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Lower bound for average delay in unblocked random access algorithm with orthogonal preambles
Currently, the first versions of 5G communication standard networks are being deployed and discussions are underway on further development of cellular networks and transition to the 6G standard. Once the Internet of Things is fully developed, it will function within the framework of Massive Machine-Type Communications. Its performance will need to satisfy a number of requirements: very high energy efficiency, relatively low delay and fairly reliable communication. Due to the nature of the traffic, it is impossible to develop a channel resource sharing policy and thus random multiple access procedures will be employed. A class of unblocked algorithms with orthogonal preambles may be used to increase the efficiency of random access. Purpose: To calculate the lower bound of the average delay for the class of unblocked random multiple access algorithms using orthogonal preambles. Results: We propose a model of a system with a potentially unlimited number of users who utilize random unblocked access to transmit data over a common communication channel using orthogonal preambles. For an infinite number of preambles, we prove that up to an input arrival rate of 0.5671, the system is stable. We obtain a closed-form expression for the average delay in a stable system depending on the intensity of the input arrival rate. We also demonstrate that this expression is the lower bound for the average delay in a system with a finite number of preambles. We perform a simulation in the case of a finite number of preambles which shows that with an increase in the number of preambles, the input arrival rate at which the system is stable approaches 0.5671, and the average delay tends to the lower bound. With an input arrival rate not exceeding 0.3, about 100 orthogonal preambles are sufficient to reach the lower bound. Practical relevance: The obtained bound allows us to estimate the lower average delay in the class of algorithms under consideration. Its application allows us to determine the possibility of using such a class of algorithms at the stage of designing random multiple access systems from the point of view of limitations on the average delay. © 2020 Saint Petersburg State University of Aerospace Instrumentation. All rights reserved.