345 ISSN 0146-4116, Automatic Control and Computer Sciences, 2018, Vol. 52, No. 5, pp. 345–353. © Allerton Press, Inc., 2018. Performance Analysis of M2M Traffic in LTE Network Using Queuing Systems with Random Resource Requirements 1 E. S. Sopin a, *, K. A. Ageev a , E. V. Markova a , O. G. Vikhrova a , and Yu. V. Gaidamaka a a Applied Probability and Informatics Department, Peoples’ Friendship University of Russia (RUDN University), Moscow, 117198 Russia *e-mail: sopin_es@rudn.university Received May 26, 2017; in final form, April 4, 2018 Abstract⎯We analyze a multiserver queuing system, in which customers require a server and a certain amount of limited resources for the duration of their service. For the case of discrete resources, we develop a recurrence algorithm to evaluate the model’s stationary probability distribution and its various stationary characteristics, such as the blocking probability and the average amount of occupied resources. The algorithm is applied to analysis of M2M traffic characteristics in a LTE network cell. We derive the cumulative distribution function of radio resource requirements of M2M devices and propose a sampling approach in order to apply the recurrence algorithm to the case of continuous resources. Keywords: Queueing system, limited resources, random requirements, recurrence algorithm, normal- ization constant, CDF approximation, M2M, LTE DOI: 10.3103/S0146411618050127 1. INTRODUCTION A model of a modern wireless network is expected to reflect user`s session dynamics and the radio resources allocation policy of the base station. We consider a resource model presented in [7], however, we also assume that each user session requires a certain amount of radio resources (e.g., number of time slots per unit of time). Allocated resources are occupied for the whole duration of the user session and are released at session termination. The quantity of resources required by a user session depends on a number of factors, among which is the type of requested service, the distance between the user equipment and the base station, obstacles between them, interference, and so on. Therefore, the required amount of resources may be considered random with a certain cumulative distribution function (CDF). Traditional multiservice models with constant resource requirements cannot adequately describe net- works with resource allocation outlined above. This problem was addressed in [8, 9], where queuing systems with limited resources and random requirements have been proposed. In [10], it was proved that, in the case of Poisson arrivals and exponential service times, keeping track only of the total amount of occupied resources is enough to describe the behavior of the system. Such a simplification allows to decrease analysis complexity compared to the model where resources occupied by each customer are traced. However, analytical formulas for the stationary distribution and other probabilistic characteristics derived in [10] are too complex to be used directly due to multiple convolutions of the resource require- ments CDF. In [11, 12], we investigated different approaches to developing an efficient algorithm for probability characteristics evaluation. In this paper, we present a recurrence convolution algorithm for calculating the stationary probability distribution, the blocking probability, and the average and the vari- ance of occupied resources in the case of discrete resources. For the case of continuous resources, we pro- pose a method of CDF sampling. Finally, we apply the proposed convolution algorithm to evaluating machine-to-machine (M2M) traf- fic characteristics in an LTE network cell. The application of a queue with limited resources to LTE net- work performance evaluation is explained in [5, 6]. An LTE resource allocation scheme is modeled by the CDF of resource requirements. We assume that the resource scheduler works under the full power policy, and derive the corresponding resource requirements CDF, for which numerical analysis is performed. 1 The article is published in the original.