A discrete-time Geo[X]/G/1 retrial queue with control of admission

Artalejo, Jesús R.; Atencia, Iván; Moreno, Pilar

doi:10.1016/j.apm.2005.02.005

Cited by 43 publications

(15 citation statements)

References 19 publications

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“…We therefore show that the pgfs of the numbers of arrivals and the service times as well as the functional equation (7) go to their continuous-time counterparts. Similar approaches were taken in [4,21].…”

Section: Continuous-time Resultsmentioning

confidence: 98%

“…3 5.0689e-3 1.3516e-2 1.8668e-2 1.8533e-2 9.6076e-3 0. 4 9.7846e-3 2.7456e-2 4.0439e-2 4.3625e-2 2.5293e-2 0.5 1.6678e-2 4.9428e-2 7.8298e-2 9.3511e-2 6.3182e-2 0.6 2.6339e-2 8.2767e-2 1.4231e-1 1.9231e-1 1.6054e-1 0.7 3.9567e-2 1.3237e-1 2.4944e-1 3.9111e-1 4.3844e-1 0.8 5.7460e-2 2.0558e-1 4.2880e-1 8.0254e-1 1.3614e+0 0.9 8.1576e-2 3.1367e-1 7.3150e-1 1.6875e+0 5.1812e+0 Table 1: First-order corrections for near-priority queues…”

Section: Examplementioning

confidence: 99%

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Power series approximations for two-class generalized processor sharing systems

2010

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Abstract:We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are non-empty, a customer of queue 1 is served with probability β and a customer of queue 2 is served with probability 1 − β. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating function U (z 1 , z 2 ) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary value problems. Then, we propose to use the same functional equation to obtain a power series for U (z 1 , z 2 ) in β. The first coefficient of this power series corresponds to the priority case β = 0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations for the mean stationary queue lengths are obtained from combining truncated power series and Padé approximation.

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Section: Continuous-time Resultsmentioning

confidence: 98%

Section: Examplementioning

confidence: 99%

Power series approximations for two-class generalized processor sharing systems

2010

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“…Most of the existing papers (see e.g. Artalejo et al 2005;Atencia and Moreno 2005;Wang and Zhao 2007 and their references) investigate single server models of Geo/G/1-type and mainly follows the methodology introduced in Yang and Li (1995). As an exception, we mention a few recent papers dealing with the multiserver case (Artalejo and Lopez-Herrero 2007b;Artalejo et al 2008) and the use of matrix-analytic methods (Alfa 2006).…”

Section: Introductionmentioning

confidence: 97%

Performance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals

Artalejo

2009

Discrete Event Dyn Syst

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In this paper, we introduce a new discrete block state-dependent arrival (D-BSDA) distribution which provides fresh insights leading to a successful generalization of the discrete-time Markovian arrival process (D-MAP). The D-BSDA distribution is related to structured Markov chains and the method of stages. The consideration of this new discrete-time state-dependent block description gives one the ability of construct new stochastic models. The retrial queue analyzed in this paper gives an example of application of the D-BSDA distribution to construct more general and sophisticated models. We assume that the primary arrivals and the retrials follow the D-BSDA description and the service times are of discrete phasetype (PH). We study the underlying level dependent Markov chain of M/G/1-type at the epochs immediately after the slot boundaries. To this end, we employ the ULtype RG-factorization which provides an expression for the stationary probabilities. We also perform an analysis of waiting times. Numerical experiments are presented to study the system performance.

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“…Note that if the moments of the continuous-time queue exist, there always exists a sufficiently small ∆ such that the discretized queue is stable and the moments of the discretized queue exist as well. Related approaches to obtain results for continuous-time systems from discrete-time results can be found, e.g., in [2][3][4][5].…”

Section: Discrete-time Modelingmentioning

confidence: 99%

Rejoinder on: Queueing models for the analysis of communication systems

Bruneel

Fiems

Walraevens

et al. 2014

TOP

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First of all, we want to express our gratitude to the former Editor-in-Chief of the journal TOP, our fondly-remembered colleague Professor Jesús Artalejo, who invited us about one year ago to write a review paper for TOP on the topic of queueing models for the analysis of communication systems. Also, we want to thank the three discussants for the effort of carefully reading our paper and adding interesting information. We mention in particular the insightful discussion of Onno Boxma on the role of transform methods in queueing analysis, their strengths and weaknesses. With respect to scheduling disciplines, Onno Boxma also adds the topic of dynamic priority scheduling schemes. As far as traffic modeling is concerned, Alexander Dudin not only refers to the well-known D-BMAP model as an alternative description of bursty, correlated traffic streams, but he also points to several related papers on continuous-time models with session-based arrivals. Harry Perros emphasizes the practical applications of discrete-time queueing models in the performance evaluation of various subsystems of modern telecommunication networks. In particular, he discusses the restriction introduced by the assumption in our paper that packets be of fixed length, which makes the results applicable in the context of ATM, in optical burst switching, and in HTTP adaptive video streaming, but not in a general IP network where packets typically are of variable length.A very striking observation is that all three discussants explicitly comment on the use of discrete-time queueing models in much of our work of the last thirty years (including the current paper), as opposed to the much more frequently encountered continuous-time models in literature. As these remarks are of a very generic nature, we isolate this topic from the more specific comments in this rejoinder. Therefore, our responses are structured around two main topics: (1) the aspect of modeling and queueing analysis in the discrete time domain and (2) possible extensions of and remarks on our presented analysis of the two-class priority queue with train arrivals. * SMACS: Stochastic Modeling and Analysis of Communication Systems

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A discrete-time Geo[X]/G/1 retrial queue with control of admission

Cited by 43 publications

References 19 publications

Power series approximations for two-class generalized processor sharing systems

Power series approximations for two-class generalized processor sharing systems

Performance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals

Rejoinder on: Queueing models for the analysis of communication systems

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