A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

Baek, Janghyun,Dudina, Olga,Kim, Chesoong UNIVERSITY OF ZIELONA GORA PRESS 2017 INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND C Vol.27 No.2

<P><B>Abstract</B></P><P>A single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered. Type-1 customers have limited preemptive priority over type-2 customers. There is an infinite buffer for type-2 customers and no buffer for type-1 customers. There is also a finite buffer (stock) for consumable additional items (semi-products, half-stocks, etc.) which arrive according to the Markovian arrival process. Service of a customer requires a fixed number of consumable additional items depending on the type of the customer. The service time has a phase-type distribution depending on the type of the customer. Customers in the buffer are impatient and may leave the system without service after an exponentially distributed amount of waiting time. Aiming to minimize the loss probability of type-1 customers and maximize throughput of the system, a threshold strategy of admission to service of type-2 customers is offered. Service of type-2 customer can start only if the server is idle and the number of consumable additional items in the stock exceeds the fixed threshold. Stationary distributions of the system states and the waiting time are computed. In the numerical example, we show some interesting effects and illustrate a possibility of application of the presented results for solution of optimization problems.</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.

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>

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.

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.

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>

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