Queueing System with Potential for Recruiting Secondary Servers

In this paper, we consider a single server queueing system in which the arrivals occur according to a Markovian arrival process (MAP). The served customers may be recruited (or opted from those customers’ point of view) to act as secondary servers to provide services to the waiting customers. Such customers who are recruited to be servers are referred to as secondary servers. The service times of the main as well as that of the secondary servers are assumed to be exponentially distributed possibly with different parameters. Assuming that at most there can only be one secondary server at any given time and that the secondary server will leave after serving its assigned group of customers, the model is studied as a QBD-type queue. However, one can also study this model as a G I/M/1-type queue. The model is analyzed in steady state, and a few illustrative numerical examples are presented

Pseudo steady-state period in non-stationary infinite-server queue with state dependent arrival intensity

An infinite-server queueing model with state-dependent arrival process and exponential distribution of service time is analyzed. It is assumed that the difference between the value of the arrival rate and total service rate becomes positive starting from a certain value of the number of customers in the system. In this paper, time until reaching this value by the number of customers in the system is called the pseudo steady-state period (PSSP). Distribution of duration of PSSP, its raw moments and its simple approximation under a certain scaling of the number of customers in the system are analyzed. Novelty of the considered problem consists of an arbitrary dependence of the rate of customer arrival on the current number of customers in the system and analysis of time until reaching from below a certain level by the number of customers in the system. The relevant existing papers focus on the analysis of time interval since exceeding a certain level until the number of customers goes down to this level (congestion period). Our main contribution consists of the derivation of a simple approximation of the considered time distribution by the exponential distribution. Numerical examples are presented, which confirm good quality of the proposed approximation

Multi-threshold Control of the BMAP/SM/1/K Queue with Group Services

We consider a finite capacity queue in which arrivals occur according to a batch Markovian arrival process (BMAP). The customers are served in groups of varying sizes. The services are governed by a controlled semi-Markovian process according to a multithreshold strategy. We perform the steady-state analysis of this model by computing (a) the queue length distributions at departure and arbitrary epochs, (b) the Laplace-Stieltjes transform of the sojourn time distribution of an admitted customer, and (c) some selected system performance measures. An optimization problem of interest is presented and some numerical examples are illustrated

A Multi-server Markovian Queueing Model with Primary and Secondary Services

We study a multi-server queueing model in which the arrivals occur according to a Markovian arrival process. An arriving customer either (a) is lost due to all main servers being busy; or (b) enters into service with one of the main servers and leaves the system (as a satisfied primary customer); (c) enters into a service with one of the main servers, gets service in self-service mode, and is impatient to get a final service with one of the main servers, may leave the system (as a dissatisfied secondary customer); or (d) enters into service with one of the main servers, gets service in self-service mode, becomes successful in getting a final service from one of the main servers, and departs. This queueing model is studied in a steady state

Optimal Threshold Control by the Robots of Web Search Engines with Obsolescence of Documents

A typical web search engine consists of three principal parts: crawling engine, indexing engine, and searching engine. The present work aims to optimize the performance of the crawling engine. The crawling engine finds new web pages and updates web pages existing in the database of the web search engine. The crawling engine has several robots collecting information from the Internet. We first calculate various performance measures of the system (e.g., probability of arbitrary page loss due to the buffer overflow, probability of starvation of the system, the average time waiting in the buffer). Intuitively, we would like to avoid system starvation and at the same time to minimize the information loss. We formulate the problem as a multi-criteria optimization problem and attributing a weight to each criterion. We solve it in the class of threshold policies. We consider a very general web page arrival process modeled by Batch Marked Markov Arrival Process and a very general service time modeled by Phase-type distribution. The model has been applied to the performance evaluation and optimization of the crawler designed by INRIA Maestro team in the framework of the RIAM INRIA-Canon research project

Self-Service System with Rating Dependent Arrivals

A multi-server infinite buffer queueing system with additional servers (assistants) providing help to the main servers when they encounter problems is considered as the model of real-world systems with customers’ self-service. Such systems are widely used in many areas of human activity. An arrival flow is assumed to be the novel essential generalization of the known Markov Arrival Process (MAP) to the case of the dynamic dependence of the parameters of the MAP on the rating of the system. The rating is the process defined at any moment by the quality of service of previously arrived customers. The possibilities of a customers immediate departure from the system at the entrance to the system and the buffer due to impatience are taken into account. The system is analyzed via the use of the results for multi-dimensional Markov chains with level-dependent behavior. The transparent stability condition is derived, as well as the expressions for the key performance indicators of the system in terms of the stationary probabilities of the Markov chain. Numerical results are provided

Optimal control for a BMAP/G/1 queue with two service modes

Queueing models with controllable service rate play an important role in telecommunication systems. This paper deals with a single-server model with a batch Markovian arrival process (BMAP) and two service modes, where switch-over times are involved when changing the service mode. The embedded stationary queue length distribution and the explicit dependence of operation criteria on switch-over levels and derived

Eastern Europe’s “Transitional Industry”? : Deconstructing the Early Streletskian

Acknowledgements We are very grateful to many friends and colleagues for discussions and various help, including Yuri Demindenko, Evgeny Giria, Brad Gravina, Anton Lada, Sergei Lisitsyn and Alexander Otcherednoy. Needless to say, they may or may not agree with our conclusions. We are also thankful to Jesse Davies and Craig Williams for the help with the illustrations and figures. Ekaterina Petrova kindly helped with ID’ing some of the sampled bones. We thank the staff of the Oxford Radiocarbon Accelerator Unit at the University of Oxford for their support with the chemical preparation and the measurement of the samples. We are also grateful to the three anonymous reviewers for their thoughtful and constructive comments, which helped improve the paper. This paper is a contribution to Leverhulme Trust project RPG-2012-800. The research leading to some of our radiocarbon results received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013); ERC grant 324139 “PalaeoChron” awarded to Professor Tom Higham. AB and AS acknowledge Russian Science Foundation grant number 20-78-10151 and Russian Foundation of Basic Research grant numbers 18-39-20009 and 20-09-00233 for support of their work. We also acknowledge the participation of IHMC RAS (state assignment 0184-2019-0001) and ZIN RAS (state assignment АААА-А19-119032590102-7).Peer reviewedPublisher PD

Is graphene on copper doped?

Angle-resolved photoemission spectroscopy (ARPES) and X-ray photoemission spectroscopy have been used to characterise epitaxially ordered graphene grown on copper foil by low-pressure chemical vapour deposition. A short vacuum anneal to 200 °C allows observation of ordered low energy electron diffraction patterns. High quality Dirac cones are measured in ARPES with the Dirac point at the Fermi level (undoped graphene). Annealing above 300 °C produces n-type doping in the graphene with up to 350 meV shift in Fermi level, and opens a band gap of around 100 meV. Dirac cone dispersion for graphene on Cu foil after vacuum anneals (left: 200 °C, undoped; right: 500 °C, n-doped). Centre: low energy electron diffraction from graphene on Cu foil after 200 °C anneal. Data from Antares (SOLEIL)