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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 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.

This paper evaluates an alternative queuing concept for marine container terminals that utilize a truck appointment system (TAS). Instead of having all lanes providing service to trucks with appointments, this study considers the case where walk-in lanes are provided to serve those trucks with no appointments or trucks with appointments but arrived late due to traffic congestion.

To enable the analysis of the proposed alternative queuing strategy, the queuing system is shown mathematically to be stationary. Due to the complexity of the model, a discrete event simulation (DES) model is used to obtain the average waiting number of trucks per lane for both types of service lanes: TAS-lanes and walk-in lanes.

The numerical experiment results indicated that the considered queuing strategy is most beneficial when the utilization of the TAS lanes is expected to be much higher than that of the walk-in lanes.

The novelty of this study is that it examines the scenario where trucks with appointments switch to the walk-in lanes upon arrival if the TAS-lane server is occupied and the walk-in lane server is not occupied. This queuing strategy/policy could reduce the average waiting time of trucks at marine container terminals. Approximation equations are provided to assist practitioners calculate the average truck queue length and the average truck queuing time for this type of queuing system.

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.

Waiting lines and delays have become commonplace in service operations. As a result, customer waiting time guarantee is a widely used competition strategy in service industries. To implement waiting time guarantee strategy, managers need to not only know the average of waiting time, but also the variance around average waiting time. This paper aims to discuss these issues.

This research provides a mathematically exact expression for the coefficient of variation of waiting time for Markov queues. It then applies the concept of isomorphism to approximate the variance of customer waiting time in a general queue. Simulation experiments are conducted to verify the accurate approximations.

A significant feature of the approximation method is that it is mathematically tractable and can be implemented in a spreadsheet format. It provides a practical way to estimate the variance of customer waiting time in practice. The results demonstrate the usefulness of the queuing models in providing guidance on implementing appointment scheduling and waiting time guarantee strategy. Also, the spreadsheet can be used to conduct what-if analysis by inputting different parameters.

This paper develops a simple, easy-to-use spreadsheet model to estimate the standard deviation of waiting time. The approximation requires only the mean and standard deviation or the coefficient of variation of the inter-arrival and service time distributions, and the number of servers. A spreadsheet model is specifically designed to analyze the variance of waiting time.

The purpose of this paper is to highlight both the contribution and the present need to reconfigure the literature on “queue culture” as a precursor of the sociology of waiting.

The study employs a legal-structural lens in comparing the initial conceptual treatment of the archetypal “waiting line” with the “line” modifying sociology of waiting that results in waiting rooms, number and telephone queues and in the experience of online waiting.

The initial conception of the culture of the queue understates the importance of three factors: first, the role of third parties in the design, management and inculcation of rules binding those experiencing thick time; second the degree to which communication technology and its attachment to the “mobilities” paradigm has thinned the experience of thick time and lastly the degree to which the increasing commodification of the wait has resulted in the creation of waiting time as a form of pay as you go flexitime.

The social construction of waiting and the experience of thick time are shown to be increasingly part of the privatized market experience where queue management innovations not only are commercialized but have strong implications for the egalitarian social assumptions imbedded in the initial queue culture based sociology of waiting. Policy implications support the present pay for use philosophy increasingly applied in the transition from public to private management of space.

The self-policing “fairness” of the waiting line is now open to scrutiny given the proliferation of the newly shaped distributional logics imbedded in the management, design and use of waiting spaces.

Deployment of optimal size of resources is a key issue in repetitive construction projects. This paper describes a simulation model based on queuing theory for the resource scheduling of a real repetitive housing project involving 320 dwelling units constructed in East Delhi, India. The optimal size of resources, defined as the minimum size required to keep the project duration a minimum, has been identified from the results of a series of sensitivity analyses in which the size of the resources was varied one at a time. The duration of the project, the period of utilization of the resources, and the queue length of activities waiting for service are also reported in this paper. It has been shown that reduction in size of resources is achievable without increasing the duration of the project and queue length of activities. Increase in the size of some specialised crews is also proved advantageous.

The purpose of this paper is to reflect 40 years of queuing theory in application to library modelling and management. It suggests that these models have not had the impact that the early queuing models promised and suggests some reasons as to why.

The paper gives a brief exposition of queuing theory as a branch of operations research (OR) and describes three snapshots of library queuing models published in the literature. Each snapshot describes a different approach to library modelling using queues and illustrates some of the problems associated with applying queuing theory. Suggestions from the literature regarding the nature of the modeller/practitioner interaction are described and linked to queuing models.

The mathematical nature of queuing models highlights the difficulties in linking modelling theory to library practice. The paper suggests that there is an urgent need to find ways to bridge the practitioner/researcher gap, broaden the application base of OR methodology within libraries, engage in constructive debate around library OR to build a consensus view as to the value of OR interventions, and identify directions for future collaborative work in libraries. Otherwise, we seem destined to continue applying OR models as a matter of faith rather than as a proven paradigm for rational analysis in libraries.

There have been some notable successes in the application of queuing theory and other OR techniques to modelling library systems over the last 40 years. However, the nature of the intersection of OR modelling and library operations has evolved over the years and modelling projects that add real value to library operations now seem to be more rarely reported. The emerging modeller/practitioner nexus requires further consideration if library OR is to develop.

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.