Optimization of the service strategy in a queueing system with energy harvesting and customers’ impatience

Dudin, Alexander,Lee, Moon Ho,Dudin, Sergey De Gruyter Open 2016 International journal of applied mathematics and c Vol.26 No.2

<P><B>Abstract</B></P><P>A single-server queueing system with an infinite buffer is considered. The service of a customer is possible only in the presence of at least one unit of energy, and during the service the number of available units decreases by one. New units of energy arrive in the system at random instants of time if the finite buffer for maintenance of energy is not full. Customers are impatient and leave the system without service after a random amount of waiting time. Such a queueing system describes, e.g., the operation of a sensor node which harvests energy necessary for information transmission from the environment. Aiming to minimize the loss of customers due to their impatience (and maximize the throughput of the system), a new strategy of control by providing service is proposed. This strategy suggests that service temporarily stops if the number of customers or units of energy in the system becomes zero. The server is switched off (is in sleep mode) for some time. This time finishes (the server wakes up) if both the number of customers in the buffer and the number of energy units reach some fixed threshold values or when the number of energy units reaches some threshold value and there are customers in the buffer. Arrival flows of customers and energy units are assumed to be described by an independent Markovian arrival process. The service time has a phase-type distribution. The system behavior is described by a multi-dimensional Markov chain. The generator of this Markov chain is derived. The ergodicity condition is presented. Expressions for key performance measures are given. Numerical results illustrating the dependence of a customer’s loss probability on the thresholds defining the discipline of waking up the server are provided. The importance of the account of correlation in arrival processes is numerically illustrated.</P>

Analysis of Priority Retrial Queue With Many Types of Customers and Servers Reservation as a Model of Cognitive Radio System

Dudin, Alexander N.,Lee, Moon Ho,Dudina, Olga,Lee, Sung Kook Institute of Electrical and Electronics Engineers 2017 IEEE Transactions on Communications Vol. No.

<P>Cognitive radio is emerging as one of the key information transmission technologies to enhance spectrum efficiency for dramatically increased wireless network capacity requested by end users. Dynamic spectrum access allows effective use of radio frequency and prevents its underutilization in many real-world networks. It enables unlicensed users to temporarily “borrow” unused spectrum while ensuring that the rights of the incumbent license holders are respected. Problems of optimization of joint access of primary and secondary users can be effectively solved by means of queueing theory. In this paper, the analysis of a novel queueing model suitable for the optimization of access is implemented under quite general assumptions about the system parameters. There are several types of primary customers having different requirements for the service time and preemptive priority over secondary customers. Secondary customers can share a server, while primary customers occupy the whole server. The arrival flow is described by the marked Markovian arrival process. The service time distribution is of phase-type. Effect of retrials of secondary customers is taken into account. An effective way for the analysis of multi-server queues with many types of customers and heterogeneous requirements to the service process is provided and applied.</P>

Analysis of a queue with heterogeneous impatient customers operating in the random environment

( Alexander Dudin ),( Sergey Dudin ),( Olga Dudina ),( Che Soong Kim ) 한국경영공학회 2015 한국경영공학회지 Vol.20 No.3

A single server queue with two types of impatient customers is considered. There is a finite buffer for type-1 customers and an infinite buffer for type-2 customers. The service time distribution depends on the type of a customer. If both buffers are not empty at a moment of the service completion, a type of the next customer, which will be picked up for service, is defined randomly. The system operates in the finite state Markovian random environment. The parameters of the arrival and service processes, intensities of impatience and probabilities, which define the randomized choice of a type of a customer for service, depend on the current state of the random environment. This queueing model can be used for analysis of various real life systems with heterogeneous impatient customers where fluctuation of the intensity of arrival and service processes is possible, especially telecommunication systems. The stationary distribution of the five-dimensional Markov chain defining the dynamics of the system is computed and the expressions for the key performance measures of the system are derived. Results of numerical experiment are presented.

