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1
Content available Queueing systems with random volume customers and a sectorized unlimited memory buffer
Tikhonenko Oleg, Ziółkowski Marcin, Kempa Wojciech M.
International Journal of Applied Mathematics and Computer Science
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2021
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Vol. 31, no. 3
471--486
EN
In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited memory buffer. In such systems, the arriving customers are additionally characterized by a non-negative random volume vector. The vector’s indications can be understood as the sizes of portions of information of a different type that are located in the sectors of memory space of the system during customers’ sojourn in it. This information does not change while a customer is present in the system. After service termination, information immediately leaves the buffer, releasing its resources. In analyzed models, the service time of a customer is assumed to be dependent on his volume vector characteristics, which has influence on the total volume vector distribution. We investigate three types of such queueing systems: the Erlang queueing system, the single-server queueing system with unlimited queue and the egalitarian processor sharing system. For these models, we obtain a joint distribution function of the total volume vector in terms of Laplace (or Laplace-Stieltjes) transforms and formulae for steady-state initial mixed moments of the analyzed random vector, in the case when the memory buffer is composed of two sectors. We also calculate these characteristics for some practical case in which the service time of a customer is proportional to the customer’s length (understood as the sum of the volume vector’s indications). Moreover, we present some numerical computations illustrating theoretical results.
2
Content available Calculating steady-state probabilities of single-channel closed queueing systems using hyperexponential approximation
Zhernovyi Yuriy, Kopytko Bohdan
Journal of Applied Mathematics and Computational Mechanics
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2020
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Vol. 19, nr 1
113--120
EN
In this paper we propose a method for calculating steady-state probability distributions of the single-channel closed queueing systems with arbitrary distributions of customer generation times and service times. The approach based on the use of fictitious phases and hyperexponential approximations with parameters of the paradoxical and complex type by the method of moments. We defined conditions for the variation coefficients of the gamma distributions and Weibull distributions, for which the best accuracy of calculating the steady-state probabilities is achieved in comparison with the results of simulation modeling.
3
Content available M/G/n/(0, V) Erlang queueing system with non-homogeneous customers, non-identical servers and limited memory space
Tikhonenko O., Ziółkowski M., Kurkowski M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2019
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Vol. 67, nr 3
489--500
EN
In the present paper, we investigate a?multi-server Erlang queueing system with heterogeneous servers, non-homogeneous customers and limited memory space. The arriving customers appear according to a?stationary Poisson process and are additionally characterized by some random volume. The service time of the customer depends on his volume and the joint distribution function of the customer volume and his service time can be different for different servers. The total customers volume is limited by some constant value. For the analyzed model, steady-state distribution of number of customers present in the system and loss probability are calculated. An analysis of some special cases and some numerical examples are attached as well.
4
Content available M/G→ /n/0 Erlang queueing system with heterogeneous servers and non-homogeneous customers
Ziółkowski M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2018
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Vol. 66, nr 1
59--66
EN
In the present paper, we investigate a multi-server queueing system with heterogeneous servers, unlimited memory space, and non-homogeneous customers. The arriving customers appear according to a stationary Poisson process. Service time distribution functions may be different for every server. Customers are additionally characterized by some random volume. On every server, the service time of the customer depends on their volume. The number of customers distribution function is obtained in the classical model of the system. In the model with non-homogeneous customers, the stationary total volume distribution function is determined in the term of Laplace–Stieltjes transform. The stationary first and second moments of a total customers volume are calculated. An analysis of some special cases of the model and some numerical examples are also included.
5
Content available Passenger level of service estimation model for queuing systems at the airport
Kierzkowski A., Kisiel T., Pawlak M.
Archives of Transport
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2018
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Vol. 47, iss. 3
29--38
EN
This paper presents a model for the management of passenger service operations at airports by the estimation of a global index of the level of service. This paper presents a new approach to the scheduling of resources required to perform passenger service operations at airports. The approach takes into account the index of level of service as a quantitative indicator that can be associated with airport revenues. Taking this index into account makes it possible to create an operating schedule of desks, adapted to the intensity of checking-in passengers, and, as such, to apply dynamic process management. This offers positive aspects, particularly the possibility of improvement of service quality that directly translates into profits generated by the non-aeronautical activity of airports. When talking about level of service, there can be distinguish other important indicators that are considered very often (eg maximum queuing time, space in square meters). In this model, however, they are considered as secondary. Of course, space in square meters is important when designing a system. Here this system is already built and functioning. The concept of the model is the use of a hybrid method: computer simulation (Monte Carlo simulation) with multiple regression. This paper focuses on the presentation of a mathematical model used to determine the level of service index that provides new functionality in the current simulation model, as presented in the authors’ previous scientific publications. The mathematical model is based on a multiple regression function, taking into account the significance of individual elementary operations of passenger service at an air terminal.
6
Content available Recurrence relations for a multi-channel closed queueing system with Erlangian service times of second order
Zhernovyi Y., Kopytko B.
