Many complex systems can be modeled by networks of queues in which customers receive service from one or more servers, where each server has its own queue. Thus, a network of queues is a collection of individual queueing systems that have common customers. In such a system, a departure from one queueing system is often an arrival to another queueing system in the network. Such networks are commonly encountered in communication and manufacturing systems. An interesting example of networks of queues is the set of procedures that patients go through in an outpatient hospital facility where no prior appointments are made before a patient can see the doctor.
In such a facility, patients first arrive at a registration booth where they are first processed on a first-come, first-served (FCFS) basis. Then they proceed to a waiting room to see a doctor on an FCFS basis. After seeing the doctor, a patient may be told to go for a laboratory test, which requires another waiting, or he may be given a prescription to get his medication. If he chooses to fill his prescription from the hospital pharmacy, he joins another queue; otherwise, he leaves the facility and gets the medication elsewhere. Each of these activities is a queueing system that is fed by the same patients. Interestingly, after a laboratory test is completed, a patient may be required to take the result back to the doctor, which means that he rejoins a previous queue. After seeing the doctor ...