Analysis of Single-Server Queue with Phase-Type Service and Energy Harvesting

Dudin, Sergey A.,Lee, Moon Ho Hindawi Limited 2016 Mathematical problems in engineering Vol.2016 No.-

<P>We propose a queueing model suitable, for example, for modelling operation of nodes of sensor networks. The sensor node senses a random field and generates packets to be transmitted to the central node. The sensor node has a battery of a finite capacity and harvests energy during its operation from outside (using solar cells, wind turbines, piezoelectric cells, etc.). We assume that, generally speaking, service (transmission) of a packet consists of a random number of phases and implementation of each phase requires a unit of energy. If the battery becomes empty, transmission is failed. To reduce the probability of forced transmission termination, we suggest that the packet can be accepted for transmission only when the number of energy units is greater than or equal to some threshold. Under quite general assumptions about the pattern of the arrival processes of packets and energy, we compute the stationary distributions of the system states and the waiting time of a packet in the system and numerically analyze performance measures of the system as functions of the threshold. Validity of Little’s formula and its counterpart is verified.</P>

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>

Queueing System with Heterogeneous Customers as a Model of a Call Center with a Call-Back for Lost Customers

Dudin, Sergey,Kim, Chesoong,Dudina, Olga,Baek, Janghyun Hindawi Limited 2013 Mathematical problems in engineering Vol.2013 No.-

<P>A multiserver queueing system with infinite and finite buffers, two types of customers, and two types of servers as a model of a call center with a call-back for lost customers is investigated. Type 1 customers arrive to the system according to a Markovian arrival process. All rejected type 1 customers become type 2 customers. Typer,r=1,2, servers serve typercustomers if there are any in the system and serve type<SUP>r′</SUP>,<SUP>r′</SUP>=1,2, <SUP>r′</SUP>≠r,customers if there are no type<I>r</I>customers in the system. The service times of different types of customers have an exponential distribution with different parameters. The steady-state distribution of the system is analyzed. Some key performance measures are calculated. The Laplace-Stieltjes transform of the sojourn time distribution of type 2 customers is derived. The problem of optimal choice of the number of each type servers is solved numerically.</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 Semi-Open Queueing Network with Customer Retrials

김제숭,Sergey Dudin 대한산업공학회 2019 대한산업공학회지 Vol.45 No.3

A semi-open queueing network is considered. The network of an arbitrary topology consists of a finite number ofnodes operation of which is modeled by single-server queueing systems with a buffer and an exponential service timedistribution. Customers arrive at the network according to a Markovian arrival process. The total number ofcustomers, which can be processed simultaneously, is restricted by a fixed in advance threshold. If the number ofcustomers in the network at a new customer arrival moment is less than the threshold, this customer is admitted forservice. Otherwise, the customer temporarily leaves the system (it is said that the customer joins the orbit) and retriesto get access to the network after the random time intervals duration of which has an exponential distribution. Thecapacity of the orbit is infinite. After the admission to the network, the customer starts sequential service in a randomnumber of nodes. The choice of the first and the subsequent nodes for service is made stochastically according to afixed stochastic vector and a transition probability matrix. The behavior of the network is described by thecontinuous-time Markov chain that belongs to the class of asymptotically quasi-Toeplitz Markov chains. This allowsto derive a transparent condition for the ergodicity of the chain and compute its steady-state distribution. Expressionsfor computation of various performance measures of the network are derived. Numerical results are presented. Themodel can be applied, e.g., for analysis and optimization of the operation of logistics and manufacturing systems,and the wireless telecommunication networks. To the best of our knowledge, queueing networks with correlatedarrival flows and retrials are not considered in the existing literature.*

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>

Multi-server Queueing Model with Many Types of Priority Customers

Seokjun Lee,Chesoong Kim,Sergey Dudin,Olga Dudina 대한산업공학회 2023 Industrial Engineeering & Management Systems Vol.22 No.2

Analysis of BMAP<SUP>(r)</SUP>/M<SUP>(r)</SUP>/N<SUP>(r)</SUP> Type Queueing System Operating in Random Environment

Chesoong Kim(김제승),Sergey Dudin 대한산업공학회 2016 대한산업공학회지 Vol.42 No.1

A multi-server queueing system with an infinite buffer and impatient customers is analyzed. The system operates in the finite state Markovian random environment. The number of available servers, the parameters of the batch Markovian arrival process, the rate of customers’ service, and the impatience intensity depend on the current state of the random environment and immediately change their values at the moments of jumps of the random environment. Dynamics of the system is described by the multi-dimensional asymptotically quasi-Toeplitz Markov chain. The ergodicity condition is derived. The main performance measures of the system are calculated. Numerical results are presented.

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.-