ABSTRACT
The interarrival times and service times of many queues in real computer networks are modeled as continuous (as opposed to discrete) random variables. Section 3.1 describes some justification and data networks applications for such a model. Many other computer systems, small scale computer networks, and some wireless networks are organized with complete synchronization. In such wireless networks, nodes synchronize their activities with the clock of one node. Channel requests, grants, data transmissions, and receptions all proceed in predetermined fixed time intervals. Data frames are necessarily of fixed sizes. Analysis and performance evaluation of such systems are crucial, especially since these systems have limited resources. A proper understanding and modeling of timing and synchronization is required to correctly analyze such discrete time queues. Identification of when a data packet cannot enter due to a full buffer is important. Making assumptions with regard to synchronization issues also influences when exactly the last customer has left the system and the buffer is empty. Analysis and performance evaluation of discrete time queues is based on discrete parameter Markov chain models. The structure and operation of simple discrete parameter Markov chains are easy to visualize. Development of their statistical properties, however, require a careful study of the possible variations in the nature of interconnections (state transitions) and probabilities of transitions. Nevertheless, the final results are simple to comprehend.
