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1

Optimization and decision-making for a service contract on machine maintenance

Luo Zeyu, Yang Zhixin, Wu Jinbiao, Lian Zhaotong

Operations Research and Decisions

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2024

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Vol. 34, No. 4

89--101

EN

We investigate a novel maintenance service contract model. The service provider of the machine must determine the optimal pricing structure and staffing levels, while the client selects an appropriate plan for the warranty duration. We consider linear, quadratic, polynomial, and exponential pricing functions for three types of warranties. By building a service model with a non-cooperative game, we obtain the Nash equilibrium of the bargaining solution. Numerical analysis reveals that the optimal warranty period decreases monotonically with service provider revenue and increases monotonically with the maximum prospective service time. Additionally, the market size does not affect the ideal warranty duration when the machine’s lifetime is constant.

2

Predictions and Application of Queueing Analysis: A Case of Regional Hospital Limbe, Cameroon

Machangara Daphne T., Boubacar Habiboulaye Amadou, Andreatta Giovanni, Ndolo Antony

Decision Making in Manufacturing and Services

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2024

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Vol. 18

39--64

EN

In this work, we apply queue analysis and the prediction of waiting time at the Regional Hospital Limbe (RHL). The main purpose of the work was to be able to make mathematical sense of a real-life scenario concerning queues (waiting lines) and to try to come up with models for performance measurement and improvement. This can be achieved using queueing theory concepts, composed of queueing models that provide some operational insights because of their analytical nature. The observations included studying patient arrival and waiting times, together with doctor service times. The results show the busy departments in the hospital, busy days, and busy times. Long waiting times were found to exist mainly in general practitioner (GP) and specialist consultations. The queueing concept was applied to only one service segment, GP consultation. Although strong scientific conclusions cannot be made on the queuing models obtained due to inefficient data, the value of this work lies mainly in the methodology and proposal of different operating systems that can be adopted. Furthermore, some predictions were made using machine learning to see how long a patient can wait in a queue for service, the model predicting with an average of 10 minutes and 53 seconds of error.

3

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.

4

Evaluation of ships turnaround time in port with approach channel

Kuznetsov Alexander L., Kirichenko Alexander V., Semenov Anton D.

Scientific Journal of Gdynia Maritime University

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2020

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nr 115

31--41

EN

The operation efficiency of a port with an approach channel to a great extent depends on decisions made by the port authority and harbor master over the channel scheduling. Currently there are no formal methods which allow to evaluate the influence of the channel schedule on the ship turnaround time, especially when the throughput capacity is restricted. The relevant system has a complex structure that rules out common mathematical methods. The paper studies some typical structures of these systems and offers an approach for developing adequate simulation models. These models enable the conduct of comparative studies of different variants of approach channel scheduling and serve as a toolkit to support the decision-making procedure for harbor master and port operators.

5

System z przelewem ruchu oraz kolejkami w zasobach pierwotnych oraz wtórnych

Kaliszan A., Kmiecik D.

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

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2018

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nr 8-9

660--665, CD

PL

W artykule zaprezentowano rezultaty badań wpływu stosowania kolejkowania zgłoszeń w hierarchicznych systemach z przelewami ruchu wielousługowego. Rozważane systemy składały się z kilku zasobów pierwotnych oraz jednego zasobu wtórnego. Systemom tym oferowane były wielousługowe strumienie ruchu. W badaniach określono wpływ struktury ruchu, pojemności kolejek, maksymalnego czasu przebywania w kolejce (ograniczony oraz nieograniczony) oraz zasobu, w którym wykorzystano kolejkowanie (zasoby pierwotne, zasoby alternatywne). Wnioski prezentowane w artykule zostały oparte na wyznaczonych prawdopodobieństwach blokady w systemach przelewowych.

EN

In this paper, the performance evaluation of call queuing in hierarchical systems with multi-service overflow traffic was presented. The considered system model consisted of a few primary resources and a single secondary resource servicing multi-service traffic streams. The study investigated the impact of the traffic structure, queue capacity, maximum queueing time (limited or unlimited) and the placement of queuing resources (primary resources or secondary resources). The presented results are based on determined blocking probabilities in the systems with overflow traffic.

