Dans ce chapitre sont proposés deux modifications à un système de file d’attente avec rappel premier entré, premier sorti, introduits par Laszlo Lakatos en 1994. Ces modèles prennent notamment en compte la réservation de temps pour le service client. Ces modèles semblent augmenter le rendement du système de file d’attente par rapport au système de file d’attente de type Lakatos.

The author suggests some modifications to a first-come first-served retrial queueing (FCFS RQ) system introduced by Hungarian mathematician Laszlo Lakatos in 1994. Elena V. Koba has investigated a number of generalizations of Lakatos-type queueing systems. She studied GI/G/1 retrial FCFS systems with generally distributed orbit times for customers. Koba's results on stability/ergodicity conditions for GI/G/1 RQ systems are outlined. It is interesting to note that in some cases, it is possible to derive elementary analytical equations for such conditions. A Lakatos-type RQ system reflects the peculiarities of some engineering systems.

Boris V. Gnedenko (1.01.1912–12.25.1995), a distinguished scientist and pedagogue and Academician of AS of UkrSSR (at present, the National Academy of Sciences (NAS) of Ukraine) lived and worked in Ukraine for 15 years (1945–1960) and created a world famous scientific school in probability&statistics. The author of this article who is a pupil of this school, a disciple and a coauthor of B. V. Gnedenko, an employee of the V. M. Glushkov Institute of Cybernetics since 1971, and an Academician of NAS of Ukraine notes the influence of the contribution of B. V. Gnedenko and his most prominent disciples V. S. Mikhalevich, K. L. Yushchenko, V. S. Koroliuk, T. P. Maryanovich, and others on the formation of cybernetics and informatics.

Laslo Lakatos [1, 2] introduced a queuing system in which waiting time V of a customer increases up to a W multiple of T. This problem statement is motivated by a problem occurred in aviation: T is aircraft go-around time when the runway is not clear. In the present paper, a queuing system is considered in which V increases up to T1x + T2 y, where T1 and T2 are given numbers (go-around times of two “circles”) and x and y are V-dependent integers (numbers of rounds). An ergodic theorem for a proper embedded Markov chain is proved. An algorithm is given to compute x and y given V.

A survey of the life and work of world renowned mathematician Boris Vladimirovich Gnedenko.

In 1956, at the Third All-Union Mathematical Congress, Boris Aleksandrovich Sevastyanov gave a talk on the ergodic theorem proved by him for Markov processes and on its application to queueing systems. In 1957, this result was published in the journal Teoriya Veroyatnostei i Ee Primeneniya (Theory of Probability and Its Applications). An important corollary to the ergodic theorem is a generalization of Erlang’s well-known formula to a queueing system with a Poisson input flow and an arbitrary distribution of the service time. This result of Sevastyanov has served as a starting point for numerous studies on the problem, which was later called the insensitivity (invariance) problem for queueing systems with losses. There are hundreds of references to this result of Sevastyanov.

A discrete-time one-channel queuing system with general inter-arrival, service, and orbit times periodically dependent on the number of arrival is considered. The service discipline is assumed to be FCFS. The sufficient condition for the ergodicity of an embedded Markov chain is derived.

Aim.The prostate tumor-inducing oncogene (PTI-1), presumably encoding a truncated form of eukaryotic translation elongation factor 1A1 (eEF1A1), was discovered as a gene overexpressed in prostate tumor samples and absent in normal tissues.The mechanism of PTI-1 oncogenicity remains obscure.Methods.Several bioinformatics methods were applied to analyze the PTI-1 mRNA structure, translation efficiency and coding potential.Results.In silico analysis of 5'UTR of its mRNA suggest that PTI-1 mRNA most probably belongs to the class of templates with low translation efficiency.Additionally, novel open reading frame (ORF) starting with alternative initiation site situated upstream of the main ORF start codon was found.Finally, the peptide that does not resemble eEF1A1 but is partially homologous to relaxin can be synthesized.Conclusions.We suggest that the alternative upstream start codon may initiate synthesis of a peptide (uPTI-1) homologous to relaxin, the hormone shown to promote the prostate cancer progression.uPTI-1 protein may interact with the respective relaxin-specific receptors, suggesting that the tumorigenic outcome of PTI-1 is possibly realized via the relaxin-dependent pathway.

A queuing system with the service time distribution being a mixture of two exponential distributions is considered. A necessary and sufficient condition is established for the probability of failure during a busy period to be equivalent to the probability of monotone failure. Conditions under which nonmonotone failures make the major contribution to the system failure are also obtained. These conditions are compared to the well-known sufficient conditions.

Some typical classes of retrial queues originating from applied problems are introduced. Retrial systems of different types are compared. Their coding is discussed.

The author reviews his publications doing justice to outstanding mathematicians who were his research supervisors and among which were B. V. Gnedenko, A. N. Kolmogorov, V. S. Mikhalevich, V. S. Korolyuk, and others.

In this paper we carry out both light-traffic and heavy-traffic analyses for the calculation of steady-state loss probabilities in the general multi-server queuing loss system, the GI/G/n/0 queue. The analysis makes use of a heuristic approach called the GM Heuristic, for which a detailed analysis in normal traffic has previously been published. Sufficient conditions are given for the GM Heuristic to be asymptotically exact in light traffic. The heuristic is also shown to be asymptotically exact in heavy-traffic when the number of servers n tends to infinity. These results are illustrated numerically using two-phase Coxian distributions for both the inter-arrival time and service time.

This paper is concerned with the solution of a specific hypercube queueing model. It extends the work that was described in a related paper by Atkinson et al. [Atkinson, J.B., Kovalenko, I.N., Kuznetsov, N., Mykhalevych, K.V., 2006. Heuristic methods for the analysis of a queuing system describing emergency medical services deployed along a highway. Cybernetics & Systems Analysis, 42, 379–391], which investigated a model for deploying emergency services along a highway. The model is based on the servicing of customer demands that arise in a number of distinct geographical zones, or atoms. Service is provided by servers that are positioned at a number of bases, each having a fixed geographical location along the highway. At each base a single server is available. Demands arising in any atom have a first-preference base and a second-preference base. If the first-preference base is busy, service is provided by the second-preference base; and, if both bases are busy, the demand is lost. In practice, because of differences in travel times from the first and second-preference bases to the atom in question, the service rate may be significantly different in the two cases. The model studied here allows for such customer-dependent service rates to occur, and the corresponding hypercube model has 3n states, where n is the number of bases. The computational intractability of this model means that exact solutions for the long-run proportion of lost demands (ploss) can be obtained only for small values of n. In this paper, we propose two heuristic methods and a simulation approach for approximating ploss. The heuristics are shown to produce very accurate estimates of ploss.

A single-channel queuing system with a Poisson incoming flow of objects is considered. Each object consists of several spaced requests. A simple ergodicity condition is established.

Consideration is given to a queueing model that describes the deployment of emergency medical service along a highway. Two heuristic methods are proposed for the approximate evaluation of stationary loss probability and utilization of ambulance cars. The high accuracy of these methods is demonstrated by several examples.