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.