Browsing by Author "Gómez-Corral, Antonio"
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PublicationA bibliographical guide to the analysis of retrial queues through matrix analytic techniques(Springer, 2006) Gómez-Corral, AntonioThis paper provides a bibliographical guide to researchers who are interested in the analysis of retrial queues through matrix analytic methods. It includes an author index and a subject index of research papers written in English and published in journals or collective publications, as well as some papers accepted for a forthcoming publication. PublicationA Markov chain model to investigate the spread of antibiotic-resistant bacteria in hospitals(2023-05-24) Chalub, Fabio A.C.C.; Gómez-Corral, Antonio; López-García, Martín; Palacios-Rodríguez, FátimaThis paper proposes a Markov chain model to describe the spread of a single bacterial species in a hospital ward where patients may be free of bacteria or may carry bacterial strains that are either sensitive or resistant to antimicrobial agents. The aim is to determine the probability law of the exact reproduction number Rexact,0 which is here defined as the random number of secondary infections generated by those patients who are accommodated in a predetermined bed before a patient who is free of bacteria is accommodated in this bed for the first time. Specifically, we decompose the exact reproduction number Rexact,0 into two contributions allowing us to distinguish between infections due to the sensitive and the resistant bacterial strains. Our methodology is mainly based on structured Markov chains and the use of related matrix-analytic methods. PublicationA matrix-geometric approximation for tandem queues with blocking and repeated attempts(Elsevier, 2002) Gómez-Corral, AntonioOur interest is in the study of the MAP/PH/1/1 --> (.)/PH/1/K + 1 queue with blocking and repeated attempts. The main feature of its infinitesimal generator is the spatial heterogeneity caused by the transitions due to successful repeated attempts. We develop an algorithmic solution by making a simplifying approximation which yields an infinitesimal generator which is spatially homogeneous and has a modified matrix-geometric stationary vector. The essential tool in our analysis is the general theory on quasi-birth-and-death processes. PublicationA note on the busy period of the M/G/1 queue with finite retrial group(Cambridge University Press, 2007-01) Artalejo, Jesús R.; Gómez-Corral, AntonioWe consider an M/G/1 retrial queue with finite capacity of the retrial group. We derive the Laplace transform of the busy period using the catastrophe method. This is the key point for the numerical inversion of the density function and the computation of moments. Our results can be used to approach the corresponding descriptors of the M/G/1 queue with infinite retrial group, for which direct analysis seems intractable. PublicationA state-dependent Markov-modulated mechanism for generating events and stochastic models(John Wiley and Sons, 2010-07-30) Artalejo, Jesús R.; 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. PublicationA stochastic SIS epidemic model with heterogeneous contacts(Elsevier, 2015-03-01) Economou, A.; Gómez-Corral, Antonio; López-García, M.A stochastic model for the spread of an SIS epidemic among a population consisting of N individuals, each having heterogeneous infectiousness and/or susceptibility, is considered and its behavior is analyzed under the practically relevant situation when N is small. The model is formulated as a finite time-homogeneous continuous-time Markov chain X. Based on an appropriate labeling of states, we first construct its infinitesimal rate matrix by using an iterative argument, and we then present an algorithmic procedure for computing steady-state measures, such as the number of infected individuals, the length of an outbreak, the maximum number of infectives, and the number of infections suffered by a marked individual during an outbreak. The time till the epidemic extinction is characterized as a phase-type random variable when there is no external source of infection, and its Laplace-Stieltjes transform and moments are derived in terms of a forward elimination backward substitution solution. The inverse iteration method is applied to the quasi-stationary distribution of X, which provides a good approximation of the process X at a certain time, conditional on non-extinction, after a suitable waiting time. The basic reproduction number R-0 is defined here as a random variable, rather than an expected value. PublicationA tandem queue with blocking and Markovian Arrival Process(Springer, 2002) Gómez-Corral, AntonioQueueing networks with blocking have proved useful in modelling of data communications and production lines. We study such a network consisting of a sequence of two service stations with an infinite queue allowed before the first station and no intermediate queue allowed between them. This restriction results in the blocking of the first station whenever a unit having completed its service in that station cannot