A Survey of Recent Results in Finite-Source Retrial Queues with Collisions

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

Tóth

2021

Self Cite

The goal of the paper is to study a finite-source retrial queuing system with collisions and customers' impatience behavior in the orbit. The situation when an incoming customer from the orbit or from the source finds the server busy causes a collision and both requests are directed toward the orbit. It is assumed that every request in the source is eligible to generate customers whenever the server is failed but these requests immediately go into orbit. A customer after some waiting in the orbit can depart without fulfilling its service requirement these are the socalled impatient/reneging/abandoned customers. In that case it returns to the source. A customer who is under service when the server fails is also sent to the orbit. The source, service, retrial, impatience, operation and repair times are supposed to be independent of each other. The novelty of the investigation is to carry out a sensitivity analysis comparing various distributions of impatience time of customers on the performance measures such as mean number of customers in the orbit, mean waiting time of an arbitrary, successfully served and reneging customers, probability of abandonment, server utilization, etc.

Section: Squared Coefficient Of Variation Is Greater Than Onesupporting

confidence: 51%

Section: Squared Coefficient Of Variation Is Greater Than Onementioning

confidence: 92%

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Some Special Features of Finite-Source Retrial Queues with Collisions, an Unreliable Server and Impatient Customers in the Orbit

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

Tóth

2021

Self Cite

“…This difference is obviously due to the introduction of a second server and a cognitive characteristic to the secondary customers which make the system more complex. However, the maximum property of the mean response time that was noticed in [27] is obtained.…”

Section: Commentsmentioning

confidence: 84%

Simulation Analysis in Cognitive Radio Networks with Unreliability and Abandonment

Nemouchi

Zaghouani

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

2021

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The current paper presents a Cognitive Radio Network with impatient customers and unreliable servers by the help of a finite-source retrial queueing system. We consider two types of customers (primary and secondary) assigned to two interconnected frequency bands. A first frequency band with a priority queue and a second frequency band with an orbit are reserved for Primary Users (PUs) and Secondary Users (SUs), respectively. If the servers are busy, both customers (licensed and unlicensed) enter either the queue or orbit. Before they enter orbit, the secondary customers receive a random retrial time according to the exponential distribution, i.e. the waiting time before the next retry. Unlicensed users (impatient) are obliged to leave the system as soon as their total waiting time exceeds a random maximum waiting time. It should be noted, that the secondary service unit of our system is subject to random breakdowns and repairs. The novelty of this work consists in the investigation of the abandonment and secondary server unreliability impact on various performance measures of the system (Cognitive Radio Network), such as the mean response and waiting time of users, the probability of abandonment of SU, etc. Several figures illustrate the problem in question through simulation.

“…As we mentioned earlier to the best of our knowledge there is no analytical solution to this kind of system thus we cannot expect rigorous proof. All in our previous papers the goodness of the proposed asymptotic solutions were tested by either numerical or simulation results which justified our constructiveness concerning the form of a solution, see for example Nazarov et al (2018. In this paper, we follow this method and in the next section, the comparisons are made.…”

Section: Asymptotic Of the Second Ordermentioning

confidence: 96%

Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs

Nazarov

Methodol Comput Appl Probab

Kvach

et al. 2021

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This paper deals with a retrial queuing system with a finite number of sources and collision of the customers, where the server is subject to random breakdowns and repairs depending on whether it is idle or busy. A significant difference of this system from the previous ones is that the service time is assumed to follow a general distribution while the server’s lifetime and repair time is supposed to be exponentially distributed. The considered system is investigated by the method of asymptotic analysis under the condition of an unlimited growing number of sources. As a result, it is proved that the limiting probability distribution of the number of customers in the system follows a Gaussian distribution with given parameters. The Gaussian approximation and the estimations obtained by stochastic simulations of the prelimit probability distribution are compared to each other and measured by the Kolmogorov distance. Several examples are treated and figures show the accuracy and area of applicability of the proposed asymptotic method.