Extended generator and associated martingales for M/G/1 retrial queue with classical retrial policy and general retrial times

A retrial queue with classical retrial policy, where each blocked customer in the orbit retries for service, and general retrial times is modeled by a piecewise deterministic Markov process (PDMP). From the extended generator of the PDMP of the retrial queue, we derive the associated martingales. These results are used to derive the conditional expected number of customers in the orbit in the transient regime.

Sojourn Times in A Queueing System with Breakdowns and General Retrial Times

This paper centers on a discrete-time retrial queue where the server experiences breakdowns and repairs when arriving customers may opt to follow a discipline of a last-come, first-served (LCFS)-type or to join the orbit. We focused on the extensive analysis of the system, and we obtained the stationary distributions of the number of customers in the orbit and in the system by applying the generation function (GF). We provide the stochastic decomposition law and the application bounds for the proximity between the steady-state distributions for the queueing system under consideration and its corresponding standard system. We developed recursive formulae aimed at the calculation of the steady-state of the orbit and the system. We proved that our discrete-time system approximates M/G/1 with breakdowns and repairs. We analyzed the busy period of an auxiliary system, the objective of which was to study the customer’s delay. The stationary distribution of a customer’s sojourn in the orbit and in the system was the object of a thorough and complete study. Finally, we provide numerical examples that outline the effect of the parameters on several performance characteristics and a conclusions section resuming the main research contributions of the paper.

Classical Fuzzy Retrial Queue with Working Vacation using Hexagonal Fuzzy Numbers

Using fuzzy techniques “Classical Fuzzy Retrial Queue with Working Vacation(WV) using Hexagonal Fuzzy Numbers” is discussed in this paper. We acquire model in fuzzy environment as the average orbit length, Probability(Pr) that the server busy, and Pr(the server is in a WV period), the sojourn time of a customer in the queue. Finally numerical results are presented.

On the Retrial-Queuing Model for Strategic Access and Equilibrium-Joining Strategies of Cognitive Users in Cognitive-Radio Networks with Energy Harvesting

This article studies the strategic access of single-server retrial queue with two types of customers, where priority is given according to their category. On the basis of this concept, a cognitive-radio network was developed as retrial queue with energy harvesting. Cognitive radio allows for a secondary user to opportunistically access the idle spectrum of a primary user (PU). Upon arrival of a primary user, the service given to the secondary user by the cognitive radio is interrupted, and the PU band is available for the primary user. After completion of service for the primary user, the PU band is again available to secondary users. Performance metrics are derived to study the equilibrium strategies of secondary users. A Stackelberg game was formulated and Nash equilibrium was derived for the noncooperative strategy of the secondary user. Game-theory concepts are incorporated with queuing theory ideas to obtain the net benefit for the noncooperative strategy and social benefit for cooperative strategy. Lastly, analytical results are verified with numerical examples, and the effects of energy-harvesting rate are discussed.