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The purpose of this paper is to carry out queuing analysis to analyse patient load in outpatient and inpatient services to facilitate more realistic resource planning.

The paper adopts an analytical approach based on real life data (e.g. not a priori or an academic one where data are mingled to fit a theoretical stance) in accordance with the service level prescribed by the hospital administration. A service level is usually specified in terms of admissible range of queuing characteristics, such as mean patient waiting time, reduction of inordinate delays, incidences of minimum delays, average queue length, etc. which the management of a health organisation may decide to aim and control.

Queuing analysis reported in this case study provides a basis for estimating medical staff size and number of beds, which are two very important resources for outpatient and inpatient services in a large hospital, and all other hospital resources in one way or another depend on them.

The study challenges and aims to replace thumb‐rule approaches, which can be very conveniently carried out with efficient computer aids available at present for any hospital. Queuing analysis provides valuable insights into a hospital system, though it may not be the best approach as several underlying assumptions may not always hold true. In hospitals, for example, there can be several interacting queues, many of which could be cyclic with interaction among them. Accordingly, treatment of each queue individually, independent of others may not be a valid assumption.

Medical staff (doctors) and beds are very basic hospital resources, which largely depend on the hospital load in terms of arrival rates of patients in outpatient and inpatient services. When hospitals are adequately staffed and equipped in terms of beds and other key resources, it is unlikely that patients will turn away to other hospitals for treatment and there will be all round satisfaction with the hospital performance.

The authors do not claim the findings to be novel or unique but rather more well‐documented and comprehensive in coverage than available in existing literature. The practice‐based themes such as this well‐documented case study may evoke global interest as a multiplier effect for using such methodologies for resource planning in hospitals.

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.

The use of queueing network models was stimulated by the appearance (1975) of the exact product form solution of a class of open, closed and mixed queueing networks obeying the local balance principle and solved, a few years later, by the popular mean value analysis algorithm (1980). Since then, research efforts have been produced to approximate solutions for non-exponential services and non-pure random mechanisms in customer processing and routing. The purpose of this paper is to examine the suitability of modeling choices and solution approaches consolidated in other domains with respect to two key logistic processes in container terminals.

In particular, the analytical solution of queueing networks is assessed for the vessel arrival-departure process and the container internal transfer process with respect to a real terminal of pure transshipment.

Numerical experiments show the extent to which a decomposition-based approximation, under fixed or state-dependent arrival rates, may be suitable for the approximate analysis of the queueing network models.

The limitation of adopting exponential service time distributions and Poisson flows is highlighted.

Comparisons with a simulation-based solution deliver numerical evidence on the companion use of simulation in the daily practice of managing operations in a finite-time horizon under complex policies.

Discussion of some open modeling issues and encouraging results provide some guidelines on future research efforts and/or suitable adaption to container terminal logistics of the large body of techniques and algorithms available nowadays for supporting long-run decisions.

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.

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.

To study the optimization of a randomized control problem in an M/G/1 queue in which a removable and unreliable server may provide two phases of heterogeneous service to arriving customers.

Arriving customers follow a Poisson process and require the first essential service (FES). As soon as FES of a customer is completed, the customer may leave the system or opt for the second optional service (SOS). The service times of FES channel and SOS channel are assumed to be general distribution functions. The server requires a startup time with random length before starting service. When the server is working, he may meet unpredictable breakdowns but is immediately repaired. The inter‐breakdown time and repair time of the removable server are exponentially random variable and generally random variable, respectively. By the convex combination property and the renewal reward theorem, several system performances are obtained. A cost model is developed to search the optimal two‐threshold policy at a minimum cost. Sensitivity analysis is performed.

Expressions for various system performances are derived. Sensitivity analysis of optimal randomized control policy (based on the developed expected cost function) with respect to system parameters is investigated.

It is the first time that analytic results of sensitivity analysis of optimal randomized control policy for the complex system have been obtained which is quite useful and significant for engineers.

An integrated queueing network focused on container storage/retrieval operations occurring on the yard of a transshipment hub is proposed. The purpose of the network is to support decisions related to the organization of the yard area, while also accounting for operations policies and times on the quay.

A discrete-event simulation model is used to reproduce container handling on both the quay and yard areas, along with the transfer operations between the two. The resulting times, properly estimated by the simulation output, are fed to a simpler queueing network amenable to solution via algorithms based on mean value analysis (MVA) for product-form networks.

Numerical results justify the proposed approach for getting a fast, yet accurate analytical solution that allows carrying out performance evaluation with respect to both organizational policies and operations management on the yard area.

Practically, the expected performance measures on the yard subsystem can be obtained avoiding additional time-expensive simulation experiments on the entire detailed model.

As a major takeaway, deepening the MVA for generally distributed service times has proven to produce reliable estimations on expected values for both user- and system-oriented performance metrics.

The purpose of this paper is to investigate into the improvement strategies for lead time reduction of military aircraft major overhaul (enhance the overhaul task from present seven to nine-plus aircrafts as agreed to customer) for ABC Company.

This research has been conducted based on the available knowledge and extensive experience gained while working in the overhaul unit of the case organization for a long period of time. The research employs an integrated approach of multi-criteria decision method (in specific analytic hierarchy process (AHP)), theory of constraint (TOC) and simulation for M/M/1/K queuing environment for investigating the improvement strategies for lead time reduction in major overhaul of military aircraft. This has mainly included: Step 1: analysis of existing activity network using actual overhaul data; Step 2: ranking of constraint activities that most affects the lead time using AHP; Step 3: revised flow activity network using time buffers (TBs) concept of TOC; Step 4: mathematical model formulation for effective utilization of TB using single server finite queuing approach (M/M/1/K queuing environment); Step 5: discrete event simulation representing present overhaul conditions and revised overhaul conditions with different scenarios; and Step 6: sensitivity analysis and interpretation of results. The proposed methodology has been tested on an industrial case study dealing with an aircraft overhaul in India (namely ABC Company).

The proposed overhaul lead-time reduction plan points out the augmentation of resources in order to achieve more than 50 per cent reduction in lead time and waiting time under two scenarios – with overtime and without overtime.

An integrated approach proposed has so far been applicable to the specific aircrafts (Jaguar/Mirage/Kiran) of the ABC Company overhaul division. However, the particular methodology can be proved potentially useful and highly practical when applying to other aircraft types.

The results indicate several problems with the current overhaul strategies that need focused process improvements and a need for capacity augmentation for achieving the enhanced overhaul task of nine+ aircrafts per year with reduced overhaul lead time. The proposed approach also provides the maintenance planners with a platform for decision analysis and support often ignored the capacity augmentation.

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.

The purpose of this paper is to show how elements from queueing theory can be used to obtain objective measures of effective capacity in the triage function at Skaraborg Hospital in Sweden without direct observation of the function itself.

Approximately 30,000 patients arrived to the emergency department at Skaraborg Hospital in Sweden during 2011. The exact time of arrival and the exact time of triage were recorded for each patient on an individual level. Basic queueing theory uses arrival rates and system capacity measures to derive average queueing times. The authors use the theoretical relation between these three measures to derive system capacity measures based on observed arrival rates and observed average queueing times.

The effective capacity in the triage process is not a linear function of the number of nurses. However, the management of capacity seems well adapted to the actual demand, even though service levels vary substantially during the day and night.

This paper uses elements from queueing theory in an innovative way to measure the effective capacity of a service process without direct observation, thereby also avoiding the potential risk of the Hawthorne effect.