Lower bound for average delay in unblocked random access algorithm with orthogonal preambles

Introduction: Currently, the first versions of 5G communication standard networks are being deployed and discussions are underway on the further development of cellular networks and the transition to the 6G standard. The work of the currently popular idea of ​​the Internet of Things (IoT) is supposed to be in the framework of a Massive Machine-Type Communications scenario, which has a number of requirements for operation characteristics: very high energy efficiency, relatively low delay and fairly reliable communication. It is assumed that random multiple access procedures are used, since, due to the nature of the traffic, it is impossible to develop a channel resource sharing policy. To increase the efficiency of random access, a class of unblocked algorithms using orthogonal preambles can be used. Purpose: to calculate the lower bound of the average delay for the class of unblocked random multiple access algorithms using orthogonal preambles. Methods: system analysis, a theory of random processes, queuing theory, and simulation. Results: A model of a system with a potentially unlimited number of users who use random unblocked access to transmit data over a common communication channel using orthogonal preambles is proposed. A closed expression is obtained for calculating the lower bound of the average delay in such a system depending on the intensity of the input arrival rate. The limit value of the intensity of the input arrival rate to which the system operates stably is determined. Shown are the results of simulation with respect to the obtained bound. Practical relevance: the obtained boundary allows us to estimate the lower average delay in the described class of algorithms. Its application allows us to determine the possibility of using the considered class of algorithms from the point of view of limitations on the average delay at the stage of designing random multiple access systems.