The impact of the correlation coefficient of interarrival and service times on queueing performance: The M/M/1 case
This paper is concerned on an M/M/1 queue with correlated interarrival and service times. In particular, we assume that the interarrival time and service time of a customer have a bivariate exponential distribution. By utilizing a Markov modulated fluid flow (MMFF) process associated with the age pr...
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| Published in | European journal of operational research Vol. 319; no. 2; pp. 625 - 637 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.12.2024
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| Abstract | This paper is concerned on an M/M/1 queue with correlated interarrival and service times. In particular, we assume that the interarrival time and service time of a customer have a bivariate exponential distribution. By utilizing a Markov modulated fluid flow (MMFF) process associated with the age process of the customer in service, we obtain a number of queueing quantities in closed form. Using the solutions, the impact of the correlation coefficient of the interarrival and service times on a variety of queueing quantities is explored quantitatively and qualitatively. Specifically, we establish a monotonic relationship between the decay rates of queueing quantities and the correlation coefficient of the interarrival and service times. We also show that the decay rates are increasing in the correlation coefficient. In addition, queues with the maximum/minimum correlation coefficient are analyzed. Two examples are presented to demonstrate the importance of using the correlation coefficient in queueing performance/economic analysis.
•A queueing model with correlated interarrival and service times is analyzed.•The Markov modulated fluid flow process is utilized in analysis.•Closed form solutions of queue quantities are obtained.•The relationship between decay rates of queueing quantities and correlation coefficient is characterized.•Decay rates for extremal M/M/1 queues are obtained. |
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| AbstractList | This paper is concerned on an M/M/1 queue with correlated interarrival and service times. In particular, we assume that the interarrival time and service time of a customer have a bivariate exponential distribution. By utilizing a Markov modulated fluid flow (MMFF) process associated with the age process of the customer in service, we obtain a number of queueing quantities in closed form. Using the solutions, the impact of the correlation coefficient of the interarrival and service times on a variety of queueing quantities is explored quantitatively and qualitatively. Specifically, we establish a monotonic relationship between the decay rates of queueing quantities and the correlation coefficient of the interarrival and service times. We also show that the decay rates are increasing in the correlation coefficient. In addition, queues with the maximum/minimum correlation coefficient are analyzed. Two examples are presented to demonstrate the importance of using the correlation coefficient in queueing performance/economic analysis.
•A queueing model with correlated interarrival and service times is analyzed.•The Markov modulated fluid flow process is utilized in analysis.•Closed form solutions of queue quantities are obtained.•The relationship between decay rates of queueing quantities and correlation coefficient is characterized.•Decay rates for extremal M/M/1 queues are obtained. |
| Author | Wu, Haoran He, Qi-Ming Xia, Li |
| Author_xml | – sequence: 1 givenname: Haoran surname: Wu fullname: Wu, Haoran email: wuhr25@mail.sysu.edu.cn organization: School of Business, Sun Yat-sen University, China – sequence: 2 givenname: Qi-Ming orcidid: 0000-0003-2381-3242 surname: He fullname: He, Qi-Ming email: q7he@uwaterloo.ca organization: Department of Management Science and Engineering, University of Waterloo, Canada – sequence: 3 givenname: Li surname: Xia fullname: Xia, Li email: xiali5@mail.sysu.edu.cn organization: School of Business, Sun Yat-sen University, China |
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| Keywords | Markov modulated fluid flow process Economic analysis Decay rate Bivariate exponential distribution Correlated M/M/1 queue Age process |
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| Snippet | This paper is concerned on an M/M/1 queue with correlated interarrival and service times. In particular, we assume that the interarrival time and service time... |
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| SubjectTerms | Age process Bivariate exponential distribution Correlated M/M/1 queue Decay rate Economic analysis Markov modulated fluid flow process |
| Title | The impact of the correlation coefficient of interarrival and service times on queueing performance: The M/M/1 case |
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