Jesús R. Artalejo 1963–2013

On June 12, 2013, Jesús R. Artalejo passed away unexpectedly while he was attending the Annual Meeting and Conference of the Society for Mathematical Biology in Tempe, Arizona. At the time of his disappearance, he was one of the Editors-in-Chief of TOP, jointly with Miguel A. Goberna.

Jesús led an extremely active mathematical life producing more than one hundred papers and one book, serving a wide variety of journals in various editorial roles, coordinating the scientific activities of the Stochastic Modelling Group at the Complutense University of Madrid (UCM), and supervising a few masters and Ph.D. students. He seemed to spend a sizeable fraction of every year traveling to conferences and meetings around the world. These lines touche on his outstanding personality and his contribution to Queuing Theory, which has been internationally renowned.

FormalPara Biographical data and scientific contributions

Jesús was born in Madrid, Spain, on January 29, 1963, and pursued a relevant and intense career as a mathematician. In the fall of 1981, he started his studies at UCM, where he got his Bachelor Degree in 1986, and where he also became an assistant. He was then a Ph.D. student with Professor Miguel Martín as advisor, and presented his thesis on April 8, 1991. He was also an assistant at the Carlos III University of Madrid from October 1990 through September 1991. Later he was an associate professor at UCM in the period October 1991–March 2003, and he was appointed full professor at UCM from March 31, 2003.

Jesús became soon known as a promising researcher in queuing theory, where his doctoral thesis [2] was an important starting point with new results in retrial queues. In the early 1990s, he and Gennadi Falin, already then a renowned expert in retrial queues, initiated a fruitful exchange program between UCM and the Moscow State University that enriched the Ph.D. students of the Department of Statistics and Operations Research at UCM. He was one of the first people in the department to understand the important role that the scientific exchange with foreign colleagues might have on his own research and that of his collaborators. His list of publications contains, in chronological order, collaborations with Gennadi Falin (Moscow State University, see e.g. [7,10,19,25,52]), Marcel Neuts (The University of Arizona, see [41,46]), Vladimir Anisimov (Bilkent University, see [47,51]), Achyutha Krishnamoorthy (Cochin University of Science and Technology, see [55,73]), Onésimo Hernández-Lerma (CINVESTAV, see [56]), Antonis Economou (University of Athens, see, e.g. [70,77,78,82,88]), Srinivas Chakravarthy (Kettering University, see [74,75,76,81]), Quan-Lin Li (Tsinghua University, see [99]), Jacques Resing (Eindhoven University of Technology, see [101]) and Qi-Ming He (University of Waterloo, see [104]), among others. Jesús always turned every professional collaboration into an enriching personal experience. For that reason, there were strong links between him and his coauthors, who became his friends. His publications have covered a wide range of topics in queuing theory, such as retrial queues (see, e.g. [7,22,52,54,78]), discrete-time queues [68,83,88,99], impatient customers [16], inventory systems with repeated attempts [73], matrix-analytic techniques applied to queueing models (see, e.g. [41,46,74,75,76,77,93,107]), maximum entropy solutions in queuing (see, e.g. [9,13,44,62,66]), mean value analysis [101], negative arrivals [23,34,39,47], optimal control [56,59], optimality of D-, N-, and T-policies [21,43,53], and unreliable servers [8,28,29]. A most recent sphere of activity has been stochastic modeling of biological systems (see, e.g. [86,103,106,111,115,116,117]), and the use of quasi-stationary and ratio of expectations distributions in epidemic models (see [102,112,119]). A list of his publications up to the year 2013, which contains his work in progress, is appended for specific reference; each item on this list is accompanied by keywords that will allow the reader to identify the model under consideration, the techniques used, and those descriptors in study.

Starting in October 1997, Jesús served during three years as the coordinator of the European project entitled “Advances in Retrial Queueing Theory,” funded by INTAS.¹ The work program was built on the topic retrial queues, and was the result of arduous but rewarding negotiations between him and Maria Fernanda Ramalhoto (IST–Technical University of Lisbon), Henk Tijms (Vrije University of Amsterdam), Vladimir Anisimov (Kiev National University), Pavel Bocharov (Peoples’ Friendship University of Russia), Alexander Dudin (Belarus State University), and Gennadi Falin (Moscow State University). Later they welcomed Christos Langaris and his team (University of Ioannina). To facilitate the exchange of information between researchers, three technical meetings were organized in Madrid (September 1998), Minsk (June 1999), and Amsterdam (March 2000), known as “International Workshops on Retrial Queues” (WRQ). An important part of the research developed within the INTAS project was published in his monograph on “Retrial Queueing Systems: A Computational Approach” (Springer-Verlag, 2008), written jointly with A. Gómez-Corral, which appropriately complements the analytical treatment of the book by G.I. Falin and J.G.C. Templeton entitled “Retrial Queues” (Chapmann & Hall, 1997). His professional interaction with colleagues within the INTAS project resulted in a sincere friendship with some of them, especially with Rein Nobel and Henk Tijms, which transcended even their families.

