don’t behave the same way. Era 2 took a different approach; today’s engine returns to the separate pair.

What carried forward: the three primitives, separate item-to-flow and flow-to-item blocks, the rule that items and flow are different things, and the practice of validating against real plants.

Era 2: Imagine That and the ExtendSim Rate Library (2008–2014)

Rates by linear programming

Cécile Damiron and Anthony Nastasi, building on Siprelle’s work, recast the method in terms of linear programming. Their 2008 paper, Discrete Rate Simulation Using Linear Programming, solved for the rate of every flow in the network at each event. Between events the rates hold and the system moves forward exactly.

That gave exact rates between events: no time-stepping, no integration error, repeatable results. The principle carries through to today’s engine, which gets there its own way.

The Interchange block

Damiron’s design merged the separate item-to-flow and flow-to-item blocks into one bidirectional Interchange block in the ExtendSim Rate Library, which converts in whichever direction material moves. It was a different design choice. Today’s engine keeps the two blocks separate, following SDI Industry.

Krahl’s 2009 paper

David Krahl’s 2009 paper, ExtendSim Advanced Technology: Discrete Rate Simulation, documented the technique as a module of ExtendSim. By then the method Siprelle created in 1990 as bulk flow simulation had its new name.

Krahl’s paper also became the standard teaching reference. Its Figure 4 extends the Valdez Tanker with tank, valve and interchange blocks, and its contrast of discrete rate with continuous and discrete event modeling became the field’s usual explanation.

What carried forward: exact rates between events, Krahl’s three-way comparison, and the Valdez Tanker example. What changed later: a return to separate item-to-flow and flow-to-item blocks.

Era 3: Today’s engine (2024–today)

Typed building blocks, separate conversion blocks kept

ChiAha’s current engine, the one behind ReliaSim, is a new implementation of the method, written from scratch rather than ported from any earlier engine. It has:

• Typed building blocks for constraints, buffers, conveyors and interrupts, so model errors are caught before a run.
• Separate flow-to-item and item-to-flow blocks, Siprelle’s original design.
• Item-based and rate-based runtimes that share state, for combined models such as the Hamburger Duo and the Valdez Tanker.
• Text-based model files in place of block-and-wire diagrams.

The three primitives are unchanged from Siprelle’s 1990 design. Exact rates between events trace to Damiron and Nastasi (2008). Publishing exact parameters comes from Koelling and Remy (1983). The aim of mixing discrete and continuous behavior in one model goes back to Pritsker (1979).

You can watch the lineage run in the Sandbox. The Hamburger Duo runs one plant as discrete event and discrete rate side by side, and the Valdez Tanker shows item-to-flow and flow-to-item working together on the classic Pritsker and Krahl example.

Validation

Fischel and Lange’s 2020 paper, High Accuracy Discrete Rate and Reliability Modeling to Drive Improvement of Plant OEE and Throughput, modeled a multi-line food plant. That model was rebuilt in ReliaSim and independently validated within 1% of the plant’s measured OEE; the published OEE validation case study has the details.

The thread runs from Pritsker’s combined framework, to Koelling and Remy’s published parameters, to Siprelle’s bulk flow blocks, to Damiron and Nastasi’s linear-programming engine, to Krahl’s teaching, to today’s typed building blocks.

What we keep and what we changed

We keep:

• Pritsker’s insight that real systems need combined approaches (1979).
• Koelling and Remy’s published parameters, because specific numbers make models reproducible (1983).
• Siprelle’s separate item-to-flow and flow-to-item blocks (1998).
• Damiron and Nastasi’s exact rates between events (2008).
• Krahl’s clear comparison of discrete rate with continuous and discrete event modeling (2009).

We changed:

• Block-and-wire diagrams to text-based model files.
• Small time steps to exact, event-driven rates.
• Single-language tools to typed, modular packages with clear boundaries.
• “The Interchange does both” back to separate item-to-flow and flow-to-item blocks.

Primary sources

• Koelling, C. P. and Remy, W. H. (1983). Determining Operational Policies for Oil Flow and Tanker Loading Through Simulation. Proceedings of the 1983 Winter Simulation Conference. The published Valdez Tanker example.
• Pritsker, A. A. B. and Pegden, C. D. (1979). Introduction to Simulation and SLAM. John Wiley and Sons. The textbook that introduced SLAM and combined discrete-continuous simulation.
• Siprelle, A. J. and Parsons, D. J. (1995). Modeling a Bulk Manufacturing System Using Extend. Proceedings of the 1995 Winter Simulation Conference, 813–817. The foundational paper.
• Siprelle, A. J. and Phelps, R. A. (1997). Simulation of Bulk Flow and High Speed Operations. Proceedings of the 1997 Winter Simulation Conference, 706–710.
• SDI Industry 0.6 Reference Manual (1998). Simulation Dynamics, Inc. Documents the bulk flow blocks and the separate item-to-flow and flow-to-item design.
• Damiron, C. and Nastasi, A. (2008). Discrete Rate Simulation Using Linear Programming. Proceedings of the 2008 Winter Simulation Conference.
• Krahl, D. (2009). ExtendSim Advanced Technology: Discrete Rate Simulation. Proceedings of the 2009 Winter Simulation Conference.
• Fischel, L. B. and Lange, T. J. (2020). High Accuracy Discrete Rate and Reliability Modeling to Drive Improvement of Plant OEE and Throughput. Proceedings of the 2020 Winter Simulation Conference.

The published record

Three decades of peer-reviewed work on discrete rate simulation, in order, starting with the first bulk flow paper in 1995.

• 1995: Modeling a Bulk Manufacturing System Using Extend. Winter Simulation Conference.
• 1997: Simulation of Bulk Flow and High Speed Operations. Winter Simulation Conference.
• 1998: SDI Industry: An Extend-Based Tool for Continuous and High-Speed Manufacturing. Winter Simulation Conference.
• 1999: SDI Industry Pro: Simulation for Enterprise-Wide Problem Solving. Winter Simulation Conference.
• 2002: Non-Item Based Discrete Event Simulation Tools. Winter Simulation Conference.
• 2008: Discrete Rate Simulation Using Linear Programming. Winter Simulation Conference.
• 2009: ExtendSim Advanced Technology: Discrete Rate Simulation. Winter Simulation Conference.
• 2011: A Mesoscopic Approach to Modeling and Simulation of Logistics Processes. Winter Simulation Conference.
• 2012: Mesoscopic Supply Chain Simulation. Harbour, Maritime & Multimodal Logistics Modelling.
• 2013: Simulation of Mixed Discrete and Continuous Systems: an Iron Ore Example. Winter Simulation Conference.
• 2014: A Global Approach for Discrete Rate Simulation.
• 2016: Comparison of Discrete Rate Modeling and Discrete Event Simulation. Springer.
• 2017: Comparison of a microscopic discrete-rate and a mesoscopic discrete-rate simulation model for planning a production line. European Modeling & Simulation Symposium.
• 2017: Application of discrete-rate-based simulation models for production and logistics planning. Harbour, Maritime & Multimodal Logistics Modelling.
• 2020: Mesoscopic Discrete-Rate-Based Simulation Models for Production and Logistics Planning.
• 2020: High Accuracy Discrete Rate and Reliability Modeling to Drive Improvement of Plant OEE and Throughput. Winter Simulation Conference.

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