CompetingClocks

Fast, composable samplers for stochastic discrete-event simulation. This package gives your simulation or simulation framework statistical features like common random numbers, likelihood tracking, and first-class support for non-Exponential distributions.

This isn't a simulation framework. It's a component you can use to sample event times for simulation or to calculate the likelihood of a sample path for statistical estimation.

• Simulations of chemical reactions.
• Queueing theory models of networks, production, and computation.
• Epidemiological models of disease spread among individuals.
• Vector-addition systems.
• Generalized stochastic Petri nets.
• Generalized semi-Markov Processes.

Implementation Based on

• P. J. Haas, Stochastic Petri Nets: Modelling, Stability, Simulation. in Springer Series in Operations Research. New York, NY: Springer-Verlag New York, Inc, 2002. doi: 10.1007/b97265.
• D. F. Anderson and T. G. Kurtz, Stochastic Analysis of Biochemical Systems. Springer International Publishing AG Switzerland, 2015.
• Continuous-time, discrete-event simulation from counting processes, by Andrew Dolgert, 2016.

Version History

• v0.3.0 (2026-07) - Split fire! from enable! for correctness.
• v0.2.0 (2025-12) - Likelihood calculation, variance reduction.
• v0.1.0 (2024-06) - Initial release of samplers.

Usage

The library provides you with samplers. Each sampler has the same interface. Here, a distribution is a Distributions.ContinuousUnivariateDistribution, RNG is a random number generator, the key is some identifier (maybe an integer, tuple, or pair) for the event, and an enabling time is a zero-time for the given distribution.

• enable!(sampler, key, distribution, enabling_time) - to start the clock on when an event will fire next.

• disable!(sampler, key) - to turn off an event so it can't fire.

• next(sampler) - to ask this library who could fire next, and it return a (time, key).

• fire!(sampler, key, time) - choose which event happens at what time.

When NOT to use Competing Clocks

• Need ODE coupling? If a firing rate is coupled to a continuously-evolving ODE state, it's easier to stay within SciML and JumpProcesses.jl. Fixed delays are supported here via Dirac distributions (see delayed reactions); coupling a full ODE state to a firing time is future work, tracked in issue #45.
• Want high-level frameworks? Try Agents.jl or ConcurrentSim.jl — or the frameworks built on this package: ChronoSim.jl for discrete-event simulation and Quarton.jl for queueing theory.

You do not have to leave for a pure-exponential or chemical-kinetics model. You should be able to write your simulation once, expressively, whether or not every clock is exponential, and a hazard-rate-only interface is rarely the fastest way to sample a distribution. The pointer to JumpProcesses.jl above is for users who need ODE coupling or the rest of the SciML ecosystem, not a suggestion that exponential clocks belong elsewhere.

CompetingClocks.jl is for:

• Building a simulation framework with
  • General distributions (Weibull, Gamma, etc.),
  • Likelihood calculations or rare events, or
  • Variance reduction.
• Advanced work in reliability models, disease models, queueing models.