After completing the INTAS project, Jesús took the initiative to continue organizing the subsequent WRQ editions in Cochin (December 2002, jointly with A. Krishnamoorthy), Seoul (September 2004, jointly with B.D. Choi), Miraflores de la Sierra (July 2006, jointly with A. Gómez-Corral), Athens (July 2008, jointly with A. Economou), Beijing (July 2010, jointly with Q.L. Li) and Seville (July 2012, jointly with P. Moreno). The next WRQ edition is planned to take place in Tokyo and his chairman, Tuan Phung-Duc, will dedicate the workshop to the memory of Jesús. Jesús has received well-merited recognition for the organization of the series of conferences known as Madrid Conferences on Queueing Theory (MCQT). He was particularly proud to bring together internationally recognized researchers and promising researchers, regardless of their countries of origin, and he always did his best to get financial support for those most disadvantaged participants. He felt that the success of the MCQT editions of 2002, 2006, and 2010 depended primarily on the plenary and invited speakers, whom he sincerely thanked them for their contributions.

Jesús has labored mightily in the editorial vineyard. He served as one of the Editors-in-Chief of TOP, jointly with Miguel A. Goberna, since 2013. He was the Area Editor responsible for Stochastic Models and Simulation of the Asia-Pacific Journal of Operational Research in 2005–2006, and the Editor of the European Journal of Operational Research responsible for Stochastic and Statistics, Queuing and Simulation in 2007–2010. He was Associate Editor of Applied Mathematical Modelling since 2012, Asia-Pacific Journal of Operational Research in 2000–2004, Computers & Operations Research since 2003, European Journal on Computational Optimization since 2012, Journal of Applied Mathematics and Stochastic Analysis in 2000–2009, Operational Research since 2008, Opsearch in 2001–2002, Quality Technology & Quantitative Management in 2003–2009, Queueing Systems in 2003–2009, Revista Matemática Complutense in 1999–2004, Statistics and Operations Research Transactions since 2003, and TOP in 1995–2012. In addition, he was a Guest Editor of Annals of Operations Research (Volumes 112–113, 2002; Volume 141, 2006; Volume 162, 2008), Computers & Operations Research (Volume 35, Issue 8, 2008), European Journal of Operational Research (Volume 189, Issue 3, 2008, jointly with A. Gómez-Corral), Mathematical and Computer Modelling (Volume 30, Issues 3–4, 1999), Quality Technology & Quantitative Management (Volume 5, Issues 1–2, 2008, jointly with A. Economou), Queueing Systems (Volume 56, Issues 3–4, 2007), and TOP (Volume 7, No. 2, 1999; Volume 19, No. 2, 2011). At the time of his death, he and Pilar Moreno were concluding a special issue for Asia-Pacific Journal of Operational Research, associated with the last WRQ edition held in Seville. He also co-edited the book entitled Advances in Stochastic Modelling (Notable Publications, Inc., 2002) with A. Krishnamoorthy. His high standards, efficiency and integrity as editor have always been greatly respected by his professional colleagues.

FormalPara Farewell to a friend

I want to take this opportunity to say something about Jesús as a person. Many persons have testified to his positive view of life, his sarcastic humor, and to his genuine interest in people he met. Many of us knew Jesús through his passions: his love for his family, his love of travel, and his commitment to excellence in all things. At the center of all these passions was a deeply caring person. This is what I think of first when I think of my friend.

For his friends and colleagues around the world, his disappearance is a severe loss. For me personally, his unexpected departure seems unreal. I shall remember him with joy and gratitude as long as I live.

Publications of Jesús R. Artalejo

[1]:

Políticas de control para el sistema M ^[g]/G/1. In: Actas de la XVIII Reunión Nacional de Estadística, Investigación Operativa e Informática, pp. 417–421. (In Spanish)

Keywords: bulk arrivals; M ^[X]/G/1 queue; optimality of T-policy.

[2]:

Contribuciones al Análisis de los Sistemas de Colas con Reintentos. Doctoral thesis. Department of Statistics and Operations Research, Complutense University of Madrid. (In Spanish)

Keywords: breakdown of the server; busy period; convolutive equations; maximum entropy; M/G/1 and M/M/c retrial queues; steady-state.

[3]:

Métodos convolutivos en sistemas de colas con reintentos. In: Actas de las XV Jornadas Luso-Espanholas de Matemática, Vol. IV, pp. 67–72. (In Spanish)

Keywords: busy period; convolutive equations; M/M/2 retrial queue; quasi-random input.

[4]:

A unified cost function for M/G/1 queueing systems with removable server. Trabajos de Investigación Operativa 7, 95–104.

Keywords: M/G/1 queue; optimality of D-, N- and T-policies.

[5]:

Information theoretic approximations for retrial queueing systems. In: Transactions of the 11th Prague Conference, Kubik S. and Vísek J.A. eds., Kluwer Academic Publishers, pp. 263–270.

Keywords: M/G/1 retrial queue; maximum entropy; steady state.

[6]:

Explicit formulae for the characteristics of the M/H ₂/1 retrial queue. Journal of the Operational Research Society 44, 309–313.

Keywords: busy period; convolutive equations; M/H ₂/1 retrial queue; steady state.

[7]:

(With G.I. Falin and M. Martín) On the single server retrial queue with priority customers. Queueing Systems 14, 439–455.

Keywords: head-of-the-line priority; heavy traffic; high and low rates of retrials; M ₂/G ₂/1 retrial queue; steady state; stochastic decomposition.

[8]:

New results in retrial queueing systems with breakdown of the servers. Statistica Neerlandica 48, 23–36.

