Steady state analysis of the M/G/1//N queue with orbit of blocked customers

Abstract

This article considers a finite-source queueing model of M/G/1 type in which a customer, arriving at a moment of a busy server, is not allowed either to queue or to do repetitions. Instead, for an exponentially distributed time interval he is blocked in the orbit of inactive customers. We carry out a steady state analysis of the system and compare it with the corresponding system with retrials. Optimization problems are considered and formulas for the Laplace-Stieltjes transform of the busy period length are obtained.

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

“…Consequently, since the asymptotic partial characteristic functions F k (w) has the form Eq. (12) and the characteristic function is the sum of the partial characteristic functions it is not difficult to see that we get the law of large numbers in probability theory, namely the normalized number of requests in the orbit under limiting condition of growing number of sources N → ∞ converges weakly to the deterministic value κ, which has been determined from Eq. (15).…”

“…This can be done with the help of finite-source, or quasi-random input models. RQ with quasi-random input are a recent interest in modeling among others magnetic disk memory systems, cellular mobile networks, computer networks, and local-area networks with non-persistent CSMA/CD protocols, with a star topology, with random access protocols, and with multiple-access protocols, see, for example Alfa and Isotupa [1], Ali and Wei [2], Almási et al [3], Do et al [9], Dragieva [12], Ikhlef, Lekadir and Aïssani [17], Lebedev and Ponomarov [21], Wüchner, Sztrik and de Meer [31].…”

Asymptotic sojourn time analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs

“…This can be done by means of finite-source, or quasi-random input models. Retrial queues with quasirandom input are recent interest in modeling magnetic disk memory systems, cellular mobile networks, computer networks, and local-area networks with non-persistent CSMA/CD protocols, with star topology, with random access protocols, and with multiple-access protocols, see, for example Alfa and Isotupa (2004), Ali and Wei (2015), Almási et al (2016), Do et al (2014), Dragieva (2016), Ikhlef et al (2016) and Wüchner et al (2010).…”

“…It is well-known that the analysis of waiting/response time and the number of retrials of a customer is much more complicated than the distribution of number of customers in the system. There exist analytic, numerical, and asymptotic methods to help this research, see for example Amador (2010), Artalejo (1998), Artalejo and Gómez-Corral (2008), Dragieva (2013Dragieva ( , 2014Dragieva ( , 2016, Falin and Artalejo (1998), Falin and Templeton (1997), Falin (1977Falin ( , 1984Falin ( , 1986Falin ( , 1988, Wang et al (2011) and Zhang and Wang (2013).…”

On the Busy Period in One Finite Queue of M/G/1 Type with Inactive Orbit

“…The steady state distributions of the system under considerations are investigated in [3]. The objective of the present paper is to investigate the busy period, which is referred to the analysis of the system at non-stationary regime.…”