Person: Artalejo Rodríguez, Jesús Manuel
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First Name
Jesús Manuel
Last Name
Artalejo Rodríguez
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Area
Estadística e Investigación Operativa
Identifiers
8 results
Search Results
Now showing 1 - 8 of 8
Item 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, HeThis 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.Item 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.Item On a single server queue with negative arrivals and request repeated(Journal of Applied Probability, 1999) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, AntonioThere 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.Item Performance analysis of a single-server queue with repeated attempts(Mathematical and Computer Modelling, 1999) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, AntonioThis 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.Item 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, AntonioIn 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.Item Information theoretic analysis for queueing systems with quasi-random input(Mathematical and Computer Modelling, 1995) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, AntonioIn 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.Item Modelling communication systems with phase type service and retrial times(IEEE Communications letters, 2007) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, AntonioThe 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.Item Steady state solution of a single-server queue with linear repeated requests(Journal of Applied Probability, 1997) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, AntonioQueueing systems with repeated requests have many useful applications in communications and computer systems modeling. In the majority of previous work the repeat requests are made individually by each unsatisfied customer. However, there is in the literature another type of queueing situation, in which the time between two successive repeated attempts is independent of the number of customers applying for service. This paper deals with the M/G/1 queue with repeated orders in its most general setting, allowing the simultaneous presence of both types of repeat requests. We first study the steady state distribution and the partial generating functions. When the service time distribution is exponential we show that the performance characteristics can be expressed in terms of hypergeometric functions.