Keywords: breakdown of the server; high rate of retrials; M/G/1 and M/M/c retrial queues; persistence function; preemptive priority; steady state.

[9]:

(With G.I. Falin and M. Martín) Information theoretic approximations for the M/G/1 retrial queue. Acta Informatica 31, 559–571.

Keywords: M/G/1 retrial queue; maximum entropy; steady state.

[10]:

(With G.I. Falin) Stochastic decomposition for retrial queues. Top 2, 329–342.

Keywords: high rate of retrials; M/G/1 retrial queue; stochastic decomposition.

[11]:

(With A. Gómez-Corral) Analysis of the modes of the stationary distribution in single server retrial queues with quasi-random input. In: Transactions of the 12th Prague Conference, Lachout P. and Vísek J.A. eds., pp. 24–27.

Keywords: M/M/1 retrial queue; quasi-random input; steady state.

[12]:

(With M. Martín) A maximum entropy analysis of the M/G/1 queue with constant repeated attempts. In: Selected Topics on Stochastic Modelling, Gutiérrez R. and Valderrama M. eds., World Scientific, pp. 181–190.

Keywords: constant retrial policy; M/G/1 retrial queue; maximum entropy; number of retrials.

[13]:

(With A. Gómez-Corral) Information theoretic analysis for queueing systems with quasi-random input. Mathematical and Computer Modelling 22, 65–76.

Keywords: M/G/1 queue; M/G/1 retrial queue; maximum entropy; quasi-random input; steady state.

[14]:

A queueing system with returning customers and waiting line. Operations Research Letters 17, 191–199.

Keywords: M/M/c retrial queue; RTA approximation; steady state.

[15]:

(With G.I. Falin) Approximations for multiserver queues with balking/retrial discipline. OR Spektrum 17, 239–244.

Keywords: diffusion approximation; M/M/c retrial queue; RTA approximation; steady state.

[16]:

(With M. Martín) Analysis of an M/G/1 queue with two types of impatient units. Advances in Applied Probability 27, 840–861.

Keywords: busy period; constant retrial policy; embedded Markov chain; fundamental period; impatience; M ₂/G ₂/1 retrial queue; number of blocked repeated attempts; steady state; Takács’ equation; waiting time.

[17]:

(With A. Gómez-Corral) Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue. Journal of Applied Mathematics and Stochastic Analysis 9, 171–183.

Keywords: departure process; embedded Markov chain; linear retrial policy; M/M/1 retrial queue; negative arrivals; quasi-input process; steady state.

[18]:

Stationary analysis of the characteristics of the M/M/2 queue with constant repeated attempts. Opsearch 33, 83–95.

Keywords: constant retrial policy; M/M/2 retrial queue; steady state; waiting time.

[19]:

(With G.I. Falin) On the orbit characteristics of the M/G/1 retrial queue. Naval Research Logistics 43, 1147–1161.

Keywords: M/G/1 retrial queue; orbit and idle periods.

[20]:

Retrial queues with negative arrivals. In: Proceedings of the International Conference on Stochastic Processes, Krishnamoorthy A. ed., pp. 159–167.

Keywords: linear retrial policy; M/G/1 and M/M/1 retrial queues; negative arrivals; steady state.

[21]:

Analysis of an M/G/1 queue with constant repeated attempts and server vacations. Computers and Operations Research 24, 493–504.

Keywords: embedded Markov chain; M/G/1 retrial queue; optimality of N- and T-policies; PASTA property; server vacations; stochastic decomposition.

[22]:

(With A. Gómez-Corral) Steady state solution of a single-server queue with linear repeated requests. Journal of Applied Probability 34, 223–233.

Keywords: linear retrial policy; M/G/1 retrial queue; steady state.

[23]:

(With A. Gómez-Corral) Generalized birth and death processes with applications to queues with repeated attempts and negative arrivals. OR Spektrum 20, 5–14.

Keywords: birth and death process; busy period; convolutive equations; head-of-the-line priority; linear retrial policy; M/M/1 retrial queue; negative arrivals; steady state; waiting time.

[24]:

(With A. Gómez-Corral) Analysis of a stochastic clearing system with repeated attempts. Stochastic Models 14, 623–645.

Keywords: busy period; catastrophes; M/G/1 retrial queue; steady state; waiting time.

[25]:

(With G.I. Falin) A finite source retrial queue. European Journal of Operational Research 108, 409–424.

Keywords: arriving customer’s distribution; busy period; discrete transformations; outside observer’s distribution; quasi-random input; waiting time.

[26]:

Retrial queues with a finite number of sources. Journal of the Korean Mathematical Society 35, 503–525.

Keywords: a survey on finite source retrial queues, concentrating on M/M/c//K and M/G/1//K retrial queues with quasi-random input.

[27]:

Some results on the M/G/1 with N-policy. Asia-Pacific Journal of Operational Research 15, 147–157.

Keywords: M/G/1 queue; N-policy; stochastic decomposition; waiting time.

[28]:

(With A. Aissani) On the single server retrial queue subject to breakdowns. Queueing Systems 30, 309–321.

Keywords: breakdown of the server; fundamental server period; M/G/1 retrial queue; steady state; stochastic decomposition.

[29]:

(With A. Gómez-Corral) Unreliable retrial queues due to service interruptions arising from facsimile networks. Belgian Journal of Operations Research, Statistics and Computer Science 38, 31–41.

