## PEPA examples

- Susanna Donatelli, Marina Ribaudo and Jane Hillston included an
example in the paper
A comparison of Performance Evaluation
Process Algebra and generalised stochastic Petri nets of
a multiprocessor system, bus and memory modules.
- The comparison paper model (48 states)

- A small model of a location tracking system based on
active badges was made by Stephen Gilmore, Jane Hillston and
Graham Clark. The paper Specifying
performance measures for PEPA appeared in the
proceedings of Fifth International AMAST Workshop on Real-Time
and Probabilistic Systems.
- The PEPA active badge model (72 states)

- A small model of the alternating bit protocol was developed by
James Edwards. The paper Process
algebras for protocol validation and analysis appeared in the
proceedings of the PREP 2001 conference in Keele.
- The alternating bit protocol (94 states)

- Two medium-sized PEPA examples are here. They model a PC-LAN as described in lecture notes from the University of Edinburgh lecture course `Modelling and Simulation''. The lecture notes explain how certain performance measures are calculated.
- A larger model of an industrial production cell was made
by Robert Holton. The paper
A PEPA specification of an industrial
production cell appeared in the Computer Journal.
- The PEPA workcell model (17846 states)

- Jane Hillston, Marina Ribaudo and Stephen Gilmore made a
model of the TOMP machine protocol. This model can be scaled very
simply by varying the number of copies of number of copies of the
processes which are competing for memory access. The description of
the model and timings for runs of the PEPA Workbench on a 500MHz
Pentium III with 128Kb of memory appear in the paper An efficient algorithm for aggregating PEPA
models which is to appear in IEEE Transactions on Software
Engineering. Here is a collection of models of the TOMP machine
with increasing numbers of copies of components.
- PEPA model of TOMP (1,1) (16 states)
- PEPA model of TOMP (2,1) (40 states)
- PEPA model of TOMP (2,2) (96 states)
- PEPA model of TOMP (3,2) (224 states)
- PEPA model of TOMP (3,3) (512 states)
- PEPA model of TOMP (4,3) (1152 states)
- PEPA model of TOMP (4,4) (2560 states)

- PEPA model of TOMP (1,1,1) (72 states)
- PEPA model of TOMP (2,1,1) (176 states)
- PEPA model of TOMP (2,2,1) (416 states)
- PEPA model of TOMP (2,2,2) (960 states)
- PEPA model of TOMP (3,2,2) (2,176 states)
- PEPA model of TOMP (3,3,2) (4,864 states)
- PEPA model of TOMP (3,3,3) (10,752 states)
- PEPA model of TOMP (4,3,3) (23,552 states)
- PEPA model of TOMP (4,4,3) (51,200 states)
- PEPA model of TOMP (4,4,4) (110,592 states)

- Jeremy Bradley and Stephen Gilmore made a model of a web server
which can be scaled by varying the number of servers, number
of readers, number of writers or buffer size. This can be
used to generate systems with very large state spaces. The
model is studied in the paper ``Derivation of Passage-time
Densities in PEPA models using ipc:
The Imperial PEPA Compiler".
- PEPA model of WS (3,3,2,2) (1,376 states)
- PEPA model of WS (4,3,3,3) (21,248 states)
- PEPA model of WS (5,4,3,3) (69,440 states)
- PEPA model of WS (6,5,3,3) (211,968 states)
- PEPA model of WS (6,5,4,4) (1,369,728 states)
- PEPA model of WS (7,6,5,5) (26,651,520 states)
- PEPA model of WS (8,7,5,5) (> 26,651,520 states)
- PEPA model of WS (9,8,6,6) (>> 26,651,520 states)
- WS system generator (ML application)

- The mobile agent system is a very simple PEPA net which models a
mobile software agent which moves from one host to another
harvesting information which it dumps to a central analysis
point. The example is discussed in the paper
PEPA nets: a structured performance
modelling formalism which appeared in the proceedings
of Tools 2002.
- PEPA net model of a mobile agent system (12 states)

- The concrete syntax for PEPA supported by the Möbius
modelling platform differs slightly from the syntax supported by other PEPA tools. Below is the tiny example in the Möbius syntax.
- Tiny PEPA example in Möbius PWB file format (9 states)