6

From exhaustive vacation queues to preemptive priority queues with general interarrival times

Fiems D., De Vuyst S.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 4

695--704

EN

We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive MX+G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.

7

Dimensioning aspects of SMS systems in mobile networks

Klink J., Uhl T.

Zeszyty Naukowe Akademii Morskiej w Szczecinie

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2017

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nr 49 (121)

110--118

EN

This paper focuses on factors affecting the dimensioning of Short Message Service (SMS) systems in mobile communications networks. Problems associated with Quality of Service (QoS) in modern communications networks in general are described, along with the main parameters that define QoS in SMS systems. The functionality of the SMS in terms of European Telecommunications Standards Institute (ETSI) standards is then explained. The creation of a queuing model is described for an SMS system which is based on ETSI documentation and will be analysed in calculations. The parameter completion rate plays an important role in SMS. Practical aspects of the End-to-End (E2E) delivery time for SMS systems are also discussed. The approach suggested in this paper and the insights gained in the course of this work can be of valuable practical use in the planning and analysis of real SMS systems.

8

Investigation into the bimodal transportation process by modelling rail module states

Lavrukhin O., Zapara V., Zapara Y., Shapatina O., Bogomazova G.

Transport Problems

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2017

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T. 12, z. 2

99--112

EN

The bimodal transportation process, which takes into account the modelling of rail module states, has been studied. The article demonstrates marked graphs of rail module states with and without running gear change in operation. It has been established which states have the greatest impact on the probability of a steady mode. The work has considered fractality of arrivals and its range in the queueing system with priorities.

9

Expected volumes of requests in systems of the queueing network with a limited number of waiting places

Zając P., Matalytski M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2017

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Vol. 22

141--160

EN

We present a method of finding the expected volume of requests in HM-network with homogeneous requests and bypass of the queueing systems of requests. The case was considered when the volume changes associated with the transitions between the states of the network are deterministic functions, depending on the state of the network and time, and the systems are single line. It is assumed that the probability of the states of the network systems, the parameters of the entrance flow of the requests and the service depend on the time.

10

Analysis of an MAP/PH/1 queue with flexible group service

Brugno A., D’Apice C., Dudin A., Manzo R.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 1

119--131

EN

A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer’s service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace–Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.

11

Estimation of Network Disordering Effects by In-depth Analysis of the Resequencing Buffer Contents in Steady-state

Pechinkin A., Razumchik R.

Journal of Telecommunications and Information Technology

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2016

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nr 1

53--41

EN

The paper is devoted to the analytic analysis of resequencing issue, which is common in packet networks, using queueing-theoretic approach. The authors propose the mathematical model, which describes the simplest setting of packet resequencing, but which allows one to make the first step in the in-depth-analysis of the queues dynamics in the resequencing buffer. Specifically consideration is given to N-server queueing system (N > 3) with single infinite capacity buffer and resequencing, which may serve as a model of packet reordering in packet networks. Customers arrive at the system according to Poisson flow, occupy one place in the buffer and receive service from one of the servers, which is exponentially distributed with the same parameter. The order of customers upon arrival has to be preserved upon departure. Customers, which violated the order are kept in resequencing buffer which also has infinite capacity. It is shown that the resequencing buffer can be considered as consisting of n, 1 ≤ n ≤ N −1, interconnected queues, depending on the number of busy servers, with i-th queue containing customers, which have to wait for i service completions before they can leave the system. Recursive algorithm for computation of the joint stationary distribution of the number of customers in the buffer and servers, and each queue in resequencing buffer are being obtained. Numerical examples, which show the dynamics of the characteristics of the queues in resequencing buffer are given.

12

Zastosowanie teorii masowej obsługi do modelowania systemów transportowych

Kisielewski P., Sobota Ł.

Autobusy : technika, eksploatacja, systemy transportowe

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2016

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R. 17, nr 6

600--604

PL

W artykule przedstawiono zastosowanie teorii masowej obsługi do analizy i modelowania wybranych systemów transportowych.

