Agassi Z. Melikov

Agassi Z. Melikov
Azerbaijan National Academy of Sciences | ANAS · Teletraffic Theory

Professor
My research interests are in Queuing Theory, Queuing-Inventory Systems, Mathematical Tele-traffic Theory

About

157
Publications
6,585
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
682
Citations
Introduction
Additional affiliations
September 2015 - present
Azerbaijan National Academy of Sciences
Position
  • Head of Department

Publications

Publications (157)
Article
Full-text available
A hybrid replenishment policy in double sources queuing-inventory system is proposed. If the inventory level drops to the reorder point s, then a regular order of the fixed volume Q = S − s is generated to a slow and cheap source, where S denotes the maximum size of the system’s warehouse. If the inventory level falls below a certain threshold valu...
Chapter
Full-text available
The Markov models of queuing-inventory systems with infinite buffer were analyzed under different replenishment policies. Besides traditional positive replenishment, the negative replenishment is considered after which inventory level instantly decreases. Some customers are assumed to leave the system without acquiring an item after the service com...
Article
Full-text available
This paper studies a Markov model of a queuing-inventory system with primary, retrial, and feedback customers. Primary customers form a Poisson flow, and if an inventory level is positive upon their arrival, they instantly receive the items. If the inventory level is equal to zero upon arrival of a primary customer, then this customer, according to...
Article
Full-text available
In this paper, models of unreliable multi-server retrial queues with delayed feedback are examined. The Bernoulli retrial is allowed upon the arrival of both primary (from outside) and feedback customers (from orbit), as well as the Bernoulli feedback that may occur after each service in this system. Servers can break down both during the service o...
Article
Full-text available
In this paper, we consider two single server queueing systems to which customers of two distinct priorities (P1 and P2) arrive according to a Marked Markovian arrival process (MMAP). They are served according to two distinct phase type distributions. The probability of a P1 customer to feedback is θ on completion of his service. The feedback (P1) c...
Chapter
The Markovian model of single server queuing system with instantaneous feedback and positive server setup time for servicing of feedback calls is proposed. Arrival rate of calls from outside depends on server status which might be in two regimes: working regime and setup regime. Calls are impatient when server is in setup regime. Two approaches are...
Article
In the paper, we consider a mathematical model for repeated customers in the form of a queuing system with N servers, instant and delayed feedback, and an orbit. It is believed that the orbit size for repeated customers is infinite. The input flow is Poisson. To find the joint probability distribution of the number of occupied servers in the system...
Article
Full-text available
A system with heterogeneous servers, Markov Modulated Poisson flow and instantaneous feedback is studied. The primary call is serviced on a high-speed server, and after it is serviced, each call, according to the Bernoulli scheme, either leaves the system or requires re-servicing. After the completion of servicing of a call in a slow server, accord...
Article
We study the Markov model of a servicing system with one server and instantaneous feedback. After servicing is complete, a part of the calls, according to the Bernoulli scheme, either leave the system or immediately return to receive re-servicing, which requires a positive (random) server switching time. The intensity of the incoming stream depends...
Article
Full-text available
In this paper, we investigate the M/M/1 retrial queue with working vacations and a constant retrial rate. In the queue, customers decide about the entry based on the information upon their arrival instants. Scenarios regarding the availability of information (i.e., the server is occupied or not, and the server is on the vacation or not) for custome...
Article
Full-text available
In the originally published article, the order of the affiliations of the first and the corresponding author was incorrectly indicated.
Article
The mathematical model of a queueing system with heterogeneous servers, without queues, and with two types of requests is investigated. High-priority requests are processed in fast servers while low-priority calls are processed in slow servers. If all servers in some group are busy, then reassigning of requests to another group is allowed. Reassign...
Chapter
In this paper, we propose an approximate method to investigate the Markovian queuing system with two separate pools of heterogeneous servers (HS) under N-policy. It is assumed that fast servers (F-servers) remain awake all the time while slow servers (S-servers) will go to sleep independently when number of calls in the buffer less than some thresh...
Chapter
Mathematical models of the single channel queuing system with MMPP flow and instantaneous feedback are proposed. After completion of the service, calls either leave the system or, immediately return to system to receive repeated services. Service times both of primary and feedback (secondary) calls has exponential distribution but with different pa...
Article
Full-text available
The model of multi-channel queuing system with Markov modulated Poisson process (MMPP) flow and delayed feedback is considered. After the customer is served completely, they will decide either to join the retrial group again for another service (feedback) with some state-dependent probability or to leave the system forever with complimentary probab...
Chapter
Mathematical models of the multichannel queueing systems with both instantaneous and delayed feedbacks are proposed. Probabilities of leaving the system, instantaneous returning to channels and entering to orbit depend on the number of calls in orbit. Both models with finite and infinite size of orbit are investigated. Refined approximate algorithm...