Journal of Applied Mathematics and Computational Mechanics
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2017
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Vol. 16, nr 3
123--128
EN
We propose a method for determining the steady-state characteristics of a multichannel closed queueing system with exponential distribution of the time generation of service requests and the second order Erlang distributions of the service times. Recurrence relations to compute the steady-state distribution of the number of customers are obtained. The developed algorithms are tested on examples using simulation models constructed with the assistance of the GPSS World tools.
7
Content available Optimization of an M/M/1/N feedback queue with retention of reneged customers
Kumar R., Jain N. K., Som B. K.
Operations Research and Decisions
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2014
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Vol. 24, No. 3
45--58
EN
Customer impatience has become a threat to the business world. Firms employ various customer retention strategies to retain their impatient (or reneged) customers. Customer retention mechanisms may help to retain some or all impatient customers. Further, due to unsatisfactory service, customers may rejoin a queue immediately after departure. Such cases are referred to as feedback customers. Kumar and Sharma take this situation into account and study an M/M/1/N feedback queuing system with retention of reneged customers. They obtain only a steady-state solution for this model. In this paper, we extend the work of Kumar and Sharma by performing an economic analysis of the model. We develop a model for the costs incurred and perform the appropriate optimization. The optimum system capacity and optimum service rate are obtained.
8
Content available On characteristics of the Mθ/G/1/m and Mθ/G/1 queues with queue-size based packet dropping
Zhernovyi Y., Kopytko B., Zhernovyi K.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 4
163--175
EN
We study the Mθ/G/1/m and Mθ/G/1 queuing systems with the function of the random dropping of customers used to ensure the required characteristics of the system. Each arriving packet of customers can be rejected with a probability defined depending on the queue length at the service beginning of each customer. The Laplace transform for the distribution of the number of customers in the system on the busy period is found, the mean duration of the busy period is determined, and formulas for the stationary distribution of the number of customers in the system are derived via the approach based on the idea of Korolyuk’s potential method. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.
9
Content available Program for modelling queuing systems in transport
Dimitrov S.
Logistics and Transport
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2012
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Vol. 15, No. 2
85-90
EN
This paper presents an example application of a software program developed using the programming language VBA and designed for modelling queuing systems in the field of transport. The program enables users to quantitatively determine the indicators of the queuing systems. In order to show the program's capabilities and how it can be used, two scenarios have been considered - modelling single-server and multi-server queuing systems of type M/M/l and M/M/S, respectively, having a Poisson incoming flow of requests and exponentially distributed service times.
10
Content available M/M/n/m queueing systems with non-identical servers
Ziółkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2011
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Vol. 16
163--168
EN
M/M/n/m queueing systems with identical servers are well known in queueing theory and its applications. The analysis of these systems is very simple thanks to the fact that the number of customers ɳ(t) in the system at arbitrary time instant t forms a Markov chain. The main purpose of this paper is to analyse the M/M/n/m system under assumption that its servers are different, i.e. they have different parameters of service time.
11
Content available remote Ontological Model of the Conceptual Scheme Formation for Queuing System
Kusztina E., Różewski P., Zaikin O.
Management and Production Engineering Review
|
2010
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Vol. 1, No. 1
85-97
EN
In the article the authors propose an extended ontological model for distance learning, concerning pedagogical and cognitive requirements of the teaching/learning process. The main characteristic of the dedicated ontological model is reusability, which manifests itself in the possibility of adapting the knowledge model to different contexts and for different users by simply enabling knowledge sharing and knowledge management. The conceptual schemes are used for modelling the knowledge about queuing systems for knowledge repository and ontology development purposes. Authors have taken advantage of the computational models theory in order to create a model which combine theoretical and procedural knowledge.
12
Content available Classical and non-classical processor sharing systems with non-homogeneous customers
Tikhonenko O.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
Vol. 14
133-150
EN
We discuss a processor sharing system with non-homogeneous customers. There are resources of two types for their service: 1) resource of the first type is discrete, there are N units (servers) of the resource; 2) resource of the second type (capacity) is not-necessary discrete. The type of a customer is defined by the amount of first type resource units which is used for the customer service. Each customer is also characterized by some random capacity or some amount of the second type resource which is also used for his service. The total capacity of customers present in the system is limited by some value V >0, which is called the memory volume of the system. The customer capacity and length (the work necessary for service) are generally dependent. The joint distribution of these random variables also depends on the customer type. For such systems we determine the stationary distribution of the number of customers of each type present in the system and stationary loss probabilities for each type of customers.
13
Content available remote General approach to determining the basic characteristics of queueing systems with finite total capacity
Tikhonenko O.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
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Vol. 12
107-114
EN
We discuss a general view of solutions for characteristics of non-classical queueing systems with random capacity customers (demands), i.e. we suppose that each customer is characterized by some random capacity (volume) and the whole capacity (total volume) of customers present in the queueing system is bounded by a constant value V > 0. We determine the general view of the stationary number distribution and loss probability in the systems under consideration as compared with corresponding classical queueing systems. It's turned that in some cases we can write expressions for non-classical characteristics of finite total capacity queues if corresponding classical characteristics are known.
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