Google

Monday, February 16, 2009

Discrete System Simulation

Reading List: System Simulation With Digital Computer by Narsingh Deo, PHI

  • Systems can either be continuous or discrete
  • In continuous systems, state changes smoothly with time
  • In discrete systems, state changes are discontinuous
  • Event - Each change in the state of the system. e.g. arrival or departure in a queue
  • Discrete Event Simulation (DES)- Simulation of a discrete system
  • DES is commonly used in Operations Research (OR) to study large, complex systems for which conventional analytical approach cannot be used.
  • Examples of such systems include: Study of
- Sea and air ports
- steel melting shops
- telephone exchanges
- production line
- inventory control
- project scheduling
  • Compared to continuous system simulation, DES
- Is more diverse
- Has less of theory
- There are no overall sets of equations to be solved

Fixed time-step vs. event-to-event (next event) model
  • Models for moving a system through time
  • Applicable in simulating an dynamic system - be it continuous or discrete
  • In a fixed time step model, a timer or clock is simulated by computer. This clock is updated by a fixed time interval (say, tau) and the system is examined to see if any event has taken place during this unit time interval. All the events that take place during this period are treated as if they occurred simultaneously at the tail end of this interval.
  • In next-event simulation model the computer advances time to the occurrence of the next event. So, shift is from event to event. The system state does not change in between. Only those points in time are kept track of when something of interest happens to the system.
  • A system can use any of the two time advancing mechanism.
  • Generally, next event model is preferred as we do not waste any computer time in scanning those points in time when nothing takes place.
  • In fixed time model, if tau is reasonably small then waste is bound to occur and if it is so large that more than one event time place during each interval then model is unrealistic and may not yield meaningful results.
  • However, implementation of next event model is complicated.

On simulating randomness
  • Stochastic Systems - Systems with inherent randomness or unpredictability in their behaviour.
  • These systems with chance can be natural or man-made
  • Examples of systems where randomness is simulated are:
- Inventory System
- Water Reservoir
- Arrival of customers in a store
- Request for telephone line at exchange
- Births and deaths in a population
- Particle collision in a reactor
- Arrival of an elevator on a given floor
  • Discrete dynamic systems could be classified as:
- Deterministic - For given input, output is fixed. So, its just a transformation and that too computationally less demanding
- Stochastic - For given input, there can be more than one output. In other words, it is system in which atleast one of the variables is given by a probability function.
  • Complex discrete, dynamic, stochastic systems often defy an analytic solution and are therefore studied through simulation

No comments: