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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 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 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.

The aim of this research study is to develop a queue assessment model to evaluate the inflow of walk-in outpatients in a busy public hospital of an emerging economy, in the absence of appointment systems, and construct a dynamic framework dedicated towards the practical implementation of the proposed model, for continuous monitoring of the queue system.

The current study utilizes data envelopment analysis (DEA) to develop a combined queuing–DEA model as applied to evaluate the wait times of patients, within different stages of the outpatients' department at the Combined Military Hospital (CMH) in Lahore, Pakistan, over a period of seven weeks (23rd April to 28th May 2014). The number of doctors/personnel and consultation time were considered as outputs, where consultation time was the non-discretionary output. The two inputs were wait time and length of queue. Additionally, VBA programming in Excel has been utilized to develop the dynamic framework for continuous queue monitoring.

The inadequate availability of personnel was observed as the critical issue for long wait times, along with overcrowding and variable arrival pattern of walk-in patients. The DEA model displayed the “required” number of personnel, corresponding to different wait times, indicating queue build-up.

The current study develops a queue evaluation model for a busy outpatients' department in a public hospital, where “all” patients are walk-in and no appointment systems. This model provides vital information in the form of “required” number of personnel which allows the administrators to control the queue pre-emptively minimizing wait times, with optimal yet dynamic staff allocation. Additionally, the dynamic framework specifically targets practical implementation in resource-poor public hospitals of emerging economies for continuous queue monitoring.

This study examined the waiting times to board an attraction at a theme park (Tokyo DisneySea in Japan) using a simulation based on measured values. Park visitors often complain that waiting times are too long; guests (Disney's term for park visitors) must stand in long, slow-moving queues outdoors in all weather, enduring heat, cold, rain and wind. This can undermine their health and reduce customer satisfaction. To date, no research has offered a scientific approach to solve the problem in the context of theme park queues.

The attraction examined two queues: a short waiting queue for guests with priority entry tickets and a long waiting queue for guests without priority entry tickets. The total number of guests with priority entry tickets remained a constant value, as in the current system; however, the author designed the number as a monotonically increasing function to reduce the waiting times for nonpriority entry. It was impractical to analyze queues or try to explain proposed wait time reduction methods using theories and mathematical models alone. Therefore, the author used a simulation study based on real data to demonstrate the proposed method of this study.

The simulation results indicated that the proposed method significantly decreased guests' waiting times in the nonpriority entry queue, without changing the number of guests in both priority and nonpriority entry queues.

Simple queues can be analyzed using theoretical calculations, but complicated queue systems require simulation methods. Therefore, this paper cannot provide a theoretical basis for the method.

The proposed method offers benefits to managers of any event or location seeking to manage queue times and not just theme parks (e.g. exhibitions, concerts, etc.). Advance tickets are equivalent to priority entry tickets, so applying the proposed method can shorten waiting times on the day of the event.

This study has important practical implications for queues management, and the proposed approach is a unique system that reduces waiting times, thus increasing customer satisfaction. The proposed method can be applied to similar types of priority entry systems.

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.