13

Wyznaczenie rozkładu objętości sumarycznej w jednoliniowym systemie kolejkowym z priorytetem bezwzględnym

Tikhonenko O.

Studia i Materiały / Europejska Uczelnia Informatyczno-Ekonomiczna w Warszawie

|

2014

|

Nr 2(8)

57--75

PL

W artykule przeanalizowano jednoliniowe systemy kolejkowe z priorytetem bezwzględnym przy założeniu, że zgłoszenie każdej klasy priorytetowej posiada objetość losową, od której zależy czas obsługi tego zgłoszenia. Założono również, że charakterystyki wspólnego rozkładu objetości zgłoszenia i jego czasu obsługi mogą być różne dla różnych klas priorytetowych. Dla rozpatrywanego systemu z nieograniczoną pojemnością pamięci otrzymano charakterystyki wspólnego rozkładu objetości sumarycznej zgłoszeń różnych klas priorytetowych.

EN

One-server preemptive priority queueing systems are analyzed under assumption that a demand of each priority has some random capacity and service time of the demand depends on its capacity. It is assumed that the joint characteristics of service time and demand capacity can be different for different priorities. For the system under consideration (with unbounded total capacity), characteristics of joint distribution of each priority total demand capacity are obtained.

14

The system M2θ/G/1/m with threshold control of the arrival rate and service time

Zhernovyi Y., Kopytko B.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 2

149--163

EN

We consider a M2θ/G/1/m queueing system with arrival of customer batches, which uses a threshold control mechanism of the service time and arrival rate. The system receives two independent flows of customers, one of which is blocked in an overload mode (under the condition that the number of customers in the system exceeds a given threshold value h). Full blocking of the input flow is carried out from the moment when the queue length reaches the number m until the beginning of the service of the first customer, for which the number of customers in the system does not exceed h. From the beginning of the service of the first customer during the excess of number of customers in the system of h until the completion of full blocking the time of service of customer is distributed under the law of F(x) (an increased service rate is used). Rest of the time the system applies the normal service rate with the distribution function F(x) of service time. Laplace transforms for the distributions of the number of customers in the system during the busy period and for the distribution function of the busy period are found. The average duration of the busy period is obtained. Formulas for the stationary distribution of the number of customers in the system, for the probability of service and for the stationary characteristics of the system are established. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.

15

Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies

Gaidamaka Y., Pechinkin A., Razumchik R., Samouylov K., Sopin E.

International Journal of Applied Mathematics and Computer Science

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2014

|

Vol. 24, no. 3

519--534

EN

Hysteretic control of arrivals is one of the most easy-to-implement and effective solutions of overload problems occurring in SIP-servers. A mathematical model of an SIP server based on the queueing system [...] with batch arrivals and two hysteretic loops is being analyzed. This paper proposes two analytical methods for studying performance characteristics related to the number of customers in the system. Two control policies defined by instants when it is decided to change the system’s mode are considered. The expression for an important performance characteristic of each policy (the mean time between changes in the system mode) is presented. Numerical examples that allow comparison of the efficiency of both policies are given.

16

A finite-buffer queue with a single vacation policy: An analytical study with evolutionary positioning

Woźniak M., Kempa W. M., Gabryel M., Nowicki R. K.

International Journal of Applied Mathematics and Computer Science

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2014

|

Vol. 24, no. 4

887--900

EN

In this paper, application of an evolutionary strategy to positioning a GI/M/1/N-type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical experiments are presented. A cost optimization problem is solved using an evolutionary strategy for a class of queueing systems described by exponential and Erlang distributions.

17

Determination of loss characteristicsfor queueing systems with bounded buffer space

Tikhonenko O., Tikhonenko-Kędziak A.

