Alexander Dudin
Doctor of Physical and Mathematical Sciences
- Head of the research Laboratory of Applied Probabilistic Analysis in/ of the Belarusian State University
- Professor of the Probability Theory and Mathematical Statistics Department at the Belarusian State University
- Chairman of the Organizing Committee of the Belarusian Winter Conference on Queueing Theory
- Head of the Research Center for Applied Probabilistic Analysis of the Institute of Applied Mathematics & Communications Technology
1976
Graduate of the faculty of applied mathematics of the Belarusian state University.
1982
Defended his PhD thesis on the specialty 01.01.05 – probability theory and mathematical statistics.
1986
Was awarded the academic title of senior researcher.
1992
Defended his doctoral thesis on the specialty 05.13.16 – application of computers, mathematical modeling and mathematical methods in scientific research.
2000
Received the academic title of Professor in "mathematics".
Lecturing experience
Lectures on the following courses: Probability Theory and Mathematical Statistics, Matrix-analytic methods in Queueing Theory (author’s course).
Social activities
- Academic Secretary of the Expert Council in Mathematics of the Higher State Certification Commission of the Republic of Belarus since 2004
- Chairman of the International program Committee of the 13-15 international conferences "Information Technologies and Mathematical Modeling" named after A. F. Terpugov, Siberia, 2014-2016
- The winner of the Elsevier Publishing House Belarus Scopus Award 2013 for outstanding achievements in mathematics
Research in the field of the analysis of random processes in queueing systems, controllable queueing systems and their optimization, queueing systems in random environment, application of Queuing theory for the analysis of telecommunication and computer networks, and call centers are conducted under Alexander Dudin’s supervision.
More than 350 scientific articles and 3 monographs have been published on the results of the research (Hirsch index: 19 Scopus, WoS 14).
Participation in international scientific projects:
2014-2016 - Development and analysis of mathematical methods of assessing the effectiveness of hybrid transmission systems of multimedia information based on laser and radio-technology (The Belarusian Republican Foundation for Fundamental Research – The Russian Foundation for Fundamental Research).
2015-2017 - Development of mathematical models and methods of solution of optimization problems for energy saving in telecommunication networks (The Belarusian Republican Foundation for Fundamental Research – The National Research Foundation of Korea).
2016-2018 - Development and analysis of mathematical methods of combining the architecture of broadband wireless networks with linear topology. (The Belarusian Republican Foundation for Fundamental Research – The Russian Foundation for Fundamental Research).
2016-2020 - Development of mathematical methods for optimizing the parameters of multi-speed transmission of information in telecommunication networks (the state program of fundamental research "Informatics and space").
2016-2020 - Analysis and optimization of stochastic processes in queueing systems with controlled modes of operation (the state program of fundamental research "Convergence").
Research interests
- stochastic processes
- the theory of queues and queues control, queues with repeated calls, queues in a random environment, the application of queueing theory in telecommunications
Abstract Crowdsourcing is getting popular after a number of industries such as food, consumer products, hotels, electronics, and other large retailers bought into this idea of serving customers. In this paper, we introduce a multi-server queueing model in the context of crowdsourcing. We assume that two types, say, Type 1 and Type 2, of customers arrive to a c-server queueing system. A Type 1 customer has to receive service by one of c servers while a Type 2 customer may be served by a Type 1 customer who is available to act as a server soon after getting a service or by one of c servers. We assume that a Type 1 customer will be available for serving a Type 2 customer (provided there is at least one Type 2 customer waiting in the queue at the time of the service completion of that Type 1 customer) with probability $$p, 0 \le p \le 1$$ p , 0 ≤ p ≤ 1 . With probability $$q = 1 - p$$ q = 1 - p , a Type 1 customer will opt out of serving a Type 2 customer provided there is at least one Type 2 customer waiting in the system. Upon the completion of a service a free server will offer service to a Type 1 customer on an FCFS basis; however, if there are no Type 1 customers waiting in the system, the server will serve a Type 2 customer if there is one present in the queue. If a Type 1 customer decides to serve a Type 2 customer, for our analysis purposes that Type 2 customer will be removed from the system as Type 1 customer will leave the system with that Type 2 customer. Under the assumption of exponential services for both types of customers we study the model in steady state using matrix analytic methods and establish some results including explicit ones for the waiting time distributions. Some illustrative numerical examples are presented.
A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer's service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace-Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.
We consider a BMAP/G/1 type queueing model with gated service and duration of vacations depending on how many times in turn the system was empty at the previous vacation completion moments. We compute stationary distributions of the queue length at the embedded moments (vacation completions) and at arbitrary time as well as of a customer waiting time. The results of our analysis can be useful for determining strategy of adaptive choosing duration of sleep periods, e.g., in mobile networks where power consumption is an important issue.
The problem of choosing the optimal hysteresis strategy of control by the number of active servers in the multi-server queue is considered. Customers of two types arrive to the system according to the marked Markovian arrival process (MMAP). Type 1 customers have a non-preemptive priority, but the buffer for these customers is finite. The buffer for type 2 customers is infinite. The service time distribution is of phase-type (PH) depending on the type of customers. Some servers are always active. The rest of servers can be switched on or off depending on the number of customers in the system. The strategy of control by the number of active servers is of hysteresis type. Such a strategy is defined by two sets of thresholds. The servers are activated or switched off depending on the relation of the number of customers and the thresholds. The main contribution of the paper is development of a procedure for computation of the stationary distribution of the system states and the value of economical cost criterion under any fixed thresholds. Numerical results show effectiveness of the hysteresis control and importance of account of correlation in the arrival process and variance of service times.
