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It is analytically difficult to derive the probability distribution function of waiting (or delay) time at the second or third queue in series of tandem queues. This paper presents a method by which approximation is done through a quasi‐isomorphic system which resembles the second queue in respect of one output, viz delay time. Through extensive simulation experiments these isomorphs have been derived. The procedure of getting a simple system to represent a part of a complex system is practised in cybernetics; this approach appears to have potentiality in studying intractable problems in communications and industrial management.

Petri net (PN) and queuing theory are used in performance analysis of a flexible manufacturing system (FMS). They are used to determine the FMS measures of performance. These measures of performance include optimal work‐in‐process (WIP), lead time, production rate, machine utilization, and number of servers at each station. The purpose of this paper is to present a comparison between PN and queuing network tools to determine the optimum values for FMS measures of performance.

PN model with dual kanban and closed queuing network are used for analysis and performance evaluation of FMS. Integrated network analyzer and Lingo softwares are used for performance evaluation of FMS by PN tool. CANQ software is used for performance evaluation of FMS by queuing network. In both the approaches, the throughput is bounded by the utilization of the bottleneck machines.

The comparison shows that for the given number of servers, PN gives better values of performance measures for FMS. The PN optimization gives minimum WIP corresponding to the maximum production rate. Minimum WIP leads to minimum lead time.

The results are concluded based on one case study. In future research, the results may be achieved by doing more case studies with different numbers of system parameters and/or parameter settings.

Using the PN model, the production manager may design, analyze, evaluate, and even optimize the layout of the production system for minimum WIP, maximum throughput, and reduced lead time. The determination of the total WIP, total number of stations in the production system, and the number of servers at each station may be helpful in shop floor management. It may result in more production efficiency along with ease of supervision.

This paper presents a first novel comparison of its kind between PN and queuing network for evaluation of FMS.

Nowadays, in many organizations, products are not delivered instantly. So, the customers should wait to receive their needed products, which will form a queueing-inventory model. Waiting a long time in the queue to receive products may cause dissatisfaction and churn of loyal customers, which can be a significant loss for organizations. Although many studies have been done on queueing-inventory models, more practical models in this area are needed, such as considering customer prioritization. Moreover, in many models, minimizing the total cost for the organization has been overlooked.

This paper will compare several machine learning (ML) algorithms to prioritize customers. Moreover, benefiting from the best ML algorithm, customers will be categorized into different classes based on their value and importance. Finally, a mathematical model will be developed to determine the allocation policy of on-hand products to each group of customers through multi-channel service retailing to minimize the organization’s total costs and increase the loyal customers' satisfaction level.

To investigate the application of the proposed method, a real-life case study on vaccine distribution at Imam Khomeini Hospital in Tehran has been addressed to ensure model validation. The proposed model’s accuracy was assessed as excellent based on the results generated by the ML algorithms, problem modeling and case study.

Prioritizing customers based on their value with the help of ML algorithms and optimizing the waiting queues to reduce customers' waiting time based on a mathematical model could lead to an increase in satisfaction levels among loyal customers and prevent their churn. This study’s uniqueness lies in its focus on determining the policy in which customers receive products based on their value in the queue, which is a relatively rare topic of research in queueing management systems. Additionally, the results obtained from the study provide strong validation for the model’s functionality.

The purpose of the paper is to analyze reliability characteristics of batch service queuing system with a single server model that envisages Poisson input process and exponential service times under first come, first served (FCFS) queue discipline.

With the help of renewal theory and stochastic processes, a model has been designed to discuss the reliability and its characteristics.

The instantaneous and steady-state availability along with the maintenance model of the systems subject to generalized M/M_b/1 queuing model is derived, and a few particular cases for availability are obtained as well. For supporting the developed model, a case study on electrical distribution system (EDS) has been illustrated, which also includes a comparison for the system subject to M/Mb/1 queuing model and the system without any queue (delay).

It is a quite realistic model that may aid to remove congestion in the system while repairing.

This study is carried out in one public and one private health-care centers based on different probabilities of patient’s no-show rate. The present study aims to determine the optimal queuing system capacity so that the expected total cost is minimized.

In this study an M/M/1/K queuing model is used for analytical properties of optimal queuing system capacity and appointment window so that total costs of these cases could be minimized. MATLAB software version R2014a is used to code the model.

In this paper, the optimal queuing system capacity is determined based on the changes in effective parameters, followed by a sensitivity analysis. Total cost in public center includes the costs of patient waiting time and rejection. However, the total cost in private center includes costs of physician idle time plus costs of public center. At the end, the results for public and private centers are compared to reach a final assessment.

Today, determining the optimal queuing system capacity is one of the most central concerns of outpatient clinics. The large capacity of the queuing system leads to an increase in the patient’s waiting-time cost, and on the other hand, a small queuing system will increase the cost of patient’s rejection. The approach suggested in this paper attempts to deal with this mentioned concern.

This paper aims to study the corresponding optimal service strategies and pricing in the styled non-preemptive M/M/1 service systems from different objectives, which consider both heterogeneous waiting costs of customers and service values in customer segmentation.