enter into the second one due to the presence of another unit there. The input of units to the network is the MAP (Markovian Arrival Process). At the first station, service requirements are of phase type whereas service times at the second station are arbitrarily distributed. The focus is on the embedded process at departures. The essential tool in our analysis is the general theory on Markov renewal processes of M/G/1-type. PublicationA Within-Host Stochastic Model for Nematode Infection(MDPI, 2018-08-21) Gómez-Corral, Antonio; López-García, M.We propose a stochastic model for the development of gastrointestinal nematode infection in growing lambs under the assumption that nonhomogeneous Poisson processes govern the acquisition of parasites, the parasite-induced host mortality, the natural (no parasite-induced) host mortality and the death of parasites within the host. By means of considering a number of age-dependent birth and death processes with killing, we analyse the impact of grazing strategies that are defined in terms of an intervention instant t0, which might imply a move of the host to safe pasture and/or anthelmintic treatment. The efficacy and cost of each grazing strategy are defined in terms of the transient probabilities of the underlying stochastic processes, which are computed by means of Strang–Marchuk splitting techniques. Our model, calibrated with empirical data from Uriarte et al. and Nasreen et al., regarding the seasonal presence of nematodes on pasture in temperate zones and anthelmintic efficacy, supports the use of dose-and-move strategies in temperate zones during summer and provides stochastic criteria for selecting the exact optimum time instant t (sub index 0) when these strategies should be applied. PublicationA. B. Clarke's Tandem Queue Revisited-Sojourn Times(Taylor & Francis, 2008) Gómez-Corral, Antonio; Escribano Martos, Manuel DavidIn telecommunications, packets or units may complete their service in a different order from the one in which they enter the station. In order to reestablish the original order resequencing protocols need to be implemented. In this article, the focus is on a two-server resequencing system with heterogeneous servers and two buffers. One buffer has an infinite capacity to hold the incoming units. The other with a finite capacity is used to resequence the serviced units. This is to maintain the order of departure of the units according to the order of their arrivals. To analyze this resequencing model, we introduce an equivalent two-stage queueing system, namely A. B. Clarke's Tandem Queue, in which the arriving units receive service from only one server, and the units departing from the first stage may be temporally prevented from leaving by occupied service units at the second stage. Our interest is to study the resequencing delay and the sojourn time as times until absorption in suitably defined quasi-birth-and-death processes and continuous-time Markov chains. PublicationAlgorithmic analysis of the Geo/Geo/c retrial queue(Elsevier Science, 2008-09-16) Artalejo, Jesús R.; Economou, A.; Gómez-Corral, AntonioIn 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. PublicationAnalysis of a single-server retrial queue with quasi-random input and nonpreemptive priority(Pergamon-Elsevier Science Ltd, 2002-07-06) Gómez-Corral, AntonioIn this paper, we model a single-server retrial queue with quasi-random input and two priority classes. In the case of blocking, a high priority unit is queued, whereas a low priority unit joins the orbit to start generating a Poisson flow of repeated attempts until it finds the server free. Since units in orbit will be served only when the high priority queue is empty, high priority units have nonpreemptive priority over low priority units. We present a simple analysis for the outside observer distribution of the system state as well as for the arriving unit distribution in steady state. Besides, we give numerical examples to illustrate the effect of the parameters on several performance characteristics. PublicationAnalysis of a stochastic clearing system with repeated attempts(Taylor & Francis Group, 1998) Artalejo, Jesús R.; Gómez-Corral, AntonioA stochastic clearing system is characterized by the existence of an output mechanism that instantaneously clears the system, i.e. removes all work currently present. In this paper we study the stochastic behavior of a single server clearing queue in wich customers cannot be continuosly in contact with the server, but can reinitiate the demand some time later. We develop a comprehensive analysis of the system including its limiting behavior, busy period, and waiting time. PublicationAnalysis of multiserver queues with constant retrial rate(Elsevier Science, 2001) Artalejo, Jesús R.; Gómez-Corral, Antonio; Neuts, M.F.We consider multiserver retrial queues in which the time between two successive repeated attempts is independent of the number of customers applying for service. We study a Markovian model where each arriving customer finding any free server either enters service or leaves