Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers

Baumann, Hendrik; Sandmann, Werner

doi:10.1016/j.ejor.2016.07.035

Cited by 46 publications

(24 citation statements)

References 22 publications

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“…To speed up computations, computation of some performance measures can be cancelled. In addition, it is possible to use more advanced computers and the results of [22]. Although we present the results of comparison of the results for the network with arrival flow having a correlation equal to 0 with the results for the network with arrival flow having relatively small correlation equal to 0.15, we can conclude that there is an essential difference in the values of N busy , P loss and P loss−no−car .…”

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confidence: 76%

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Queueing Network with Moving Servers as a Model of Car Sharing Systems

2019

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We consider a queueing network with a finite number of nodes and servers moving between the nodes as a model of car sharing. The arrival process of customers to various nodes is defined by a marked Markovian arrival process. The customer that arrives at a certain node when there is no idle server (car) is lost. Otherwise, he/she is able to start the service. With known probability, which depends on the node and the number of available cars, this customer can balk the service and leave the system. The service time of a customer has an exponential distribution. Location of the server in the network after service completion is random with the known probability distribution. The behaviour of the network is described by a multi-dimensional continuous-time Markov chain. The generator of this chain is derived which allows us to compute the stationary distribution of the network states. The formulas for computing the key performance indicators of the system are given. Numerical results are presented. They characterize the dependence of some performance measures of the network and the nodes on the total number of cars (fleet size of the car sharing system) and correlation in the arrival process.

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confidence: 76%

“…Note that often it is possible to skip the computation of the stationary distribution of the Markov chain if only the values of some performance measures of the network are of interest. This can be done via the use of a memory-efficient method developed in [22].…”

Section: Process Of the Network Statesmentioning

confidence: 99%

Queueing Network with Moving Servers as a Model of Car Sharing Systems

2019

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“…Considering waiting costs, they find a sufficient condition under which it is optimal to allocate both servers to Stage 1 for any number of jobs in Stages 1 and 2. More recently, Baumann and Sandmann () study multiserver tandem queues where both stages have a finite buffer and service times are assumed to follow phase‐type distribution. Two‐stage systems with multiple flexible servers are also studied by Andradóttir, Ayhan, and Kırkızlar (), Schiefermayr and Weichbold (), and Wu, Lewis, and Veatch ().…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal control policies in service systems with limited information on the downstream stage

Ansari

Iravani

Qi-feng

2019

Naval Research Logistics

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Existing models in multistage service systems assume full information on the state of downstream stages. In this paper, we investigate how much the lack of such information impacts jobs' waiting time in a two‐stage system with two types of jobs at the first stage. The goal is to find the optimal control policy for the server at the first stage to switch between type‐1 and type‐2 jobs, while minimizing the long‐run average number of jobs in the system. We identify control policies and corresponding conditions under which having no or partial information, the system can still capture the most benefit of having full information.

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“…The efficiency of Markov chains in finding solutions to real world problems is well established (Liu, Chiu, & Chiu, 2011;Pourmoayed, Nielsen, & Kristensen, 2016;Baumann & Sandmann, 2017). However, the application of Markov chains is relatively new to the applications of QFD method (Asadabadi, 2016) and has not been used to address the supplier selection problem.…”

Section: Markov Chains and Qfdmentioning

confidence: 99%

A customer based supplier selection process that combines quality function deployment, the analytic network process and a Markov chain

Asadabadi

2017

European Journal of Operational Research

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The overall objective of this paper is to introduce a customer oriented supplier selection method. Although the supplier selection problem has previously been investigated, an effective solution to consider the dynamics of Customer Needs (CNs) in finding the best supplier has not yet been proposed. Such a method takes into account customer needs as a determinant factor in finding the best supplier and considers possible changes in the priorities of customer needs as time passes. In this study a method integrating the analytic network process (ANP), quality function deployment (QFD), and a Markov chain is used to address the supplier selection problem. This proposed method utilizes a Markov chain to trace the changing-priorities of customer needs and find a pattern for them. The ANP-QFD method then connects this pattern to product requirements (PRs) and PRs to supplier qualifications. This combination develops a customer based supplier selection method. The best supplier is selected based on the changing-priorities of customer needs. Although the customer needs priorities keeps changing, one supplier is selected as the best one. This study introduces an innovative customer based approach to select the best supplier that is independent of initial CNs.

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Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers

Cited by 46 publications

References 22 publications

Queueing Network with Moving Servers as a Model of Car Sharing Systems

Queueing Network with Moving Servers as a Model of Car Sharing Systems

Optimal control policies in service systems with limited information on the downstream stage

A customer based supplier selection process that combines quality function deployment, the analytic network process and a Markov chain

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