Analysis of a semi-open queueing network with Markovian arrival process

Kim, Jiseung,Dudin, Alexander,Dudin, Sergey,Kim, Chesoong Elsevier 2018 Performance evaluation Vol.120 No.-

<P><B>Abstract</B></P> <P>A semi-open queueing network having a finite number of nodes is considered. The nodes are modeled by single-server queueing systems with a finite buffer and an exponential service time distribution. Customers arrive to the network according to a Markovian arrival process. The number of customers, which can be processed in the network simultaneously, is restricted by a threshold. If the number of customers in the network is less than this threshold, when a new customer arrives, the customer is processed in the network. Choice of the first and the subsequent nodes for service is performed randomly according to a fixed stochastic vector and a transition probability matrix. If the number of customers in the network at the customer arrival epoch is equal to the threshold, the customer is queued into an input buffer with an infinite capacity. Customers in the input buffer are impatient. The stationary behavior of network states is analyzed. The Laplace–Stieltjes transform of the distribution of the customer’s waiting time in the input buffer is obtained. Expressions for computing performance measures of the network are derived. Numerical results are presented. The model is suitable, e.g., for analysis and optimization of wireless telecommunication networks and manufacturing systems with a finite number of machines and workers.</P>

Queueing System Operating in Random Environment as a Model of a Cell Operation

Kim, Chesoong,Dudin, Alexander,Dudina, Olga,Kim, Jiseung Korean Institute of Industrial Engineers 2016 Industrial Engineeering & Management Systems Vol.15 No.2

We consider a multi-server queueing system without buffer and with two types of customers as a model of operation of a mobile network cell. Customers arrive at the system in the marked Markovian arrival flow. The service times of customers are exponentially distributed with parameters depending on the type of customer. A part of the available servers is reserved exclusively for service of first type customers. Customers who do not receive service upon arrival, can make repeated attempts. The system operation is influenced by random factors, leading to a change of the system parameters, including the total number of servers and the number of reserved servers. The behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is constructed and the ergodicity condition is derived. Formulas for computation of the main performance measures of the system based on the stationary distribution of the Markov chain are derived. Numerical examples are presented.

Queueing System Operating in Random Environment as a Model of a Cell Operation

Chesoong Kim,Alexander Dudin,Olga Dudina,Jiseung Kim 대한산업공학회 2016 Industrial Engineeering & Management Systems Vol.15 No.2

We consider a multi-server queueing system without buffer and with two types of customers as a model of operation of a mobile network cell. Customers arrive at the system in the marked Markovian arrival flow. The service times of customers are exponentially distributed with parameters depending on the type of customer. A part of the available servers is reserved exclusively for service of first type customers. Customers who do not receive service upon arrival, can make repeated attempts. The system operation is influenced by random factors, leading to a change of the system parameters, including the total number of servers and the number of reserved servers. The behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is constructed and the ergodicity condition is derived. Formulas for computation of the main performance measures of the system based on the stationary distribution of the Markov chain are derived. Numerical examples are presented.

Mathematical analysis of the multi-server queueing model for dynamic channel reservation in wireless networks

Lee, Moon Ho,Dudin, Alexander,Klimenok, Valentina IEEE 2006 IEEE COMMUNICATIONS LETTERS Vol.10 No.12

<P>We consider a multi-server queueing model with two types of customers offered in Y. C. Kim et al. (1999) for modeling dynamic channel reservation based on mobility in wireless networks. Mathematical analysis given contains essential errors what makes some results negligible. We provide a correct analysis of the model</P>

Analysis of Multiserver Queueing System with Opportunistic Occupation and Reservation of Servers

Sun, Bin,Lee, Moon Ho,Dudin, Sergey A.,Dudin, Alexander N. Hindawi Limited 2014 Mathematical problems in engineering Vol.2014 No.-

Computation of the steady state distribution for multi-server retrial queues with phase type service process

Kim, Che Soong,Mushko, Vilena V.,Dudin, Alexander N. Springer-Verlag 2012 Annals of operations research Vol.201 No.1