Keywords: breakdown of the server; linear retrial policy; M/G/1 retrial queue; steady state.

[30]:

Accessible bibliography on retrial queues. Mathematical and Computer Modelling 30, 1–6.

Keywords: a bibliography on retrial queues including references (books and papers published in scientific journals) written in English.

[31]:

(With A. Gómez-Corral) Performance analysis of a single-server queue with repeated attempts. Mathematical and Computer Modelling 30, 79–88.

Keywords: busy period; catastrophes; linear retrial policy; M/M/1 retrial queue; steady state.

[32]:

(With A. Gómez-Corral) Computation of the limiting distribution in queueing systems with repeated attempts and disasters. RAIRO 33, 371–382.

Keywords: linear retrial policy; M/G/1 retrial queue; regenerative analysis; state-dependent arrivals; steady state.

[33]:

A classified bibliography of research on retrial queues: Progress in 1990–1999. Top 7, 187–211.

Keywords: a classified bibliography of the work on retrial queues performed in the period 1990–1999, which consists of an author classification and a subject classification.

[34]:

(With A. Gómez-Corral) On a single server queue with negative arrivals and request repeated. Journal of Applied Probability 36, 907–918.

Keywords: Fredholm integral equation; linear retrial policy; M/G/1 retrial queue; negative arrivals; regenerative analysis; steady state.

[35]:

Numerical investigation of multiserver retrial queues operating under the constant retrial policy. In: Proceedings of the 15th Belarussian Workshop on Queueing Theory & 2nd International Workshop on Retrial Queues, pp. 13–16.

Keywords: constant retrial policy; M/M/c retrial queue; QBD process; steady state.

[36]:

(With A. Rodrigo). On the single server queue with linear retrial policy and exhaustive vacations. In: Stochastic Processes and their Applications, Vijayakumar A. and Sreenivasan M. eds., Narosa Publishing House, pp. 196–205.

Keywords: linear retrial policy; M/G/1 retrial queue; regenerative analysis; server vacations; steady state.

[37]:

(With M.J. López-Herrero) On the busy period of the M/G/1 retrial queue. Naval Research Logistics 47, 115–127.

Keywords: busy period; M/G/1 retrial queue; second moment.

[38]:

(With M.J. López-Herrero) On the single server retrial queue with balking. Infor 38, 33–50.

Keywords: balking; linear retrial policy; M/G/1 and M/M/1 retrial queues; regenerative analysis; steady state.

[39]:

G-networks: A versatile approach for work removal in queueing networks. European Journal of Operational Research 126, 233–249.

Keywords: a survey on queueing networks with negative arrivals.

[40]:

(With V. Rajagopalan and R. Sivasamy) On finite Markovian queues with repeated attempts. Investigación Operativa 9, 83–94.

Keywords: finite QBD process; state-dependent events; steady state.

[41]:

(With A. Gómez-Corral and M.F. Neuts) Numerical analysis of multiserver retrial queues operating under a full access policy. In: Advances in Algorithmic Methods for Stochastic Models, Latouche G. and Taylor P.G. eds., Notable Publications Inc., NJ, pp. 1–19.

Keywords: full access policy; M/M/c retrial queue; QBD process; steady state; successful, vain and ideal retrials.

[42]:

(With M.J. López-Herrero) Low retrial analysis of multiserver queues with repeated attempts due to impatience. In: Proceedings of the 12th European Simulation Symposium, Möller D.F.P. ed., A Publication of the Society for Computer Simulation International, pp. 535–538.

Keywords: diffusion approximation; impatience; low rate of retrials; M/M/c retrial queue; RTA approximation.

[43]:

The D-policy for the M/G/1 queue: Queue length and optimality. Electronic Modeling 23, 35–43.

Keywords: M/G/1 and M/M/1 queues; optimality of D-, N- and T-policies; regenerative analysis; steady state.

[44]:

(With M.J. López-Herrero) Analysis of the busy period for the M/M/c queue: An algorithmic approach. Journal of Applied Probability 38, 209–222.

Keywords: busy period; M/M/c queue; maximum entropy; number of customers served.

[45]:

(With A.N. Dudin and V.I. Klimenok) Stationary analysis of a retrial queue with preemptive repeated attempts. Operations Research Letters 28, 173–180.

Keywords: M/M/1 retrial queue; preemptive priority; steady state.

[46]:

(With A. Gómez-Corral and M.F. Neuts) Analysis of multiserver queues with constant retrial rate. European Journal of Operational Research 135, 569–581.

Keywords: constant retrial policy; M/M/c retrial queue; optimization of the retrial rate; QBD process; steady state.

[47]:

(With V.V. Anisimov) Analysis of Markov multiserver retrial queues with negative arrivals. Queueing Systems 39, 157–182.

Keywords: averaging principle; constant and linear retrial policies; negative arrivals; overloading case; QBD process; steady state.

[48]:

On the M/G/1 queue with D-policy. Applied Mathematical Modelling 25, 1055–1069.

Keywords: D-policy; M/G/1 and M/M/1 queues; regenerative analysis; steady state.

[49]:

(With M.J. López-Herrero) On the M/G/1 queue with quadratic repeated attempts. Statistical Methods 3, 60–78.

Keywords: M/G/1 and M/M/1 retrial queues; quadratic retrial policy; regenerative analysis; steady state.

