Number of Retrials in a Finite Source Retrial Queue With Unreliable Server

Abstract

The object of this paper is to continue investigation of a single server retrial queue with finite number of sources in which the server is subjected to breakdowns and repairs. The server life time as well as the intervals between repetitions are exponentially distributed, while the repair and the service times are generally distributed. Using the formulas for the stationary system state distributions, obtained by Wang et al. [in Wang, J, L Zhao and F Zhang (2011). Analysis of the finite source retrial queues with server breakdowns and repairs. Journal of Industrial and Management Optimization, 7, 655–676.] we investigate the distribution of the number of retrials, made by a customer before he reaches the server free. Recurrent schemes for computing this distribution in steady state as well as any arbitrary of its moments are established. Numerical results for five different distributions of the service and repair times are also presented.

Asymptotic Waiting Time Analysis of a Finite-Source M/M/1 Retrial Queueing System

“…In this paper, we will investigate the distribution of the number of retrials of a customer together with the distribution of the waiting time of a request in a RQ-system since they are connected to each other. Related results can be found, for example in Alfa and Isotupa [1], Dragieva [10], Dragieva [11], Falin and Artalejo [13], Gharbi and Dutheillet [14], Kvach and Nazarov [20], Nazarov, Kvach and Yampolsky [25], Nazarov and Sudyko [22], Wang, Zhao and Zhang [29], Wang, Zhao and Zhang [30], Zhang and Wang [32]. We will use the method of asymptotic analysis under limiting condition of a growing number of sources as it has been applied, for example in Kvach and Nazarov [20], Nazarov, Kvach and Yampolsky [25], Nazarov and Moiseeva [22].…”

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

“…The generalisation to generally distributed service times and repair times was later performed by Gaver Jr. (1962), Avi-Itzhak and Naor (1963), and Thiruvengadam (1963). Further extensions include phase-type distributions for the available periods (Federgruen and Green, 1986), arrival correlation (Takine and Sengupta, 1997), processor-sharing service (Núñez Queija, 2000), retrials (Dragieva, 2014;Zhang and Zhu, 2013;Gao et al, 2016), priorities (Sahba et al, 2013) and multi-server systems (Kim et al, 2017). Tang (1997) considers Poisson breakdowns when the server is working and renewal type breakdowns when it is idle, whereas Li et al (1997) investigate the transient behaviour of the M/G/1 queue subject to Poisson breakdowns.…”

Analysis of Retrial Queueing System M/G/1 with Impatient Customers, Collisions and Unreliable Server Using Simulation

“…In real-life systems typical problems arise like a power outage, human errors, or in wireless communication packets can suffer transmission failure, interruptions throughout their transfer and unfortunately it can happen at any time. These systems with an unreliable server were analyzed in several papers, for example in [3,6,10,18,20].…”