Queuing Models

This chapter deals with another classic model type of SDES, namely queuing models. Their underlying idea comes from the everyday experience of requiring some sort of service, which is restricted in a way that not all concurrent requests can be answered at the same time. We are forced to wait for an available teller at a bank, a seat in a cafeteria, or when crossing the street. When it is our turn, we block the service for others that are waiting and release the server for the subsequent customer afterwards. The same sort of behavior is frequently found in technical systems, in which we are mainly interested in this text. Communication packets queue at a switch, data base access requests are performed one at a time, or parts pile up in front of a bottleneck machine. The main reason for not having enough servers for every possible request is that installation and maintenance of servers cost money, and it is therefore not economically reasonable to have too many of them. On the other hand, customers often request service in an unknown and stochastic pattern, which means that an infinite number of servers would be required in theory to fulfill all requests in parallel.