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The authors consider parallel four-state tandem open queueing network. The queue capacity is infinite. Passenger arrival rate is Poisson distribution and service rate is exponential distribution. The queue is constructed in the form of tandem queue, and each and every queue of tandem queue is single server (M/M/1) queue. In tandem queue, passengers will leave the system once they receive service from both the states. The purpose of this paper is to provide performance analysis for four-state tandem open queue network, and a governing equation is formulated with the help of transition diagram. Using Burke theorem, the authors formulated equation for average number of passenger in the system, average waiting time of passenger in the system, average number of passenger in the queue and average waiting time of passenger in the queue.

This paper used Burke’s theorem.

In this paper, performance analysis is done for parallel four-state tandem open queueing network and performance measure solved using Burkes theorem formula. K. Sreekanth et al. has done performance analysis for single tandem queue with three states. In this paper, the authors have done performance analysis for two tandem queues parallel with four states. This four-state tandem open queueing network is suitable for real world applications. This paper can extend for more number of service states and multi-server states according to the application, and in such case, the authors have to prove and explain with numerical examples. This analysis is more useful for the applications such as airports, railway stations, bus-stands and banks.

In this paper, parallel four-state tandem open queueing network and performance measure has been solved using Burke’s theorem formula.

The purpose of this paper is to provide a traffic route selection strategy based on minimum carbon dioxide (CO₂) emission by vehicles over different route choices.

The study used queuing theory for Markovian M/M/1 model over the road junctions to assess total time spent over each of the junctions for a route with junctions in tandem. With parameters of distance, mean service rate at the junction, the number of junctions and fuel consumption rate, which is a function of variable average speed, the CO₂ emission is estimated over each of the junction in tandem and collectively over each of the routes.

The outcome of the study is a mathematical formulation, using queuing theory to estimate CO₂ emissions over different route choices. Research finding estimated total time spent and subsequent CO₂ emission for mean arrival rates of vehicles at junctions in tandem. The model is validated with a pilot study, and the result shows the best vehicular route choice with minimum CO₂ emissions.

Proposed study is limited to M/M/1 model at each of the junction, with no defection of vehicles. The study is also limited to a constant mean arrival rate at each of the junction.

The work can be used to define strategies to route vehicles on different route choices to reduce minimum vehicular CO₂ emissions.

Proposed work gives a solution for minimising carbon emission over routes with unsignalised junctions in the tandem network.

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.

Computer networks are very complex and somewhat unpredictable systems in dynamic operations. Cybernetic modelling, incorporating stochastic, fuzzy variables, wherever appropriate, approximating interactions not easily tractable via a black‐box systems approach, may be more accurate. A method of analysis of computer networks is considered by representing subsystems and interactions, accurately as far as possible, and then utilising the results of systems sciences for analysis, including specifics, e.g. queuing systems. The aim is to identify correspondences between the behaviour of subsystems of networks and suitable analytic tools. Automation along such lines for the analysis and design of networks and other systems may be a possibility.

Examines the distribution of the time spent by particular jobs in a two‐station reliable production line with a single machine at each station and FIFO queuing discipline. The processing times are assumed to follow the exponential distribution with different means. Develops an analytic model to determine the Laplace‐Stieltjes transform (LST) of the distribution function of the passage time in the system. Inversion of the LST gives the required distribution. Gives a counter‐example to demonstrate the method and its limitations.

The aim of this paper is to develop an efficient analytical procedure to evaluate performance of the most general pull production systems particularly when multiple‐part‐types are involved. The authors consider a kanban controlled production system that can be modelled as a closed queuing network with different product classes. The production line is decomposed into stages which consist of one or several stations and an output buffer. Each stage is associated with a given number of kanbans. The main idea of this analytical algorithm is to analyze each subnetwork individually using a product form approximation technique. The iterative procedure is used to find the unknown parameters.

The authors design a multiclass queuing network that can be used to represent kanban controlled production systems. To solve this model, three procedures are used: decompose the original network into M subnetworks, convergence of unknown parameters in each subnetwork, and convergence of unknown parameters in the original network. The authors now describe these procedures separately.

The main contribution of this paper is the formulation of the problem of kanban controlled production systems with several part‐types. The methodology is based on approximate formula with decomposition and is applicable to more general manufacturing environments. The authors' method can be applied to both limited and unlimited demands. The analytical algorithm designed in this work has demonstrated excellent performance in analyzing kanban controlled production systems.

The methodology of this algorithm is based on approximate formula and is applicable to more general manufacturing environments.

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.

Omnichannel sales have provided new impetus for the development of catering merchants. The authors thus focus on how catering merchants should manage capacities at the ordering, production and delivery stages to meet customers’ needs in different channels under third-party platform delivery and merchant self-delivery. This is of great significance for the development of the omnichannel catering industry.

This paper formulates the capacity decisions of omnichannel catering merchants under the third-party platform delivery and merchant self-delivery mode. The authors mainly use queuing theory to analyze the queuing behavior of online and offline customers, and the impact of waiting time on customer shopping behavior. In addition, the authors also characterize the merchant’s capacity by the rate in queuing model.

The authors find that capacities at ordering stage and food production stage are composed of base capacities and safety capacities, but the delivery capacities only have the latter. And in the self-delivery mode, merchants can develop higher safety capacities by charging delivery fees. The authors prove that regardless of the delivery mode, omnichannel sales can bring higher profits to merchants by integrating demand.

The authors focus on analyzing the capacity management of omnichannel catering merchants at the ordering, production and delivery stages. And the authors also add the delivery process into the omnichannel for analysis, so as to solve the problem of capacity decision-making under different delivery modes. The management of delivery capacity and its impact on other stages’ capacities are not covered in other literature studies, which is one of the main innovations of this paper.