[50]:

(With G.I. Falin) Standard and retrial queueing systems: A comparative analysis. Revista Matemática Complutense 15, 101–129.

Keywords: a survey on M/G/1 and M/M/c retrial queues, with similarities and differences between the retrial models and their standard counterparts.

[51]:

(With V.V. Anisimov) Approximation of multiserver retrial queues by means of generalized truncated models. Top 10, 51–66.

Keywords: convergence; generalized truncated model; M/M/c retrial queue; steady state; synchronization mechanism.

[52]:

(With G.I. Falin and M.J. López-Herrero) A second order analysis of the waiting time in the M/G/1 retrial queue. Asia-Pacific Journal of Operational Research 19, 131–148.

Keywords: M/G/1 retrial queue; second moment; waiting time.

[53]:

A note on the optimality of the N- and D-policies for the M/G/1 queue. Operations Research Letters 30, 375–376.

Keywords: M/G/1 queue; optimality of D- and N-policies.

[54]:

(With M. Pozo) Numerical calculation of the stationary distribution of the main multiserver retrial queue. Annals of Operations Research 116, 41–56.

Keywords: generalized truncated model; M/M/c retrial queue; steady state.

[55]:

(With V.C. Joshua and A. Krishnamoorthy) An M/G/1 retrial queue with orbital search by the server. In: Advances in Stochastic Modelling, Artalejo J.R. and Krishnamoorthy A. eds., Notable Publications Inc., NJ, pp. 41–54.

Keywords: linear retrial policy; M/G/1 and M/M/1 retrial queues; orbital search; regenerative analysis.

[56]:

(With O. Hernández-Lerma) Performance analysis and optimal control of the Geo/Geo/c queue. Performance Evaluation 52, 15–39.

Keywords: discrete-time Geo/Geo/c queue; late arrival system, delayed access; optimal control; steady state; value function.

[57]:

(With A. Gómez-Corral) Channel idle periods in computer and telecommunication systems with customer retrials. Telecommunication Systems 24, 29–46.

Keywords: channel idle periods; M/M/c retrial queue; optimal design; random order, and first free first busy assignments.

[58]:

(With M.J. López-Herrero) On the M/M/m queue with removable servers. In: Stochastic Point Processes, Srinivasan S.K. and Vijayakumar A. eds., Narosa Publishing House, pp. 124–144.

Keywords: M/M/c queue; optimal design; removable server; steady state.

[59]:

(With A. Economou) Optimal control and performance analysis of an M ^X/M/1 queue with batches of negative customers. RAIRO 38, 121–151.

Keywords: bulk arrivals; M ^[X]/M/1 queue; negative arrivals; optimal control; steady state; stochastic domination; threshold type policy; total discounted cost, and average cost criteria.

[60]:

(With I. Atencia) On the single server retrial queue with batch arrivals. Sankhya 66, 140–158.

Keywords: bulk arrivals; linear retrial policy; M ^[X]/G/1 retrial queue; steady state.

[61]:

(With G. Choudhury) Steady state analysis of an M/G/1 queue with repeated attempts and two-phase service. Quality Technology and Quantitative Management 1, 189–199.

Keywords: embedded Markov chain; M/G/1 retrial queue; steady state; stochastic decomposition; two-phase service.

[62]:

(With M.J. López-Herrero) Entropy maximization and the busy period of some single-server vacation models. RAIRO 38, 195–213.

Keywords: busy period; D-, N- and T-policies; M/G/1 queue; maximum entropy; server vacations.

[63]:

(With D.S. Orlovsky and A.N. Dudin) Multi-server retrial model with variable number of active servers. Computers and Industrial Engineering 48, 273–288.

Keywords: asymptotically quasi-Toeplitz Markov chain; M/M/c retrial queue; optimal design; QBD process; steady state; threshold type policy.

[64]:

(With A. Economou) On the non-existence of product-form solutions for queueing networks with retrials. Electronic Modeling 27, 13–19.

Keywords: linear retrial policy; product-form solution; queueing network with retrials; steady state.

[65]:

(With A. Gómez-Corral) Waiting time in the M/M/c queue with finite retrial group. Bulletin of Kerala Mathematics Association 2, 1–17.

Keywords: convergence; M/M/c/K retrial queue; waiting time.

[66]:

(With M.J. López-Herrero) The M/G/1 retrial queue: An information theoretic approach. Statistics and Operations Research Transactions 29, 119–137.

Keywords: a survey on the use of information theoretic principles in M/G/1 retrial queues.

[67]:

(With N.M. Apaolaza) On the time to reach a certain orbit level in multi-server retrial queues. Applied Mathematics and Computation 168, 686–703.

Keywords: finite truncated model; M/M/c retrial queue; QBD process; steady state; time to reach an orbit size.

[68]:

(With I. Atencia and P. Moreno) A discrete-time Geo ^[X]/G/1 retrial queue with control of admission. Applied Mathematical Modelling 29, 1100–1120.

Keywords: bulk arrivals; convergence to the continuous-time model; discrete-time Geo ^[X]/G/1 retrial queue; steady state; stochastic decomposition.

[69]:

(With A. Economou) Markovian controllable queueing systems with hysteretic policies: Busy period and waiting time analysis. Methodology and Computing in Applied Probability 7, 353–378.