In this paper, the authors consider two service situations where customers cannot leave the service system (i.e. monopoly service system) and customers can leave the service system freely (i.e. non-monopoly service system), respectively. The authors study the following four different perspectives that are revenue, social welfare, social cost and utility of customers. The authors first build up a new model, then propose the related objective functions. Further, the authors optimize the corresponding functions and achieve the optimal results. Later, the authors propose the corresponding optimal strategies. Finally, the authors use a practical numerical case to verify the proposed results.

The results of this paper indicates that the service provider should adopt classification services to gain the maximum revenue, the maximum social welfare and the minimum social costs by charging a priority fee in above two service systems. However, the service provider should cancel customer classification and keep regular customer only to obtain maximum utility. In the monopoly service system, both the optimal proportion priority customers and the revenue decrease with the increasing of the service rate, while in a non-monopoly service system, both of them are increasing with the service rate improving.

This paper first considers both heterogeneity of service values and waiting costs in queuing system, then the author set up a new model based on this assumption. Moreover, the authors draw the corresponding management insights based on the optimal results, which were unavailable before.

This paper aims to consider a single server queue with system disasters and impatience behavior are evident in our daily life. For this purpose, authors require to know the general behavior of these systems. Transient analysis shows for us how the system will operate up to some time instant t.

In this paper, authors consider a single server queue with system disaster and impatient behavior of customers in a multi-phase random environment, in which the system transits to a repair state after each system disaster. When the system is in a failure phase or going through a repair phase, the new arrivals would be impatient. In case the system is not repaired before the customer’s time expires, the customer would leave the queue and never return. Moreover, after repair, the system becomes ready for service in an operative phase with probability $q_{i} \ge 0.$. Using generating functions along with continued fractions and some properties of the confluent hypergeometric function, authors obtained on their own results.

Explicit expressions have been obtained for the time-dependent probabilities of the underlying queuing model. Also, time-dependent mean and variance of customers in the system are deduced.

The system authors are dealing with is somewhat complicated, there are some performance measures that cannot be achieved, but some of them have been obtained, such as the expectation and variance of the number of customers in the system.

Based on the obtained results, some numerical examples are some numerical examples are presented to illustrate the effect of various parameters on the behavior of the proposed system.

Authors’ studied transient analysis of a single server queue with system disaster and impatient customer system is suitable for behavior interpretation of many systems in our lives, such as telecommunication networks, inventory systems and impatient telephone switchboard customers, manufacturing system and service system.

To the best of the author’s/authors’ knowledge and according to the literature survey, in a multi-phase random environment, no previous published article is presented for transient analysis of a single server queue with system disaster and impatient customer behavior in a random environment.

Consumers are inclined to join longer queues due to social interactions in service consumptions. This purchase behavior brings in operational challenges in terms of capacity planning, which affects consumers’ demand, leading to an unstable and fluctuated arrival process. This paper aims to investigate the dynamic characteristics of the arrival process of a service system with boundedly rational consumers whose purchase decisions are influenced by the queue length under social interactions.

Consumers’ bounded rationality is modeled based on the random utility theory. Due to social interactions, the equilibrium queue length and its interaction with the expected waiting time affect consumers’ value perception. The authors first analyze the optimal service capacity decision with or without considering the influence of social interactions in a static setting. They then focus on the dynamic characteristics of the arrival process by a one-dimensional dynamical model in terms of the arrival rate.

This paper finds that the service system can behave chaotic in terms of arrival rate dynamics under social interactions. The results highlight the dynamical complexity of a simple service system due to consumers’ behavioral factors and the influence of social interactions, which may be the critical drivers leading to fluctuated and uneven demand.

The findings demonstrate that due to consumers’ limited cognitive ability and the influence of social interactions, the demand to a service system can be stable, periodic or even chaotic in terms of the arrival process. This study provides an alternative explanation to the observed demand fluctuations in various service processes under the influence of social interactions, which is important for service providers to effectively manage service capacity to achieve a stable service process and improve operational efficiency.

Service experiences and waiting lines are often – unfortunately – seen to go hand in hand. This chapter explains why this is the case. Beginning with an exploration of capacity and operating constraints, discussion then delves into both the mathematical origins and psychological implications of waiting lines. The final section offers hope to managers and guests alike, with a survey of different operations strategies and tactics that can eliminate or abate the need to wait.

The purpose of this paper is to introduce a reconfigurable model that is a combination of a schedule model and a queuing system M/M/m/K to reduce the duration of the wind turbine construction project closure phase and reduce the project documentation waiting time in the queue.

This research was implemented in a wind farm project. The schedule model deals with reducing the duration of the turbines closure phase by an activity overlapping technique, and the queuing system deals with reducing the turbine documentation waiting time in the queue, as well as reducing the probability of server idleness during the closure phase.

After the implementation of the model, the obtained results were compared to those of similar previously conducted projects in terms of duration, and the model was found effective.

Project closure is an important and mandatory process in all projects. More often than not, this process is faced with problems including prolonged project duration, disputes, lawsuits, and also in projects like the implementation of wind farms, a queue of documents at closing stage may also cause difficulties in project closure phase.

The contributions of this research are twofold: first, a combination of project management and queuing system is presented, and second, a reconfigurable model is introduced to enhance the performance and productivity of the closure phase of the project through reducing the implementation time and reducing the turbine documentation waiting time in the queue, as well as reducing the probability of server idleness during the closure phase of the wind farm project.