A Markov model to evaluate system performances under slotted Aloha protocol

The Multiple access system deals with a situation where multiple nodes are required to access a commonly shared channel. These multiple accesses can be viewed as uncoordinated nodes which compete for bandwidth. Various random access mechanisms, such as ALOHA protocol and its corresponding variations, have been widely studied as efficient methods to coordinate the medium access among competing users. In such situations, one of the most important objectives is to evaluate the system performances under such protocol. In this paper we enhanced a model already studied in a previous work by expanding the number of states in a Markov model for a system implementing slotted Aloha protocol; and we use a three state Markov process in order to represent and evaluate the performances of the system under different scenarios. In this model we are interested in representing the time occupancy of the system, evaluating the throughput system under different fairness conditions, and evaluating the probability that the system is in a backlogged state or in an idle state.