Modified M-timed Petri nets in modelling and performance evaluation of systems
read more
Citations
The Definition of Extended High-level Timed Petri Nets
Modeling and verification of a class of real-time systems by the use of high level petri nets
The definition of an interruptible Petri nets
References
A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems
Performance Analysis Using Stochastic Petri Nets
Recoverability of Communication Protocols--Implications of a Theoretical Study
Related Papers (5)
Frequently Asked Questions (15)
Q2. how many times does a class-1 job take to be processed?
Since the average terminal time and the average service time for class-1 jobs are equal to 0.5 and 0.2, respectively, the class-1 jobs spend, on average, 0.756-0.5-02=0.056 time units in the waiting queue (when the server is processing another class-1 job; the states s3, s7 and s9).
Q3. what is the selection function e of a marking m in a net?
A selection function e of a marking m in a net N is any function e : T → {0, 1, ...} such that(1) there exists a sequence of transitions u = (ti1 , ti2 , ..., tk) in which tij ∈ En(mij−1) for j = 1, ..., k, and for mi0 = m where∀p ∈ P : mij (p) = mij−1(p)−{1, if p ∈ Inp(tij ), 0, otherwise,(2) the set of transitions enabled by mik , En(mik), is empty,(3) for each tinT , e(t) is equal to the number of occurrences of t in the sequence u;i.e., a selection function e indicates (by nonzero values) all those transitions which can initiate their firings simultaneously (and some transitions may initiate several firings).
Q4. What is the definition of a non-singular net?
The description of non-singular nets must take into account ”sequences” of consecutive interrupts in a net when one interrupted transition, through its input places, interrupts another transition(s).
Q5. What are the main reasons why Petri nets are used in the literature?
Petri nets [1,7,11] have been successfully used in modelling, validation and analysis of systems of events in which it is possible for some events to occur concurrently, but there are constraints on the occurrence, precedence, or frequency of these occurrences [6,11].
Q6. What is the state space of the Petri net?
The state space can easily be derived from net specifications, and many performance measures can be obtained from stationary probabilities of states using standard rules of operational analysis.
Q7. What are the main characteristics of timed Petri nets?
Merlin and Farber [9] discussed timed Petri nets where a time threshold and maximum delay were assigned to each transition of a net to allow modelling of timeouts used to recover from failures in communication systems.
Q8. What is the stationary probability that the system is idle?
Since the server is idle in the state s6 (m6(p1) = 1, and also Markov state q0), the stationary probability that the system is idle is equal to the stationary probability x(s6) = 0.107 (Tab.1).
Q9. What is the common approach to Petri nets?
Another approach to Petri nets ”with time” assumes that the firing times are exponentially distributed random variables, and the corresponding rates are assigned to transitions of a net; such nets are called stochastic Petri nets [2,10].
Q10. What is the meaning of the term ”multiple enablings”?
It should be noticed that in M-timed nets without multiple arcs, non-simple behaviour can occur only in the initial states, when the initial marking function introduces ”multiple enablings” of some transitions.
Q11. What is the average throughput rate for class-2 jobs?
for class-2 jobs, the average throughput rate, the average turnaround time and the average waiting time are equal to 0.728, 2.747 and 1.247, respectively.
Q12. What are the main features of simple nets?
such initial markings can usually be convertedto equivalent ones, which preserve the behaviour of a net, and which provide simple selection functions.
Q13. What is the definition of a simple net?
Nonsimple nets can be described by a straightforward extension of simple nets [18,19] that takes into account combinations of multiple firings and their corresponding probabilities.
Q14. What is the utilization of the system for class-1 jobs?
Then the utilization of the system is immediately 1-0.107=0.893 or 89.3(x(s2) + x(s4) since f2(t3) = f4(t3) = 1) and 0.529 for class-1 jobs.
Q15. What is the definition of the set of reachable states?
the set S(T) of reachable states is defined as the set of all states of a net T which are reachable from the initial states of the net T (including the initial state(s)).