1. 1 Petri Nets H Plan: –Introduce basics of Petri Net models –Define notation and terminology used –Show examples of Petri Net models u Calaway Park model u IEEE 802.11 channel access protocol –Discuss variations and extensions u Generalized Stochastic Petri Nets (GSPN) u Stochastic Reward (SR) Nets

2. 2 Introduction H Petri Nets are another general modeling formalism for the performance analysis of “systems” (e.g., computer systems) H A graphical tool and notation for formal specification of system behaviour H A mathematical tool for quantifying the performance characteristics of systems H Fits in the analytical category of tools

3. 3 Overview (1 of 2) H Petri Nets combine ideas from: –Markov chains –Queueing theory –Finite state automata (and board games!) H New features introduced: –Concurrency; Mutual exclusion –Barrier synchronization; Non-determinism –Timed transitions; Colours; etc.

4. 4 Overview (2 of 2) H Petri Nets do not explicitly model queues and scheduling policies, but do model states and state transitions H Can compute steady-state performance metrics for a system, such as throughput, mean response time, etc. H More popular in European research community than in North America (?)

5. 5 Key Concepts H A Petri Net model can be drawn visually as a state machine with: –Places: nodes to represent states or servers –Arcs: arrows indicating valid next states –Tokens: markers indicating current state(s) –Marking: initial locations of tokens H Can be thought of as an “executable” model of the system with firing of transitions, producing an execution path

6. 6 Some Modeling Details H Transitions can fire only when enabled H If multiple transitions are enabled, then firing order is non-deterministic H Firing times: exponential distributions H There is a one-to-one correspondence between a Petri Net model and an underlying Continuous-Time Markov Chain (CTMC)

7. 7 Some Examples H Example 1: A day at Calaway Park H Example 2: IEEE 802.11 MAC protocol

8. 8 Generalized Stochastic Petri Nets H Generalizes Petri Net models H Can have weights (probabilities or priorities) associated with transitions H Can have timings on transitions H Allows non-exponential distributions H Can have guard functions on transitions H Can have coloured tokens (multi-class)

9. 9 Stochastic Reward Nets H Another extension of Petri Net models H Associates a “reward” value with certain states of the model: –Job completion –Customer departure –Successful packet transmission H The average reward rate is the primary performance metric in an SR Net model

10. 10 Summary H Petri Nets provide another analysis tool for system performance modeling H Formally equivalent to Markov chains H There are entire books on this topic H There are conferences on this topic H There are good software packages for the construction and evaluation of Petri Net models and for SR Net models