Showing posts with label MS. Show all posts
Showing posts with label MS. Show all posts

Modeling and Simulation - Unit-3 Notes

POISSON PROCESS
 In probability theory, a Poisson process is a stochastic process which counts the number of events and the time that these events occur in a given time interval. The time between each pair of consecutive events has an exponential distribution with parameter λ and each of these inter-arrival times is assumed to be independent of other inter-arrival times.
The basic form of Poisson process, often referred to simply as "the Poisson process", is a continuous-time counting process {N(t), t ≥ 0} that possesses the following properties:
  • N(0) = 0
  • Independent increments (the numbers of occurrences counted in disjoint intervals are independent from each other)
  • Stationary increments (the probability distribution of the number of occurrences counted in any time interval only depends on the length of the interval)
  • No counted occurrences are simultaneous.
Consequences of this definition include:
  • The probability distribution of N(t) is a Poisson distribution.
  • The probability distribution of the waiting time until the next occurrence is an exponential distribution.
  • The occurrences are distributed uniformly on any interval of time. (Note that N(t), the total number of occurrences, has a Poisson distribution over (0, t], whereas the location of an individual occurrence on t (a, b] is uniform.)
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Modelling & Simulation - 2 Mark Question & Answers

 For Unit - I & II
UNIT I
System and System Environment: Component of a System – Continuous and discrete systems
– Types of model; Steps in Simulation study; Simulation of an event occurrence using random
number table – Single server queue –two server queues – inventory system.
UNIT II
Random number generation: Properties of random numbers – Generation of Pseudo – random
numbers – techniques of generating pseudo random numbers; Test for random numbers: the
Chisquare test-the kolmogrov Smirnov test – Runs test – Gap test – poker test.

Click Here to download the 2 mark Q & A Document