# Agassi Z. MelikovAzerbaijan National Academy of Sciences | ANAS · Teletraffic Theory

Agassi Z. Melikov

Professor

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

## About

172

Publications

10,088

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

960

Citations

Introduction

**Skills and Expertise**

Additional affiliations

September 2015 - present

## Publications

Publications (172)

In this paper, we create a framework for the uniform algorithmic analysis of queueing systems with the Markov arrival process and the simultaneous service of a restricted number of customers, described by a multidimensional Markov chain. This chain behaves as the finite-state quasi-death process between successive service-beginning epochs, with jum...

This is the PREFACE to the Special Issue “Queueing-inventory: analytical and simulation modeling and classical and retrial queues and inventory”. The year 2022 was the 30th anniversary of Queueing-inventory. It was in that connection that the guest editors requested Professor Endre Boros, the Editor-in-Chief of Annals of Operations Research, for pe...

We consider a single-server queuing-inventory system (QIS) with catastrophes under the base stock policy. Consumer customers (c-customers) that arrived to buy inventory, can be a form of queue in an infinite buffer. All items in the warehouse are destroyed if a catastrophe is occurring, but in such cases, the c-customers in the system (on the serve...

A model of a single-server queuing-inventory system (QIS) with a limited waiting buffer for consumer customers (c-customers) and catastrophes has been developed. When a catastrophe occurs, all items in the system’s warehouse are destroyed, but c-customers in the system are still waiting for replenishment. In addition to c-customers, negative custom...

A model of a single-server queuing-inventory system (QIS) with catastrophes and a finite waiting room for consumer customers (c-customers) has been developed. When a catastrophe occurs, all inventory in the system's warehouse is destroyed, but c-customers in the system are still waiting for restocking. In addition to c-customers, negative customers...

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an infinite buffer. The service time of a consumer customer follows a...

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to Poisson process and upon arrival of a catastrophe all inventory in the system is instantly destroyed. But consumer customers in the system (in the server or in the buffer) continue still waiting for the replenishment of the stock. The arriv...

This article deals with the queuing-inventory system, composed of c junior servers, a senior server, two finite waiting halls, and an infinite orbit. On occasion, junior servers encounter challenges during customer service. In these instances, they approach the senior server for guidance in resolving the issue. Suppose the senior server is engaged...

In this paper, we consider a single server production inventory model with server breakdown and customer impatience while server is down. We assume that customer arrivals are according to a Markovian Arrival Process. If the server is busy at the time of arrival of a customer, the customer joins a queue of infinite capacity. The server is subjected...

A hybrid replenishment policy in double sources queuing-inventory system with MAP flow of consumer customers is proposed. The service time of the consumer customer has a phase type distribution. If the inventory level drops to the reorder point s, then a regular order of volume \(S-s\) is generated to a slow and cheap source, where S denotes the ma...

This article deals with the queueing-inventory system, composed of c junior servers, a senior server, two finite waiting halls, and an infinite orbit. On occasion, junior servers encounter challenges during customer service. In these instances, they approach the senior server for guidance in resolving the issue. Suppose the senior server is engaged...

In this paper, we studied single-server models of queuing-inventory systems (QIS) with catastrophes in the warehouse part and negative customers (n-customers) in service facility. Consumer customers (c-customers) that arrived to buy inventory can be queued in an infinite buffer. Under catastrophes, all inventory of the system is destroyed but custo...

Models of double-source queuing-inventory systems are studied in the presence of a finite buffer for waiting in the queue of consumer customers, where instant destruction of inventory is possible. It is assumed that the lead times of orders, as well as the cost of delivery from various sources, differ from each other. Replenishment of stocks from v...

We consider a multi-server production inventory system with an unlimited waiting line. Arrivals occur according to a non-homogeneous Poisson process and exponentially distributed service time. At the service completion epoch, one unit of an item in the on-hand inventory decreases with probability δ, and the customer leaves the system without taking...

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...

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...

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...

The model of perishable inventory system with orbit is examined under (s, S) and (s, Q) policies. The stability condition of the system is derived and the joint distribution of the number of customers in orbit and the inventory level is obtained by using matrix-geometric method. Formulas for calculation of the performance measures are developed. Th...

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...

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...

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...

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...

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...

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...

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...

In the originally published article, the order of the affiliations of the first and the corresponding author was incorrectly indicated.

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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....

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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.

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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.

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...

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....

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...

Major errors in the indicated work are point out.

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...

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...

A space merging approach to study t