Keywords: busy period; hysteretic policy; M/M/c queue; number of customers served; removable servers; waiting time.

[70]:

(With A. Economou and M.J. López-Herrero) Analysis of a multiserver queue with setup times. Queueing Systems 52, 53–76.

Keywords: busy period; M/M/c queue; maximum queue length; setup times; steady state; waiting time.

[71]:

(With M.J. López-Herrero) A discrete-time multiserver retrial queue: Performance analysis and simulation. In: Proceedings of the 5th St. Petersburg Workshop on Simulation, Ermakov S.M., Melas V.B. and Pepelyshev A.N. eds., pp. 85–90.

Keywords: discrete-time Geo/Geo/c/K retrial queue; simulation; steady state.

[72]:

(With A. Economou and M.J. López-Herrero) Algorithmic analysis for the number of customers served in a busy period of the M/M/c retrial queue. In: Proceedings of the Third National Conference on Mathematical and Computational Models, Arumuganathan R. and Nadarajan R. eds., Allied Publishers, pp. 3–15.

Keywords: busy period; M/M/c retrial queue; number of customers served; truncated models.

[73]:

(With A. Krishnamoorthy and M.J. López-Herrero) Numerical analysis of (s,S) inventory systems with repeated attempts. Annals of Operations Research 141, 67–83.

Keywords: continuous review (s,S) inventory system; retrials; steady state; truncated models.

[74]:

(With S.R. Chakravarthy) Algorithmic analysis of the maximum level length in general-block two-dimensional processes. Mathematical Problems in Engineering, Article ID 53570, 15 pages.

Keywords: absorbing Markov chain; application to M ^[X]/M/c retrial queues with negative arrivals; busy period; maximum level; two-dimensional Markov chains.

[75]:

(With S.R. Chakravarthy) Algorithmic analysis of the MAP/PH/1 retrial queue. Top 14, 293–332.

Keywords: absorbing Markov chain; busy period; logarithmic reduction algorithm; MAP/PH/1 retrial queue; Markovian arrival process; maximum orbit size; phase-type distribution; QBD process; steady state.

[76]:

(With S.R. Chakravarthy) Computational analysis of the maximal queue length in the MAP/M/c retrial queue. Applied Mathematics and Computation 183, 1399–1409.

Keywords: absorbing Markov chain; busy period; MAP/M/c retrial queue; Markovian arrival process; maximum orbit size; phase-type distribution; QBD process.

[77]:

(With A. Economou and A. Gómez-Corral) Applications of maximum queue lengths to call center management. Computers and Operations Research 34, 983–996.

Keywords: absorbing Markov chain; application to a call center with multiple servers, balking, impatience and retrials; application to a resource-sharing call center; maximum orbit size; QBD process.

[78]:

(With A. Economou and M.J. López-Herrero) Algorithmic approximations for the busy period distribution of the M/M/c retrial queue. European Journal of Operational Research 176, 1687–1702.

Keywords: busy period; generalized truncated models; M/M/c retrial queue; number of customers served.

[79]:

(With M.J. López-Herrero) On the distribution of the number of retrials. Applied Mathematical Modelling 31, 478–489.

Keywords: M/G/1 and M/M/c retrial queues; number of retrials made by a tagged customer.

[80]:

(With A. Gómez-Corral) A note on the busy period of the M/G/1 queue with finite retrial group. Probability in the Engineering and Informational Sciences 21, 77–82.

Keywords: busy period; convergence; finite retrial group; M/G/1 retrial queue.

[81]:

(With S.R. Chakravarthy and M.J. López-Herrero) The busy period and the waiting time analysis of a MAP/M/c queue with finite retrial group. Stochastic Analysis and Applications 25, 445–469.

Keywords: busy period; finite QBD process; finite retrial group; MAP/M/c retrial queue; Markovian arrival process; number of customers served; number of retrials made by a tagged customer; steady state; waiting time.

[82]:

(With A. Economou and M.J. López-Herrero) Algorithmic analysis of the maximum queue length in a busy period for the M/M/c retrial queue. INFORMS Journal on Computing 19, 121–126.

Keywords: busy period; M/M/c retrial queue; maximum orbit size.

[83]:

(With M.J. López-Herrero) A simulation study of a discrete-time multiserver retrial queue with finite population. Journal of Statistical Planning and Inference 137, 2536–2542.

Keywords: discrete-time Geo/Geo/c retrial queue; finite population; simulation; steady state.

[84]:

(With J. Amador) On the distribution of the successful and blocked events in the M/M/c retrial queue: A computational approach. Applied Mathematics and Computation 190, 1612–1626.

Keywords: M/M/c retrial queue; successful and blocked retrials, and primary arrivals; truncated models.

[85]:

(With A. Gómez-Corral) Waiting time analysis of the M/G/1 queue with finite retrial group. Naval Research Logistics 54, 524–529.

Keywords: finite orbit group; M/G/1 retrial queue; waiting time.

[86]:

(With A. Economou and M.J. López-Herrero) Evaluating growth measures in an immigration process subject to binomial and geometric catastrophes. Mathematical Biosciences and Engineering 4, 573–594.

Keywords: basic immigration process; binomial and geometric catastrophes; extinction time; maximum population size; number of individuals removed; survival time of a tagged individual.

[87]:

(With A. Gómez-Corral) Modelling communication systems with phase type service and retrial times. IEEE Communications Letters 11, 955–957.

