SynchronousApproximations provides Mathematica routines for testing synchronous approximations of the M/D/2/K queue as described in Reinhard German: On Synchronous Approximations of Non-Markovian Processes with Dual Bounds, 21st Europ. Performance Engineering Workshop (EPEW 2025), June 26th, 2025, Catania, Italy, submitted version available at: https://epew-workshop.github.io/. An improved extended final version is submitted and will appear in the Lecture Notes in Computer Science (LNCS) Series by Springer if accepted.
The routines are based on SPNica, a Mathematica library for solving non-Markovian stochastic Petri nets, described in Reinhard German: Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets. John Wiley (2000). A manual of SPNica is provided in manual.pdf. Here a slightly improved version of SPNica is provided which has been updated to run with version 14.2 of Mathematica.
At first SPNica needs to be installed. For this adapt the path in TestSPNica/InitTests.nb where you put SPNica and execute the cell in the notebook. Then the computations of the paper are possible:
- MD2Kfasterslower.nb: slower and faster approximations without phase expansion,
- MD2Kfasterslowerexpanded.nb: slower and faster approximations with phase expansion
- MD2KErlang.nb: Erlang approximations