Accurate Approximation for Resource Queuing Systems with Losses and Signals

Alexander Maslov, Eduard Sopin () and Konstantin Samouylov
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Alexander Maslov: Probability Theory and Cybersecurity Department, Peoples’ Friendship University of Russia (RUDN University), Moscow 117198, Russia
Eduard Sopin: Probability Theory and Cybersecurity Department, Peoples’ Friendship University of Russia (RUDN University), Moscow 117198, Russia
Konstantin Samouylov: Probability Theory and Cybersecurity Department, Peoples’ Friendship University of Russia (RUDN University), Moscow 117198, Russia

Mathematics, 2025, vol. 13, issue 4, 1-21

Abstract: We consider a queuing system with a finite number of servers and a finite pool of resources, where an arriving customer requires a server and random number of resources. During the service, each customer is associated with a Poisson flow of “signals”, where upon a signal arrival, the currently allocated resources for a customer are released, and an attempt is made to allocate a new random amount of resources. Recently, such systems have received significant attention for their use in the analysis of 5G/6G cellular systems with non-elastic traffic demands and blockage impairments. Such queuing systems do not allow closed-form analytical solutions, and are conventionally solved using numerical methods. These methods are sensitive to the dimensions of the state space and can lead to inaccuracies. In this paper, we propose a new method for the approximate analysis of performance metrics in resource systems with signals using analytical solutions for similar systems without signals. Our detailed comparison with simulations shows that the relative error is limited to 5–10% over a wide range of system and load parameters.

Keywords: resource loss system; embedded Markov chain; loss probability; termination probability; 5G network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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