Keywords: finite QBD process; phase-type distribution; quasi-random input; steady state.

[88]:

(With A. Economou and A. Gómez-Corral) Algorithmic analysis of the Geo/Geo/c retrial queue. European Journal of Operational Research 189, 1042–1056.

Keywords: busy period; discrete-time Geo/Geo/c retrial queue; steady state; truncated models; waiting time.

[89]:

(With A. Gómez-Corral) Retrial Queueing Systems: A Computational Approach. Springer-Verlag, Berlin.

Keywords: a monograph on retrial queues, with special emphasis on computational aspects.

[90]:

Retrial queues: An algorithmic approach. In: Proceedings of the 2nd International Conference on Mathematics: Trends and Developments, Obada, A.F.S. ed., Al Hakim Press, pp. 101–118.

Keywords: a survey on efficient algorithmic methods in retrial queues.

[91]:

(With J. Amador) The M/G/1 retrial queue: New descriptors of the customer’s behavior. Journal of Computational and Applied Mathematics 223, 15–26.

Keywords: M/G/1 retrial queue; number of retrials made by a tagged customer; phase-type distribution; successful and blocked retrials, and primary arrivals; truncated models.

[92]:

(With V. Pla) On the impact of customer balking, impatience and retrials in telecommunication systems. Computers and Mathematics with Applications 57, 217–229.

Keywords: application to call center design; balking/reneging; generalized truncated models; impatience; M/M/c retrial queue; single- and bi-threshold truncations.

[93]:

(With J. Amador) Transient analysis of the successful and blocked events in retrial queues. Telecommunication Systems 41, 255–265.

Keywords: M/M/c and M/PH/1 retrial queues; successful and blocked retrials, and primary arrivals; transient behavior; truncated models.

[94]:

Retrial queues: An algorithmic approach. Journal of the Egyptian Mathematical Society 17, 83–101.

Keywords: a survey on efficient algorithmic methods in retrial queues.

[95]:

Number of removals in the stochastic SIR model. In: Proceedings of the 6th St. Petersburg Workshop on Simulation, Ermakov S.M., Melas V.B. and Pepelyshev A.N. eds., pp. 779–784.

Keywords: number of removals; stochastic SIR epidemic model; transient behavior.

[96]:

(With M.J. López-Herrero) Cellular mobile networks with repeated calls operating in random environment. Computers and Operations Research 37, 1158–1166.

Keywords: alternating, arithmetic average, and doubly stochastic environments; finite QBD process; guard channels; handover calls; Markov chain model; random environment; retrials; static average approximation; steady state; waiting time.

[97]:

(With A. Economou and M.J. López-Herrero) The maximum number of infected individuals in SIS epidemic models: Computational techniques and quasi-stationary distributions. Journal of Computational and Applied Mathematics 233, 2563–2574.

Keywords: absorbing Markov chain; birth and death process; maximum number of infected individuals; quasi-stationary distribution; stochastic SIS epidemic model;

[98]:

Accessible bibliography on retrial queues: Progress in 2000–2009. Mathematical and Computer Modelling 51, 1071–1081.

Keywords: a bibliography on retrial queues which updates the bibliography [33] published in 1999.

[99]:

(With Q.L. Li) Performance analysis of a block-structured discrete-time retrial queue with state-dependent arrivals. Discrete Event Dynamic Systems 20, 325–347.

Keywords: D-BSDA approach; discrete phase-type distribution; discrete-time Markovian arrival process; discrete-time BSDA/PH/1 retrial queue; finite population; RG-factorization; steady state; structured Markov chains; waiting time.

[100]:

(With A. Gómez-Corral) A state-dependent Markov-modulated mechanism for generating events and stochastic models. Mathematical Methods in the Applied Sciences 33, 1342–1349.

Keywords: batch Markovian arrival process; BSDE approach; MAP/PH/1 queue; state-dependent controllable queue; state-dependent QBD process; state-dependent SIS epidemic model.

[101]:

(With J.A.C. Resing) Mean value analysis of single server retrial queues. Asia-Pacific Journal of Operational Research 27, 335–345.

Keywords: bulk arrivals; impatience; M/G/1 queue; M/G/1 retrial queue; mean value analysis; network blocking; priority subscribers; two way communication.

[102]:

(With M.J. López-Herrero) Quasi-stationary and ratio of expectations distributions: A comparative study. Journal of Theoretical Biology 266, 264–274.

Keywords: application to stochastic population models; birth and death process; linear growth model; quasi-stationary distribution; radio of expectations distribution; stochastic SIR and SIS epidemic models.

[103]:

(With A. Economou and M.J. López-Herrero) On the number of recovered individuals in the SIS and SIR stochastic epidemic models. Mathematical Biosciences 228, 45–55.

Keywords: extinction time; number of infections; number of recovered individuals; outbreak; stochastic SIR and SIS epidemic models; transient behavior.

[104]:

(With A. Gómez-Corral and Q.-M. He) Markovian arrivals in stochastic modelling: A survey and some new results. Statistics and Operations Research Transactions 34, 101–144.

Keywords: a survey (with discussion) on the batch Markovian arrival process, its variants and generalizations, and an application of the BSDE approach to epidemic models.