the service area and joins a pool of unsatisfied customers called 'orbit'. This system is analyzed as a quasi-birth-and-death (QBD) process and its main performance characteristics are efficiently computed. PublicationApplications of maximum queue lengths to call center management(Pergamon-Elsevier Science Ltd, 2007-04) Artalejo, Jesús R.; Economou, A.; Gómez-Corral, AntonioThis paper deals with the distribution of the maximum queue length in two-dimensional Markov models. In this framework, two typical assumptions are: (1) the stationary regime, and (2) the system homogeneity (i.e., homogeneity of the underlying infinitesimal generator). In the absence of these assumptions, the computation of the stationary queue length distribution becomes extremely intricate or, even, intractable. The use of maximum queue lengths provides an alternative queueing measure overcoming these problems. We apply our results to some problems arising from call center management. PublicationChannel idle periods in computer and telecommunication systems with customer retrials(Kluwer Academic, 2003) Artalejo, Jesús R.; Gómez-Corral, AntonioNew developments in mobile communication technology lead to substantial increases in the retrial phenomenon and its effect on the quality of service (QoS). One aspect of this problem is considered in this paper, where we investigate the distribution of the channel idle periods between two successive connections. PublicationComputation of the limiting distribution in queueing systems with repeated attempts and disasters(EDP Sciences, 1999) Artalejo, Jesús R.; Gómez-Corral, AntonioSingle 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. PublicationControl strategies for a stochastic model of host-parasite interaction in a seasonal environment(Elsevier, 2014-08-07) Gómez-Corral, Antonio; López-García, M.We examine a nonlinear stochastic model for the parasite load of a single host over a predetermined time interval. We use nonhomogeneous Poisson processes to model the acquisition of parasites, the parasite-induced host mortality, the natural (no parasite-induced) host mortality, and the reproduction and death of parasites within the host. Algebraic results are first obtained on the age-dependent distribution of the number of parasites infesting the host at an arbitrary time t. The interest is in control strategies based on isolation of the host and the use of an anthelmintic at a certain intervention instant t(0). This means that the host is free living in a seasonal environment, and it is transferred to a uninfected area at age t(0). In the uninfected area, the host does not acquire new parasites, undergoes a treatment to decrease the parasite load, and its natural and parasite-induced mortality are altered. For a suitable selection of t(0), we present two control criteria that appropriately balance effectiveness and cost of intervention. Our approach is based on simple probabilistic principles, and it allows us to examine seasonal fluctuations of gastrointestinal nematode burden in growing lambs. PublicationExtinction times and size of the surviving species in a two-species competition process(Springer Verlag, 2012-02-01) Gómez-Corral, Antonio; López-García, M.We investigate a stochastic model for the competition between two species. Based on percentiles of the maximum number of individuals in the ecosystem, we present an approximating model for which the extinction time can be thought of as a phase-type random variable. We determine formulae for the probabilities of extinction and the moments of the extinction time. We discuss the use of several quasi-stationary assumptions. We include a comparative study between existing asymptotic results, results obtained from a simulation of the process, and our solution. PublicationExtreme values in SIR epidemic models with two strains and cross-immunity(AIMS Press, 2019-03-08) Amador Pacheco, Julia; Armesto, D.; Gómez-Corral, AntonioThe paper explores the dynamics of extreme values in an SIR (susceptible → infectious → removed) epidemic model with two strains of a disease. The strains are assumed to be perfectly distinguishable, instantly diagnosed and each strain of the disease confers immunity against the second strain, thus showing total cross-immunity. The aim is to derive the joint probability distribution of the maximum number of individuals simultaneously infected during an outbreak and the time to reach such a maximum number for the first time. Specifically, this distribution is analyzed by distinguishing between a global outbreak and the local outbreaks, which are linked to the extinction of the disease and the extinction of particular strains of the disease, respectively. Based on the mass function of the maximum number of individuals simultaneously infected during the outbreak, we also present an iterative procedure for computing the final size of the epidemic. For illustrative purposes, the twostrain SIR-model with cross-immunity is applied to the study of the spread of antibiotic-sensitive and antibiotic-resistant bacterial strains within a hospital ward.