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Discrete Events

Discrete event models model phenomena occurring at particular moments in time. Anything that one may think of as “traffic” usually may be modeled as discrete events.

Many situations may be modeled as “discrete events”. Discrete events are events occurring at particular instants in time, usually with some randomness involved.

A canonical example for comes from public transport: A bus arrives at a stop at a particular instant. When exactly this instant occurs has some randomness involved in it, depending on many variables such as time of day, traffic conditions, etc. A model of the arrival of the bus is thus a discrete event model.

Many phenomena which can be modeled as discrete events are some sort of “traffic”:

• Vehicular traffic
• Public transport
• Internet data
• Electronic data
• Photons (light)
• Customers arriving at an establishment

Many other non-traffic phenomena are also discrete events. When the occurrence being modeled does not refer to a moment in time, but a (pinpointed) location in space or some other model domain, the same mathematical concept is called a “point process”. Some examples of non-traffic and non-time point processes are:

• Machine failure
• Electron shot noise
• Heterogeneous media
• Particles in a suspension
• Crowd behavior
• Particle interactions

Discrete event models are thus applicable to a variety of situations, and use a variety of mathematics such as queuing theory, reliability theory, random point processes, arrival processes, discrete event simulations, etc. These models can be used to understand and optimize allied systems, such as systems for order fulfillment, public transport, noise cancellation, traffic routing, etc.

Projects

Following are some interesting projects performed by us, involving discrete event modeling and/or simulation:

INTERNET EMU-SIMULATOR. A single router which behaves as if it were the internet!

NETWORK TRAFFIC SHAPING. Simulations of an algorithm for regulating network bandwidth usage. The simulations were carried out using NS/2.

COMMUNICATION PROTOCOLS. Extensive modeling, debugging and optimization of communication protocols of a system. Tools: C++, System C.

BUS SCHEDULING. Public transport demand prediction, and optimization of routes and schedules.

LOGISTICS. Logistic optimization of a multi-commodity fulfillment problem. A sub-part of the optimizer was a discrete event simulator, expressed as the optimization function.

RELIABILITY. Reliability analysis of a new class of industrial machines developed by a partner company.

LIGHT SENSING NOISE. Light sensing noise may be estimated by modeling photon arrivals as a memoryless arrival process. This is useful to design the correct amount of integration time, to minimize a combination of photon noise, electrical noise and quantization noise.

CROWD SIMULATION. Simulation of the behavior of a crowd in calamitous situations.

MURA. Mura is a physical phenomenon observed in displays and lights, which can be modeled using random point processes.

NOUMENON MULTIPHYSICS PROVIDES MULTI-DISCIPLINARY MODELING AND SIMULATION SERVICES TO THE ENGINEERING INDUSTRY