MAD Dispersion Measure Makes Extremal Queue Analysis Simple

A notorious problem in queueing theory is to compute the worst possible performance of the GI/G/1 queue under mean-dispersion constraints for the interarrival- and service-time distributions. We address this extremal queue problem by measuring dispersion in terms of mean absolute deviation (MAD) instead of the more conventional variance, making available methods for distribution-free analysis. Combined with random walk theory, we obtain explicit expressions for the extremal interarrival- and service-time distributions and, hence, the best possible upper bounds for all moments of the waiting time. We also obtain tight lower bounds that, together with the upper bounds, provide robust performance intervals. We show that all bounds are computationally tractable and remain sharp also when the mean and MAD are not known precisely but are estimated based on available data instead. Summary of Contribution: Queueing theory is a classic OR topic with a central role for the GI/G/1 queue. Although this queueing system is conceptually simple, it is notoriously hard to determine the worst-case expected waiting time when only knowing the first two moments of the interarrival- and service-time distributions. In this setting, the exact form of the extremal distribution can only be determined numerically as the solution to a nonconvex nonlinear optimization problem. Our paper demonstrates that using mean absolute deviation (MAD) instead of variance alleviates the computational intractability of the extremal GI/G/1 queue problem, enabling us to state the worst-case distributions explicitly.

Managing the resource allocation for the COVID-19 pandemic in healthcare institutions: a pluralistic perspective

PurposeAs COVID-19 outbreak has created a global crisis, treating patients with minimum resources and traditional methods has become a hectic task. In this technological era, the rapid growth of coronavirus has affected the countries in lightspeed manner. Therefore, the present study proposes a model to analyse the resource allocation for the COVID-19 pandemic from a pluralistic perspective.Design/methodology/approachThe present study has combined data analytics with the K-mean clustering and probability queueing theory (PQT) and analysed the evolution of COVID-19 all over the world from the data obtained from public repositories. By using K-mean clustering, partitioning of patients’ records along with their status of hospitalization can be mapped and clustered. After K-mean analysis, cluster functions are trained and modelled along with eigen vectors and eigen functions.FindingsAfter successful iterative training, the model is programmed using R functions and given as input to Bayesian filter for predictive model analysis. Through the proposed model, disposal rate; PPE (personal protective equipment) utilization and recycle rate for different countries were calculated.Research limitations/implicationsUsing probabilistic queueing theory and clustering, the study was able to predict the resource allocation for patients. Also, the study has tried to model the failure quotient ratio upon unsuccessful delivery rate in crisis condition.Practical implicationsThe study has gathered epidemiological and clinical data from various government websites and research laboratories. Using these data, the study has identified the COVID-19 impact in various countries. Further, effective decision-making for resource allocation in pluralistic setting has being evaluated for the practitioner's reference.Originality/valueFurther, the proposed model is a two-stage approach for vulnerability mapping in a pandemic situation in a healthcare setting for resource allocation and utilization.

Simulation of railway marshalling yards using the methods of the queueing theory

Aim. The paper primarily aims to simulate the operation of railway transportation systems using the queueing theory with the case study of marshalling yards. The goals also include the development of the methods and tools of mathematical simulation and queueing theory. Methods. One of the pressing matters of modern science is the development of methods of mathematical simulation of transportation systems for the purpose of analyzing the efficiency, stability and dependability of their operation while taking into account random factors. Research has shown that the use of the most mature class of such models, the singlephase Markovian queueing systems, does not enable an adequate description of transportation facilities and systems, particularly in railway transportation. For that reason, this paper suggests more complex mathematical models in the form of queueing networks, i.e., multiple interconnected queueing systems, where arrivals are serviced. The graph of a queueing network does not have to be connected and circuit-free (a tree), which allows simulating transportation systems with random structures that are specified in table form as a so-called “routing matrix”. We suggest using the BMAP model for the purpose of describing incoming traffic flows. The Branch Markovian Arrival Process is a Poisson process with batch arrivals. It allows combining several different arrivals into a single structure, which, in turn, significantly increases the simulation adequacy. The complex structure of the designed model does not allow studying it analytically. Therefore, based on the mathematical description, a simulation model was developed and implemented in the form of software. Results. The developed models and algorithms were evaluated using the case study of the largest Russian marshalling yard. A computational experiment was performed and produced substantial recommendations. Another important result of the research is that significant progress was made in the development of a single method of mathematical and computer simulation of transportation hubs based on the queueing theory. That is the strategic goal of the conducted research that aims to improve the accuracy and adequacy of simulation compared to the known methods, as well as should allow extending the capabilities and applicability of the model-based approach. Conclusions. The proposed model-based approach proved to be a rather efficient tool that allows studying the operation of railway marshalling yards under various parameters of arrivals and different capacity of the yards. It is unlikely to completely replace the conventional methods of researching the operation of railway stations based on detailed descriptions. However, the study shows that it is quite usable as a primary analysis tool that does not require significant efforts and detailed statistics.