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The estimation of queue length and delays in queues that are oversaturated for some part of a study period is of substantial importance in a range of traffic engineering applications. Whiting’s co-ordinate transformation has provided the basis for several approaches to this. We analyse this approach and present an explicit form for the derivative of queue length with respect to time, which we then use to establish various properties. We also report the results of numerical comparisons with exact formulae for certain special cases and show that these offer little or no advantage over the co-ordinate transformation approximations and can be computationally impractical in study periods of moderate duration.

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 normal concept of a queueing situation is that of a static service point which is visited by customers who wait for service in a formal line or queue. This paper outlines the concepts of queueing theory and examines its application to congestion situations where the queueing entities themselves are dispersed and static and where the servers must visit the customer. Results from studies into two diverse categories of such types of situation are presented. These are the servicing of large installations by mobile teams and the provision of centralised emergency medical services to communities.

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.

Purpose – This chapter investigates fathers who have both biological and social children from different relationships in order to examine how they prioritize between their children, both in theory and in practice.

Methodology – Interviews were conducted with 57 low-income fathers in Oakland experiencing multiple-partner fertility.

Findings – These fathers used nine criteria to prioritize children: timing of life course interruptions, distance, formal child support, desirability of the pregnancy, restraining orders, other resources available to the child, age of the child, gender of the child, and the child's reaching-out behavior.

Research implications – These fathers distribute finite resources of time and money using priority-ordered queuing. This method allowed them to maximize their impact by focusing on a small number of children, rather than having their scarce resources become so diffuse that they became virtually meaningless.

Practical implications – These fathers utilized priority-ordered queuing, in contrast to the equal-distribution queuing method preferred by child support enforcement agencies. The difference in queuing model preference may explain fathers’ noncompliance with child support orders.

Value – In contrast with previous research findings, this chapter finds that these fathers were more likely to be simultaneously “good fathers” and “bad fathers” to different children at the same time, rather than one or the other (Furstenberg, 1988). This chapter also demonstrates a novel use of queuing theory for family research.

Since waiting in a queue may induce both negative and positive effects on customers’ quality perceptions of which the queue is formed, an optimal queuing wait which is long enough but not too long to have positive effects on the pursued service is critical for successful queuing management. This study examined the existence of an optimal queuing wait at theme parks by merging the interpretative approach of institutional norms with the measuring application of the adapted Return Potential Model from crowding studies. Using quota and systematic sampling techniques, survey data were collected from 1,440 visitors to five leading theme parks in Taiwan. An optimal queuing wait represented by an institutional norm among visitors with moderate consensus for the longest acceptable waiting time (LAWT) was revealed in this study. As a critical reversal point of visitors’ quality perception, significant ascent of visitors’ crowding perception did occur when their actual waiting times exceeded their LAWT.

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.

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.