Article
Markov models of systems with heterogeneous servers, various types of requests, and jump priorities are proposed. It is assumed that there are high and low priority requests; the high priority requests are assigned to the server with the high service rate, and the low priority requests are assigned to the server with the low service rate. Models of...
Chapter
Full-text available
In this paper, a single server retrial queue MMPP/M/1 with impatient calls is analysed under the heavy load condition. The retrial queue has a dynamical rate of the calls patience depending on the number of calls in the orbit. It is proved that under the heavy load condition the asymptotic characteristic function of the number of calls in the orbit...
Article
We propose a model of a queueing system with a single server, perishable inventory and repeated customers that can form an orbit of infinite size. In the absence of inventory in the system, primary customers according to the Bernoulli scheme either enter the queue or go into the orbit. The system uses the (s, S)-policy of replenishing the inventory...
Article
Предложена модель системы обслуживания с одним сервером, портящимися запасами и повторными заявками, которые могут образовывать орбиту бесконечного размера. При отсутствии запасов в системе первичные заявки согласно схеме Бернулли либо становятся в очередь, либо уходят в орбиту. В системе используется (s,S)-политика пополнения запасов. Разработан м...
Article
Three-dimensional Perishable Queueing-Inventory System (PQIS) models with positive service time and delayed feedback are studied in this paper. We assume that the customers either leave the system with/without purchasing an item or join the orbit for the decision making. We apply the replenishment policy with the exponentially distributed positive...
Article
Full-text available
This paper focusses on a perishable inventory model with two stations, namely, station 1 and station 2 with two dedicated servers and one flexible server, where service rates are different with respect to stations and servers. By using matrix analysis method, the joint stationary distribution of the number of customers in station 1 and station 2, t...
Article
Markov models of queuing-inventory systems with demands of two types are proposed. In these systems, two restocking policies are used: policies with fixed and variable demand size. High-priority demands have no access constraints while low-priority demands are accepted if the total number of demands in the system is less than a given threshold. Met...
Article
Markov models of perishable inventory systems where some customers are withdrawn after completion of the service without buying the stock are studied. It is assumed that the service time and filling supply orders are positive random variables. The inventory replenishment size is a variable and depends on the current inventory level. Exact and appro...
Conference Paper
The three-dimensional Perishable Queuing-Inventory System (PQIS) models with positive service time and delayed feedback are studied in this paper. We assume that the customers either leave the system with/without purchasing an item or join the orbit for the decision making. We apply the (s, S) replenishment policy with the positive order lead time....
Article
The model of perishable queueing-inventory system with server vacations is studied. Upon service completion, server takes vacation if there are no customers in the queue and it starts service at the end of the vacation if the number of customers in the system exceeds some threshold; otherwise, it takes new vacation. Exact and approximate methods ar...
Article
Изучаются марковские модели систем управления портящимися запасами, в которых некоторые заявки после завершения обслуживания не покупают запасы. Предполагается, что времена обслуживания заявок и выполнения заказов на поставку запасов являются положительными случайными величинами. Объем пополнения запасов является переменной величиной и зависит от и...
Article
We propose a model for a servicing system with perishable inventory and a finite queue of impatient claims where the server can be in one of three states: operational, early and delaying vacations. We develop a method for approximate computation of the system’s characteristics. We show results of numerical experiments.
Conference Paper
Full-text available
In this paper, model of inventory system with positive service time and perishable inventory is studied. It is assumed that some demands do not acquire the item after service completion and order replenishment lead time is a positive random variable. \((S-1, S)\) order replenishment policy is applied. The exact and approximate methods are developed...
Article
Markov models of queueing–inventory systems with variable order size are investigated. Two classes of models are considered: with instant service and with nonzero service time. The model with nonzero service time assumes that impatient customers can form a queue of either finite or infinite length. The exact and approximate methods are developed to...
Article
Models of the systems of service with perishable stocks under the presence of different types of requests are proposed. It is foreseen that some requests after completion of their service do not buy stocks. Time of the requests service and time of stocks replenishment are positive random values. The policy of refreshment belongs to a class of two l...
Article
Models of the systems of service with perishable stocks under the presence of different types of requests are proposed. It is foreseen that some requests after completion of their service do not buy stocks. Time of the requests service and time of stocks replenishment are positive random values. The policy of refreshment belongs to a class of two l...
Article
The Markov model of a two-stage queueing network with feedback is proposed. Poisson flows arrive to both stages from outside. A part of already serviced calls at the first node instantaneously enter the second node (if there is free space here) while the other calls leave the network. After the service is completed at the second node, there are thr...
