Introduction

The purpose of this chapter is to introduce the user to modeling process with TANGRAM-II using a very simple example. By following this tutorial, the user will be able to:

• Construct a model based on the TANGRAM-II object-oriented paradigm.
• Specify and solve the model, and obtain the measures of interest.

The first example we choose to model is the M/M/1/k queueing system. In this system there is a maximum number of customers that may be stored in a queue. This model has two types of objects: a source of packets, and the queue with its server. Objects of each type will be instantiated to create the system model.

The source object generates packets to the server object from a Poisson distribution with rate $\lambda$ . The server object has a limited queue, and serves packets in FCFS order with exponentially-distributed service time. If a packet arrives at the server when the queue is full, the packet is dropped.

In the next sections we will present each one of the steps to create/evaluate a model:

• First we create the model with the Model Specification Module. In this step, the objects and the messages exchanged between them are defined.
• Next, we generate the state transition rate matrix. The Mathematical Model Module is used for that.
• Then we solve the model with the Analytical Model Solution Module and evaluate some measures of interest with the Measures of Interest Module.
• Finally, we simulate the model using the Simulation Module.