Person:
Artalejo Rodríguez, Jesús Manuel

First Name

Jesús Manuel

Last Name

Artalejo Rodríguez

URI

https://hdl.handle.net/20.500.14352/82709

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Area

Estadística e Investigación Operativa

Identifiers

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Now showing 1 - 10 of 19

Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue
(Journal of Applied Mathematics and Stochastic Analysis, 1996) Gómez-Corral, Antonio; Artalejo Rodríguez, Jesús Manuel
This paper is concerned with the stochastic analysis of the departure and quasi-input processes of a Markovian single-server queue with negative exponential arrivals and repeated attempts. Our queueing system is characterized by the phenomenon that a customer who finds the server busy upon arrival joins an orbit of unsatisfied customers. The orbiting customers form a queue such that only a customer selected according to a certain rule can reapply for service. The intervals separating two successive repeated attempts are exponentially distributed with rate α+jμ, when the orbit size is j≥1. Negative arrivals have the effect of killing some customer in the orbit, if one is present, and they have no effect otherwise. Since customers can leave the system without service, the structural form of type M/G/1 is not preserved. We study the Markov chain with transitions occurring at epochs of service completions or negative arrivals. Then we investigate the departure and quasi-input processes.
Markovian arrivals in stochastic modelling: a survey and some new results
(Sort: Statistics and Operations Research Transactions, 2010) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio; Qi-Ming, He
This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, non-homogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension.
Algorithmic analysis of the Geo/Geo/c retrial queue
(European journal of operational research, 2008) Artalejo Rodríguez, Jesús Manuel; Economou, A.; Gómez-Corral, Antonio
In this paper, we consider a discrete-time queue of Geo/Geo/c type with geometric repeated attempts. It is known that its continuous counterpart, namely the M/M/c queue with exponential retrials, is analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused from the retrial feature. In discrete-time, the occurrence of multiple events at each slot increases the complexity of the model and raises further computational difficulties. We propose several algorithmic procedures for the efficient computation of the main performance measures of this system. More specifically, we investigate the stationary distribution of the system state, the busy period and the waiting time. Several numerical examples illustrate the analysis.
Stochastic descriptors to study the fate and potential of naive T cell clonotypes in the periphery
(Journal of Mathematical Biology, 2016) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio; López-García, M.; Molina París, C.
The population of naive T cells in the periphery is best described by determining both its T cell receptor diversity, or number of clonotypes, and the sizes of its clonal subsets. In this paper, we make use of a previously introduced mathematical model of naive T cell homeostasis, to study the fate and potential of naive T cell clonotypes in the periphery. This is achieved by the introduction of several new stochastic descriptors for a given naive T cell clonotype, such as its maximum clonal size, the time to reach this maximum, the number of proliferation events required to reach this maximum, the rate of contraction of the clonotype during its way to extinction, as well as the time to a given number of proliferation events. Our results show that two fates can be identified for the dynamics of the clonotype: extinction in the short-term if the clonotype experiences too hostile a peripheral environment, or establishment in the periphery in the long-term. In this second case the probability mass function for the maximum clonal size is bimodal, with one mode near one and the other mode far away from it. Our model also indicates that the fate of a recent thymic emigrant (RTE) during its journey in the periphery has a clear stochastic component, where the probability of extinction cannot be neglected, even in a friendly but competitive environment. On the other hand, a greater deterministic behaviour can be expected in the potential size of the clonotype seeded by the RTE in the long-term, once it escapes extinction.
On a single server queue with negative arrivals and request repeated
(Journal of Applied Probability, 1999) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio
There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Hanison and Pitel (1996) investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the Limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary 'truncated' system which can easily be evaluated with the help of a regenerative approach.
Performance analysis of a single-server queue with repeated attempts
(Mathematical and Computer Modelling, 1999) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio
This paper is concerned with the performance evaluation of a single-server queue with repeated attempts and disasters. Our queueing system is characterized by the phenomenon that a customer who finds the server busy upon arrival joins a group of unfilled customers called 'orbit' and repeats his request after some random time. In addition, we consider in this paper the possibility of disasters. When a disaster occurs, all the work (and therefore customers) in the system is destroyed immediately. Our queueing system can be used to model the behaviour of a buffer in computers with virus infections.
A state-dependent Markov-modulated mechanism for generating events and stochastic models
(Mathematical Methods in the Applied Sciences, 2010) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio
In this paper, we introduce a versatile block-structured state-dependent event (BSDE) approach that provides a methodological tool to construct non-homogeneous Markov-modulated stochastic models. Alternatively, the BSDE approach can be used to construct even a part (e.g. the arrival process) of the model. To illustrate the usefulness of the BSDE approach, several arrival patterns as well as queueing and epidemic models are considered. In particular, we deal with a state-dependent quasi-birth-and-death process that gives a constructive generalization of the scalar birth-and-death process and the homogeneous quasi-birth-and-death process.
Information theoretic analysis for queueing systems with quasi-random input
(Mathematical and Computer Modelling, 1995) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio
In this paper, information theoretic inference methodology for system modeling is applied to estimate the stationary distribution for the number of customers in single server queueing systems with service capacity utilized by a finite population. The customers demand i.i.d. service times. Three different models are considered. In Model I, a customer who finds the server busy can be queued, whereas in Models II and III, any customer finding the server busy upon arrival will make repeated attempts to enter service until he eventually finds the server free. Models II and III differ in the retrial policy. Numerical examples illustrate the accuracy of the proposed maximum entropy estimation when it is compared with the classical analysis.
Computation of the limiting distribution in queueing systems with repeated attempts and disasters
(RAIRO - Recherche opérationnelle - Operations Research, 1999) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio
Single server queues with repeated attempts are useful in the modeling of computer and telecommunication systems. In addition, we consider iii this paper the possibility of disasters. When a disaster occurs, all the customers present in the sq stein are destroyed immediately. Using a regenerative approach, we derive a numerically stable recursion scheme for the stare probabilities. This model can be employed to analyze the behaviour of a buffer in computers with virus infections.
Modelling communication systems with phase type service and retrial times
(IEEE Communications letters, 2007) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio
The retrial phenomenon and its significant effect on network performance have been taking into account in the literature (e.g., random access protocols in computer networks, cellular mobile telephony). Most studies assume exponential distributions to guarantee the tractability of the mathematical model. However, this is a serious drawback in practice where the exponentiality is not a realistic assumption. The objective is to find a good balance between realistic assumptions and tractability. In this paper, the objective is achieved by proposing a multichannel queueing model with quasi-random input and retrial and service times of phase type.