Conference Paper
A Markov model of two stage queuing network with feedback is proposed. Poisson flows arriving to both stages from outside and part of already serviced calls in the first node instantaneously enter to the second node (if there is free space here) while the remaining part leaves the network. At the completion of call processing in the second node the...
Article
Two schemes of partitioning the shared channel pool between the calls of speech and data in the integral cellular communication networks were proposed. One uses the isolated partitioning procedure, the other, the virtual partitioning. The isolated partitioning forbids channel reassignment from one zone to another, whereas the virtual partitioning r...
Article
The authors propose a mathematical model for a multi-channel queueing system with feedback in which one part of calls instantaneously enters the system for repeated service and the other part either retries in some random time or finally leaves the system. The behavior of the serviced calls is randomized. Both exact and asymptotic methods are devel...
Conference Paper
We consider infinite-server queue with Markov modulated Poisson arrivals and feedback. Asymptotic analysis of the aggregate arrival process is made under conditions of frequent changing of the underlying chain states of the arrival process and increasing service time. It is proved that the aggregate arrival process is Poisson asymptotically. Parame...
Conference Paper
This paper deals with performance modeling of radio frequency licensing. Licensed users (Primary Users - PUs) and normal users (Secondary Users - SUs) are considered. The main idea, is that the SUs are able to access to the available non-licensed radio frequencies. A finite-source retrial queueing model with two non-independent frequency bands (con...
Article
Full-text available
New models of queueing-inventory systems with finite and infinite queues of impatient consume customers are proposed. Here level of inventory is reduced only after servicing customers. Both exact and approximate methods to calculate the characteristics of the proposed models are developed. The results of numerical experiments are shown.
Article
Full-text available
Models of perishable queueing systems with repeated consume customers are proposed. A life time of inventory is assumed finite and with inventory the consume customers are serviced immediately but without it they can either leave the system or repeat some time later. Restocking time is a positive random quantity and restocking policy belongs to a c...
Article
In this paper, exact and approximate approaches for studying queuing models with state-dependent jump priorities are developed. Both models with finite separate buffers and finite common buffer for heterogeneous calls are investigated. It is shown that both models might be described by two-dimensional Markov Chains (2-D MC). Exact approach based on...
Article
Full-text available
The models of the queueing-inventory systems with randomized lead policy and either finite or infinite queue of impatient consume customers are proposed. The exact and approximate methods to calculate the characteristics of the systems under the given lead policies are developed.
Article
Models of perishable queueing systems with repeated consume customers are proposed. A life time of inventory is assumed finite and with inventory the consume customers are serviced immediately but without it they can either leave the system or repeat some time later. Restocking time is a positive random quantity and restocking policy belongs to a c...
Conference Paper
Full-text available
The new Markov models of multi-channel queueing systems with instantaneous and delayed feedback are proposed. In these models part of already serviced calls instantaneously feeds back to channel while the rest part either leaves the system or feeds back to channel after some delay in orbit. Behavior of already serviced calls is handled by randomize...
Article
Full-text available
A mathematical model of the multichannel queueing system with feedback is proposed. The feedback occurs as returning a part of serviced calls to get a new service. The probability of returning to orbit depends on the number of busy channels. Both models with finite and infinite orbits are examined. Both exact and approximate methods to calculate ch...
Article
The queuing system with dynamic priorities which have a multiplicative form of the priority functions is considered. Solving the problem of minimizing the total length of the queues of the requests of diverse types is reduced to some problem of fractional-linear programming. The simulation models of the investigated system are constructed. The expe...
Conference Paper
A new access scheme in integrated wireless networks which is based on virtual partition of channels among voice and data calls is proposed. In this scheme a voice call occupies a free channel in its own zone and if there is no available channel in the given zone a handover voice call searches for an idle channel in another zone. A threshold for num...
Book
Full-text available
The increasing complexity of telecommunication networks requires us to develop adequate mathematical models. We must find their characteristics, optimize them subject to chosen criteria, and develop the corresponding control algorithms. Multidimensional queueing models are used to design and optimize modern and next-generation networks (NGN). The c...
Article
We propose a new admission strategy in integrated cellular networks based on virtual partitioning of channels between voice and data calls. Access of new data calls to channels is restricted depending on the total number of data calls in the cell. A method is developed to calculate the quality of service metrics of the partitioning scheme.
Article
Full-text available
A unified approach to the analysis of models of cellular communication networks with queues of data calls was developed. Consideration was given to the models with two types of strategies for admission to the cell channels and the buffer. In one strategy, admission to the voice call channels is based on reservation of channels for handover of calls...
Chapter
This chapter presents the foundations of multidimensional Erlang’s models, and the discussion has been concentrated on Markov models with pure losses. Both single-rate and multi-rate Erlang’s loss models with uncontrolled access schemes are considered. Effective computational procedures to calculate the main quality of service (QoS) metrics are sho...
