Resource System with Losses in a Random Environment

Abstract

The article deals with queueing systems with random resource requirements modeled as bivariate Markov jump processes. One of the process components describes the service system with limited resources. Another component represents a random environment that submits multi-class requests for resources to the service system. If the resource request is lost, then the state of the service system does not change. The change in the state of the environment interacting with the service system depends on whether the resource request has been lost. Thus, unlike in known models, the service system provides feedback to the environment in response to resource requests. By analyzing the properties of the system of integral equations for the stationary distribution of the corresponding random process, we obtain the conditions for the stationary distribution to have a product form. These conditions are expressed in the form of three systems of nonlinear equations. Several special cases are explained in detail.

Retrial Queueing System for Analyzing Impact of Priority Ultra-Reliable Low-Latency Communication Transmission on Enhanced Mobile Broadband Quality of Service Degradation in 5G Networks

“…Additionally, we proposed a model of radio admission control for URLLC and adaptive bit rate eMBB in [41]. In [42], we introduced a model as a resource queuing system, and in [43], we extended this model to consider eMBB bit rate degradation due to the impact of path loss, based on the methods used in [44,45].…”

A PH i /PH i

“…Queuing models in an RE where the interarrival time and service time are subject to exponential distribution M, such as M/M/1, M/M/C, and M/M/∞ queuing models were later explored by Yechiali and Naor [27]; Neuts [39]; O'cinneide and Purdue [40]; Krenzler and Daduna [30]; and Yu and Liu [29]. More recent works can be found in the study by Pang et al [41] and Naumov and Samouylov [42]. Using the M/M/C queue in an RE in modeling traffic systems was conducted by Baykal-Gürsoy et al [3].…”

Infinite-Server Resource Queueing Systems with Different Types of Markov-Modulated Poisson Process and Renewal Arrivals

“…In their works, the authors considered a QS with a random volume of requirements, as a class of systems with some capacity, which is dependent upon or independent of the volume of requirements and the time of service. Resource QSs with limited resources have been used in some works as models of the next generation of wireless communication networks [13][14][15].…”