이산시간 직렬형 대기행렬 네트워크 모형의 근사적 분석방법
Approximate Analyses of Discrete-Time Tandem Queueing Networks
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In this paper, we consider the discrete-time Jackson queueing network (which is the discrete-time version of the well-known continuous-time Jackson queueing network), particularly, the one with queues in tandem. Analysis of such a discrete-time network is notoriously difficult except for some special cases. To analyze it in general, we approximate each node of the network with a continuous-time single-arrival M/M/1 queue, a continuous-time batch-arrival MX/M/1 queue, a discrete-time single-arrival Geo/Geo/1 queue, and a discrete-time batch-arrival GeoX/Geo/1 queue, in turn. To evaluate the performance of these approximations, we compare the mean queue lengths obtained from each approximation with those obtained from simulation. As a result, the approximation with GeoX/Geo/1 queue turns out to be the best, among others, and pretty stable in its performance over wide ranges of parameter values. It is because the GeoX/Geo/1 model better describes the discrete nature of the discrete-time tandem queuing network than its continuous-time M/M/1 and MX/M/1 counterparts, and because it better describes arrivals in multiple at a single slot than its single-arrival Geo/Geo/1 counterpart. We conclude that the approximation with GeoX/Geo/1 queue discussed in this paper would be a reasonable way to analyze the discrete-time tandem queueing networks in practice.
Abstract
In this paper, we consider the discrete-time Jackson queueing network (which is the discrete-time version of the well-known continuous-time Jackson queueing network), particularly, the one with queues in tandem. Analysis of such a discrete-time network is notoriously difficult except for some special cases. To analyze it in general, we approximate each node of the network with a continuous-time single-arrival M/M/1 queue, a continuous-time batch-arrival MX/M/1 queue, a discrete-time single-arrival Geo/Geo/1 queue, and a discrete-time batch-arrival GeoX/Geo/1 queue, in turn. To evaluate the performance of these approximations, we compare the mean queue lengths obtained from each approximation with those obtained from simulation. As a result, the approximation with GeoX/Geo/1 queue turns out to be the best, among others, and pretty stable in its performance over wide ranges of parameter values. It is because the GeoX/Geo/1 model better describes the discrete nature of the discrete-time tandem queuing network than its continuous-time M/M/1 and MX/M/1 counterparts, and because it better describes arrivals in multiple at a single slot than its single-arrival Geo/Geo/1 counterpart. We conclude that the approximation with GeoX/Geo/1 queue discussed in this paper would be a reasonable way to analyze the discrete-time tandem queueing networks in practice.
참고문헌 (11)
- Miyazawa, M., "Editorial introduction", Queueing Systems, 18(1-2), pp.1~3 (1994)
- Bruneel, H., "Discrete-Time Models for Communication Systems Including ATM" (1993), Kluwer Academic Publishers
- Jackson, J. R., "Networks of waiting lines", Operations Research, 5(4), pp.518~527 (1957)
- Daduna, H., "Queueing Networks: A Fundamental Approach", pp.269~312 (2011), Springer
- Alfa, A. S., "Applied Discrete-Time Queues" (2016), Springer
- Kim, N. K., "A note on approximations of discrete-time queueing systems with their continuous-time counterparts", Industrial Engineering and Management Systems, 19(2), pp.358~366 (2020)
- Jacobi, C., "Point and interval estimation of decomposition error in discrete-time open tandem queues", Operations Research Letters, 50, pp.529~535 (2022)
- Jacobi, C., "Regression analyses of the data sets for the analysis of decomposition error in discrete-time open tandem queues", Data in Brief, 45, pp.108640~ (2022)
- Lee, H. W., "대기행렬이론: 확률과정론적 분석" (2006), (주)시그마프레스
- Hsu, J., "Behavior of Tandem Buffers with Geometric Input and Markovian Output", IEEE Transactions on Communications, 24(3), pp.358~361 (1976)
- Rockwell Automation, "Arena Simulation Software, Version 16.1", ~ (2020)