A tandem queueing system with infinite and finite intermediate buffers, heterogeneous customers and generalized phase-type service time distribution at the second stage is investigated. The first stage of the tandem has a finite number of servers without buffer. The second stage consists of an infinite and a finite buffers and a finite number of servers. The arrival flow of customers is described by a Marked Markovian arrival process. Type 1 customers arrive to the first stage while type 2 customers arrive to the second stage directly. The service time at the first stage has an exponential distribution. The service times of type 1 and type 2 customers at the second stage have a phase-type distribution with different parameters. During a waiting period in the intermediate buffer, type 1 customers can be impatient and leave the system. The ergodicity condition and the steady-state distribution of the system states are analyzed. Some key performance measures are calculated. The Laplace–Stieltjes transform of the sojourn time distribution of type 2 customers is derived. Numerical examples are presented.
A multi-server retrial queue with two types of calls (handover and new calls) is analyzed. This queue models the operation of a cell of a mobile communication network. Calls of two types arrive at the system according to the Marked Markovian Arrival Process. Service times of both types of the calls are exponentially distributed with different service rates. Handover calls have priority over new calls. Priority is provided by means of reservation of several servers of the system exclusively for service of handover calls. A handover call is dropped and leaves the system if all servers are busy at the arrival epoch. A new call is blocked if all servers available to new calls are busy. Such a call has options to balk (to leave the system without getting the service) or to retry later on. The behavior of the system is described by the four-dimensional Markov chain belonging to the class of the asymptotically quasi-Toeplitz Markov chains (AQTMC). In the paper, a constructive ergodicity condition for this chain is derived and the effective algorithm for computing the stationary distribution is presented. Based on this distribution, formulas for various performance measures of the system are obtained. Results of numerical experiments illustrating the behavior of key performance measures of the system depending on the number of the reserved servers under the different shares of the handover and the new calls are presented. An optimization problem is considered and high positive effect of server's reservation is demonstrated.
In this paper, we are concerned with the analytical treatment of an GI/M/1 retrial queue with constant retrial rate. Constant retrial rate is typical for some real world systems where the intensity of individual retrials is inversely proportional to the number of customers in the orbit or only one customer from the orbit is allowed to make the retrials. In our model, a customer who finds the server busy joins the queue in the orbit in accordance with the FCFS (first-come-first-out) discipline and only the oldest customer in the queue is allowed to make the repeated attempts to reach the server. A distinguishing feature of the considered system is an arbitrary distribution of inter-arrival times, while the overwhelming majority of the papers is devoted to the retrial systems with the stationary Poisson arrival process. We carry out an extensive analytical analysis of the queue in steady state using the well-known matrix analytic technique. The ergodicity condition and simple expressions for the stationary distributions of the system states at pre-arrival, post-arrival and arbitrary times are derived. The important and difficult problem of finding the stationary distribution of the sojourn time is solved in terms of the Laplace–Stieltjes transform. Little’s formula is proved. Numerical illustrations are presented.
A multi-server queueing system with two types of customers and an infinite buffer operating in a random environment as a model of a contact center is investigated. The arrival flow of customers is described by a marked Markovian arrival process. Type 1 customers have a non-preemptive priority over type 2 customers and can leave the buffer due to a lack of service. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. The criterion of ergodicity for a multi-dimensional Markov chain describing the behavior of the system and the algorithm for computation of its steady-state distribution are outlined. Some key performance measures are calculated. The Laplace-Stieltjes transforms of the sojourn and waiting time distributions of priority and non-priority customers are derived. A numerical example illustrating the importance of taking into account the correlation in the arrival process is presented.
A tandem queueing system with a Markovian Arrival Process (MAP) useful in modeling a call center with Interactive Voice Response (IVR) is investigated. The first stage has a finite number of servers without buffer while the second stage of the tandem has a finite buffer and a finite number of servers. The service time at the first (second) stage has an exponential (phase type) distribution. A special approach for reducing the number of states of the stochastic process that describes the behavior of the system is used. The main performance measures are calculated. The Laplace–Stieltjes transform of the sojourn time distribution is derived. The numerical results are presented.
Single server retrial queueing models in which customers arrive according to a batch Poisson process are considered here. An arriving batch, finding the server busy, enters an orbit. Otherwise, one customer from the arriving batch enters for service immediately while the rest join the orbit. The customers from the orbit (the orbital customers) try to reach the server subsequently with the inter-retrial times exponentially distributed. Additionally, at each service completion epoch, two different search mechanisms, that is, type I and type II search, to bring the orbital customers by the system to service, are switched on. Thus, when the server is idle, a competition takes place among primary customers, customers who come by retrial and by two types of searches. The type I search selects a single customer whereas the type II search considers a batch of customers from the orbit. Depending on the maximum size of the batch being considered for service by a type II search, two cases are addressed here. In the first case, no restriction on batch size is assumed, whereas in the second case, maximum size of the batch is restricted to a pre-assigned value. We call the resulting models as model 1 and model 2 respectively. In all service modes other than type II search, only a single customer is qualified for service. Service times of the four types of customers, namely, primary, repeated, and those who come by two types of searches are arbitrarily distributed (with different distributions which are independent of each other). Steady state analysis is performed and stability conditions are established. A control problem for model 2 is considered and numerical illustrations are provided.
A multiserver queuing system with an infinite buffer is considered. The incoming customer is described by a Markovian input flow. The heating time of the servers and the time of the customer service have a phase type distribution. The heating of all the free servers starts at the customer’s arrival moment, and the customer receives the service by all these servers after the heating’s termination. The steady state distribution of the customers and their sojourn time in a system are found. The basic performance measures of the system are calculated. The results of the numerical experiments show the potential usability of the proposed service discipline in comparison with the classical one.