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Petri Nets

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

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Petri Nets

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

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

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

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

  5. Key Concepts • 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 • Can be thought of as an “executable” model of the system with firing of transitions, producing an execution path

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

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

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

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

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

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