State probabilities for an M/M/1 queuing system with two capacity levels

Hübl, Alexander; Altendorfer, Klaus

doi:10.1109/wsc.2015.7408334

Cited by 3 publications

(3 citation statements)

References 17 publications

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“…To overcome the challenges posed by the fundamentally stochastic nature of such systems, simulation or approximation methods (Ignaccolo 2003, Hübl andAltendorfer 2015) or a step function indicating the expected demand during successive time periods (FAA 1976) is used, under the assumption that transient effects are of negligible importance. Other research in the literature utilizes dynamic queues (Odoni and Roth 1983, Pyrgiotis, Malone, and Odoni 2013, Schwarz, Selinka, and Stolletz 2016, Di Crescenzo et al 2018 to address the in-homogeneous (time-variant) nature of such systems.…”

Section: Capacity Acquisition and Congestionmentioning

confidence: 99%

Hub Network Design Problem with Capacity, Congestion, and Stochastic Demand Considerations

Bayram

Yıldız

Farham

2023

Transportation Science

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Our study introduces the hub network design problem with congestion, capacity, and stochastic demand considerations (HNDC), which generalizes the classical hub location problem in several directions. In particular, we extend state-of-the-art by integrating capacity acquisition decisions and congestion cost effect into the problem and allowing dynamic routing for origin-destination (OD) pairs. Connecting strategic and operational level decisions, HNDC jointly decides hub locations and capacity acquisitions by considering the expected routing and congestion costs. A path-based mixed-integer second-order cone programming (SOCP) formulation of the HNDC is proposed. We exploit SOCP duality results and propose an exact algorithm based on Benders decomposition and column generation to solve this challenging problem. We use a specific characterization of the capacity-feasible solutions to speed up the solution procedure and develop an efficient branch-and-cut algorithm to solve the master problem. We conduct extensive computational experiments to test the proposed approach’s performance and derive managerial insights based on realistic problem instances adapted from the literature. In particular, we found that including hub congestion costs, accounting for the uncertainty in demand, and whether the underlying network is complete or incomplete have a significant impact on hub network design and the resulting performance of the system. Funding: This work was supported by Türkiye Bilimsel ve Teknolojik Araştırma Kurumu [Grant 218M520]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.0112 .

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Section: Capacity Acquisition and Congestionmentioning

confidence: 99%

Hub Network Design Problem with Capacity, Congestion, and Stochastic Demand Considerations

Bayram

Yıldız

Farham

2023

Transportation Science

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“…A Markov chain is a stochastic process defined by a transition matrix. Hubl et al [18] applied the Markov chain to calculate the state probability of M/M/1 queuing system that considers the flexible capacity of production system. Liu et al [19] applied the Markov chain analysis queuing system with working breakdown.…”

Section: Introductionmentioning

confidence: 99%

Container Terminal Berth-Quay Crane Capacity Planning Based on Markov Chain

Jiang

Zheng

et al. 2021

PROMET

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This paper constructs a berth-quay crane capacity planning model with the lowest average daily cost in the container terminal, and analyzes the influence of the number of berths and quay cranes on the terminal operation. The object of berth-quay crane capacity planning is to optimize the number of berths and quay cranes to maximize the benefits of the container terminal. A steady state probability transfer model based on Markov chain for container terminal is constructed by the historical time series of the queuing process. The current minimum time operation principle (MTOP) strategy is proposed to correct the state transition probability of the Markov chain due to the characteristics of the quay crane movement to change the service capacity of a single berth. The solution error is reduced from 7.03% to 0.65% compared to the queuing theory without considering the quay crane movement, which provides a basis for the accurate solution of the berth-quay crane capacity planning model. The proposed berth-quay crane capacity planning model is validated by two container terminal examples, and the results show that the model can greatly guide the container terminal berth-quay crane planning.

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“…In the past decades, much research has been performed regarding queueing systems, whereby two literature streams are dominating. On the one hand, analytical solutions are developed (Hübl and Altendorfer 2015;Altendorfer and Jodlbauer 2011;Altendorfer and Minner 2011;Buzacott and Shanthikumar 1993;de Groot and Hübl Medhi 1991) and on the other hand, those queueing problems that are most likely real-world problems are solved with discrete event simulation (Altendorfer et al 2014;Hübl et al 2011). Due to the stochastic nature of real-world problems, it is often the case that analytical models and techniques cannot represent a particular queueing system adequately (Kolker 2010;Shortle et al 2018).…”

Section: Introductionmentioning

confidence: 99%

Developing a Calibrated Discrete Event Simulation Model of Shops of a Dutch Phone and Subscription Retailer During COVID-19 to Evaluate Shift Plans to Reduce Waiting Times

Groot

Hübl²

2021

2021 Winter Simulation Conference (WSC)

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Belsimpel deals with large waiting times during peak times under COVID-19 circumstances compared to non-COVID-19 times. Therefore, a discrete event simulation model of the Belsimpel shops has been developed. However, the model is not validated due to data scarcity. This paper proposes a model calibration procedure based on the idea that service times decrease during high-demanded hours and increase otherwise. The results show that the proposed procedure enables the generation of realistic Key Performance Indicator values. The calibrated simulation model can be used for analyzing the performance of possible improvements. Accordingly, the calibrated model is applied to investigate the impact of an improved employee scheduling. The results show that the mean waiting time decreases by 20-33 %, the maximum waiting time decreases by 12-20 %, and the mean service level increases by 3-11 %. These improvements enhance customer satisfaction while scheduling the same number of working hours.

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State probabilities for an M/M/1 queuing system with two capacity levels

Cited by 3 publications

References 17 publications

Hub Network Design Problem with Capacity, Congestion, and Stochastic Demand Considerations

Hub Network Design Problem with Capacity, Congestion, and Stochastic Demand Considerations

Container Terminal Berth-Quay Crane Capacity Planning Based on Markov Chain

Developing a Calibrated Discrete Event Simulation Model of Shops of a Dutch Phone and Subscription Retailer During COVID-19 to Evaluate Shift Plans to Reduce Waiting Times

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