[105]:

(With A. Gómez-Corral) Markov chains with block-structured state dependent events: Formulation and correlation analysis. In: Proceedings of the 5th International Conference on Queueing Theory and Network Applications, ACM Digital Library, pp. 23–28.

Keywords: BSDE approach; correlation between events, and between arrivals; state-dependent QBD process.

[106]:

(With M.J. López-Herrero) The SIS and SIR stochastic epidemic models: A maximum entropy approach. Theoretical Population Biology 80, 256–264.

Keywords: extinction time; final size; maximum entropy; stochastic SIR and SIS epidemic models.

[107]:

On the transient behavior of the maximum level length in structured Markov chains. In: Modern Mathematical Tools and Techniques in Capturing Complexity, Pardo L., Balakrishnan N. and Gil M.A. eds., Springer Series in Synergetics, pp. 379–390.

Keywords: absorbing Markov chain; M/M/c retrial queue; maximum level; stochastic SIR epidemic model; structured Markov chains; transient behavior.

[108]:

Retrial queues. In: Wiley Encyclopedia of Operations Research and Management Science, Cochran J.J. ed., 7 pages.

Keywords: a basic overview of the main aspects in retrial queues.

[109]:

Queueing networks with retrials due to unsatisfactory service. In: Handbook of Optimization Theory, Varela J. and Acuña S. eds., Nova Science Publishers, Inc., pp. 565–576.

Keywords: open and closed queueing networks; product-form solution; retrials; steady state.

[110]:

(With T. Phung-Duc) Markovian single server retrial queues with two way communication. In: Proceedings of the 6th International Conference on Queueing Theory and Network Applications, ACM Digital Library, pp. 1–7.

Keywords: M/M/1 retrial queue; steady state; two way communication.

[111]:

(With A. Economou and M.J. López-Herrero) Stochastic epidemic models revisited: Analysis of some continuous performance measures. Journal of Biological Dynamics 6, 189–211.

Keywords: application to head lice infections; birth and death process; extinction time; recovery time; removal time; stochastic SIR and SIS epidemic models; time to infection.

[112]:

On the time to extinction from quasi-stationarity: A unified approach. Physica A 391, 4483–4486.

Keywords: discrete-time and continuous-time Markov chains; extinction time; quasi-stationary distribution.

[113]:

(With M.J. López-Herrero) The single server retrial queue with finite population: A BSDE approach. Operational Research: An International Journal 12, 109–131.

Keywords: BSDE approach; finite population; finite QBD process; retrials; steady state; waiting time.

[114]:

(With T. Phung-Duc) Markovian retrial queues with two way communication. Journal of Industrial and Management Optimization 8, 781–806.

Keywords: asymptotic analysis; M/M/1 and M/M/c retrial queues, QBD process; steady state; two way communication.

[115]:

(With J. Amador) Modeling computer virus with the BSDE approach. Computer Networks 57, 302–316.

Keywords: application to the propagation of the CodeRed-II virus; BSDE approach; number of infections; stochastic SIS epidemic model; warning signals.

[116]:

(With J. Amador) Stochastic modeling of computer virus spreading with warning signals. Journal of the Franklin Institute 350, 1112–1138.

Keywords: extinction time; finite QBD process; hazard time; number of infections; quasi-stationary distribution; stochastic SIRS epidemic model.

[117]:

(With M.J. López-Herrero) On the exact measure of disease spread in stochastic epidemic models. Bulletin of Mathematical Biology 75, 1031–1050.

Keywords: basic reproduction number; exact reproduction number; population transmission number; stochastic SIR and SIS epidemic models; vaccination coverage.

[118]:

(With T. Phung-Duc) Single server retrial queues with two way communication. Applied Mathematical Modelling 37, 1811–1822.

Keywords: asymptotic analysis; embedded Markov chain; light-tailed behavior; M/G/1 retrial queue; steady state; two way communication.

[119]:

(With A. Economou and M.J. López-Herrero) Stochastic epidemic models with random environment: quasi-stationarity, extinction and final size. To appear in Journal of Mathematical Biology.

Keywords: alternating and cyclic environments; extinction time; final size; quasi-stationary distribution; random environment; ratio of expectations distribution; stochastic SIR and SIS epidemic models; transmission factor; two average approximation.

[120]:

On the Markovian approach for modeling the dynamics of nosocomial infections.

Keywords: exact reproduction number; finite QBD process; Markov chain model; nosocomial infection in intensive care units.

[121]:

(With A. Economou and M.J. López-Herrero) The stochastic SEIR model: Duration of an epidemic and final size.

Keywords: application to Marburg fever 2005 outbreak in Angola; extinction time; final size; quasi-stationary distribution; ratio of expectations distribution; stochastic SEIR epidemic model.

[122]:

(With A. Gómez-Corral and C. Molina-París) Stochastic descriptors for a mathematical model of naive T cell homeostasis.

Keywords: birth and death process; extinction time; maximum clonotype size; number of birth events to reach a given clonotype size; T cell homeostasis; TCR diversity; time to expand to a given clonotype size; times to reach and to contract to a given number of birth events.

[123]:

(With M.J. López-Herrero) Stochastic epidemic models: New behavioral indicators of the disease spreading.

Keywords: an application to head lice infections; birth and death process; final size; number of infections per individual; stochastic SIR and SIS epidemic models; time to reach a critical number of infections; time to reach an individual run of infections.