Studia i Materiały / Europejska Uczelnia Informatyczno-Ekonomiczna w Warszawie

|

2013

|

Nr 2(6)

29--38

EN

We investigate non-classical queueing systems with demands characterized by some random capacity under assumption that demand service time generally depends on its capacity. This dependency can be defined by the joint distribution function. The total demands capacity (i.e. the sum of capacities of demands present in the system at arbitrary time instant) is bounded by some constant value V that is named buffer space volume of the system. Such systems have been used to model and solve various problems occurring in the design of computer and communicating systems. The main steady-state performance characteristics of such systems are loss probability (the relative part of demands that was lost in the system during infinite time interval) and probability of capacity unit losing (the relative part of total demands capacity that was lost during infinite time interval). In the paper we determine these characteristics for some systems with bounded buffer space and compare the results of our calculations with the results of calculations of loss probability in classical regenerative queueing systems using the relation obtained in [3]. Numerical examples and results of simulation are attached as well.

PL

W artykule zbadano nieklasyczne systemy kolejkowe, w których zgłoszenia są charakteryzowane losową objętością przy założeniu, że czas obsługi zgłoszenia ogólnie zależy od jego objętości. Wskazana zależność może być określona za pomocą wspólnej dystrybuanty. Objętość sumaryczna (tj. suma objętości zgłoszeń obecnych w systemie w dowolnej chwili czasu) jest ograniczona wielkością stałą V, którą nazywamy pojemnością pamięci systemu. Systemy podobnego typu są wykorzystywane do rozwiązywania rożnych zagadnień w trakcie projektowania systemów komputerowych i sieci komunikacyjnych. Podstawowymi charakterystykami wydajności takich systemów w trybie stacjonarnym są prawdopodobieństwo utraty (część względna utraconych zgłoszeń w ciągu nieskończonego przedziału czasowego działania systemu) oraz prawdopodobieństwo utraty jednostki objętości (część względna utraconej sumarycznej objętości zgłoszeń w ciągu nieskończonego przedziału czasowego działania systemu). W artykule przedstawiono sposób obliczania wskazanych charakterystyk dla pewnych systemów kolejkowych z ograniczoną pojemnością pamięci oraz porównanie otrzymanych wielkości prawdopodobieństwa utraty z wynikami podobnych obliczeń otrzymanych w [3] dla klasycznych systemów kolejkowych o zachowaniu opisywanym procesem regenerującym się. Podano także wyniki obliczeń numerycznych i symulacji komputerowej.

18

Queueing system M/M/n/(m, V ) with non-identical servers

Małek J., Ziółkowski M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

|

2013

|

Vol. 18

29--39

EN

We investigate multi-server queueing systems with Poisson arrivals, non-identical servers and customers of random volume, under assumption that customer’s service time having an exponential distribution doesn’t depend on his volume, but service time parameters can be different for different servers. We also assume that the total volume of customers present in the system at arbitrary time instant is bounded by some constant value V > 0. For such systems the stationary customers number distribution and loss probability are determined.

19

The busy period for the Mθ /G/1/m system with service time dependent of the queue length

Zhernovyi Y., Kopytko B., Zhernovyi K.

Journal of Applied Mathematics and Computational Mechanics

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2013

|

Vol. 12, nr 4

127--133

EN

We consider the Mθ/G/1/m system wherein the service time depends on the queuelength and it is determined at the beginning of customer service. Using an approach basedon the potential method proposed by V. Korolyuk, the Laplace transforms for the distribution f the number of customers in the system on the busy period and for the distribution function of the busy period are found.

20

The analytical modl of IP/MPLS network

Olszewski I.

Image Processing & Communications

|

2009

|

Vol. 14, no 4

63-71

EN

In this paper, the analysis of multi-servicing IP network with Multi-Protocol Label Switching (MPLS) protocol based on the proposed analytical and simulation models has been carried out. In the models two classes of service with different QoS parameters have been analyzed: class High, responsible for example for the Premium service, and class Low services for transmission of data. In this paper the changes of packet delays and lengths of queues for the given class of services in the network were taken into account, depending on the changes of average packet lengths, load of the network and the amount of inelastic traffic in the whole traffic. The results obtained in this paper have proved, that proposed analytical model is useful for analysis of the IP networks with MPLS protocol.