Chapter
In the previous chapter, the second-generation cellular networks which are primarily concerned with single service class (voice traffic) communications were investigated. However, future generation wireless networks need to incorporate multimedia services (e.g., voice, video, data, etc.). In such networks all traffics (type of services) can be broa...
Chapter
The classical theory of multidimensional queueing systems is based on many assumptions, one of them is basic: one call—one channel. However, in modern integral (multiservice) communication networks, this assumption is not carried out. Thus, in them, for example, a video information requires the wider band in a digital transmission line than data or...
Chapter
In this chapter, methods for exact and approximate evaluation of the characteristics of mono-service cellular networks with single traffic are developed. In other words, models with only one type of traffic in which new and handover calls have the same bandwidth requirements and identically distributed channel holding time with common average value...
Chapter
In this chapter, new queueing models of switching equipment in packet networks and corresponding algorithms necessary for their analyzing are developed. Traditional approaches to solving the indicated problems focused mainly on simple queueing models with single traffic and do not take into account various QoS requirements of heterogeneous cells (p...
Article
A new hybrid access strategy in an isolated cell of the wireless communication network, which provides the sharing of channels reservation schemes for new calls and the cutting off scheme for h-calls, is proposed. It is assumed that the channel holding time by the calls of various types is different. The exact and approximate methods of calculating...
Article
Full-text available
The indicated work states that the system of equilibrium equations for stationary probabilities of states of the investigated model has a solution in multiplicative form. We show that this fact is not true.
Article
Full-text available
A numerical method is proposed to calculate the quality of service (QoS) of multi-service cellular networks with multi-parameter call admission control. A finite or infinite queue for non-real time traffic only is allowed. A decision for the access of new and handover voice calls is chosen on the basis of the number of such calls in channels while...
Article
Full-text available
This paper proposes a space merging approach to studying the queuing models with finite buffers and jump priorities. Upon the arrival of a call with low priority, one call of such kind is assumed to be transferred to the end of the queue of high priority calls. The transfer probabilities depend on the state of the queue of the heterogeneous calls....
Article
A numerical method for calculating the parameters of quality of service (QoS) metrics in multi-service cellular networks, which allow the formation of bounded or unbounded queues for data calls, is proposed. The access of voice calls is controlled via two-parameter strategy, and access of data calls is determined using one threshold parameter. The...
Article
An algorithmic approach to study queuing models with common finite and infinite buffer and jump priorities is developed. It is assumed that upon arrival of a low-priority call, one call of such kind can be transferred with some probability to the end of the queue of high-priority calls. The transition probability depends on the state of the queue o...
Article
Full-text available
An approximate method for analysis of the queuing models with jump priorities was developed. It is assumed that upon arrival of a low-priority call one call of such kind might be immediately transferred to the end of the queue of the high-priority calls. The transfer probabilities depend on the state of the queue of heterogeneous calls. Considerati...
Conference Paper
A space merging approach to study the queuing models with finite buffers and jump priorities is proposed. It is assumed that upon arriving a call with low priority one call of such kind might be transfer to the end of queue of high priority calls. Transfer probabilities are depending on state of the queue of heterogeneous calls. The algorithms to c...
Article
We develop an analytical approach to the performance analysis and optimization of wireless cellular networks for which different types of calls are prioritized based on a channel reservation scheme. We assume that the channel occupancy time differs for new and handover calls. We obtain simple formulas for calculating quality of service (QoS) metric...
Article
Full-text available
Data transmission in multimedia WSNs are required high bandwidth and reliable transfer because of large amount of data size. However, some applications of WSNs are required high quality. In this context, main factor in quality of ser-vices (QoS) metrics in WSNs becomes longevity of the network and high quality. In sensor nodes, choosing relevant tr...
Article
An algorithmic approach to studying the queuing models with finite queues and jump-like properties is developed. It is assumed that upon a low priority call arriving, one call of such kind with certain probability can be transferred to the end of the queue of high priority calls. Transfer probability depends on the state of the queue of heterogeneo...
Article
We propose an analytical approach for investigating the quality of service metrics in cellular wireless networks that support narrowband voice calls and wideband data calls. Call admission is controlled by a randomized access strategy that takes into account the number of busy channels and type of call. Explicit formulas for calculating the QoS met...
Article
Full-text available
Numerical method to calculate the quality of service (QoS) metrics of multiservice wireless cellular communication networks is proposed. Here finite of infinite queue for nonreal time traffic is allowed while access of real time traffic is regulated by two-parametric strategy. Decision for access of new and handover calls of real time traffic is ma...
Article
Full-text available
An analytical method is proposed for the analysis of a multidimensional Erlang model with randomized call admission control strategy. The applications of this model in both wireless multiservice cellular networks and integrated voice/data networks are demonstrated.