(N, n)-Preemptive Repeat-Different Priority Queues
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Priority disciplines are an important scheme for service systems to differentiate their services for different classes of customers. (N, n)-preemptive priority disciplines enable system engineers to fine-tune the performances of different classes of customers arriving to the system. Due to this virtue of controllability, (N, n)-preemptive priority queueing models can be applied to various types of systems in which the service performances of different classes of customers need to be adjusted for a complex objective. In this paper, we extend the existing (N, n)-preemptive resume and (N, n)-preemptive repeat-identical priority queueing models to the (N, n)-preemptive repeat-different priority queueing model. We derive the queue-length distributions in the M/G/1 queueing model with two classes of customers, under the (N, n)-preemptive repeat-different priority discipline. In order to derive the queue-length distributions, we employ an analysis of the effective service time of a low-priority customer, a delay cycle analysis, and a joint transformation method. We then derive the first and second moments of the queue lengths of high- and low-priority customers. We also present a numerical example for the first and second moments of the queue length of high- and low-priority customers. Through doing this, we show that, under the (N, n)-preemptive repeat-different priority discipline, the first and second moments of customers with high priority are bounded by some upper bounds, regardless of the service characteristics of customers with low priority. This property may help system engineers design such service systems that guarantee the mean and variance of delay for primary users under a certain bounds, when preempted services have to be restarted with another service time resampled from the same service time distribution.
Abstract
Priority disciplines are an important scheme for service systems to differentiate their services for different classes of customers. (N, n)-preemptive priority disciplines enable system engineers to fine-tune the performances of different classes of customers arriving to the system. Due to this virtue of controllability, (N, n)-preemptive priority queueing models can be applied to various types of systems in which the service performances of different classes of customers need to be adjusted for a complex objective. In this paper, we extend the existing (N, n)-preemptive resume and (N, n)-preemptive repeat-identical priority queueing models to the (N, n)-preemptive repeat-different priority queueing model. We derive the queue-length distributions in the M/G/1 queueing model with two classes of customers, under the (N, n)-preemptive repeat-different priority discipline. In order to derive the queue-length distributions, we employ an analysis of the effective service time of a low-priority customer, a delay cycle analysis, and a joint transformation method. We then derive the first and second moments of the queue lengths of high- and low-priority customers. We also present a numerical example for the first and second moments of the queue length of high- and low-priority customers. Through doing this, we show that, under the (N, n)-preemptive repeat-different priority discipline, the first and second moments of customers with high priority are bounded by some upper bounds, regardless of the service characteristics of customers with low priority. This property may help system engineers design such service systems that guarantee the mean and variance of delay for primary users under a certain bounds, when preempted services have to be restarted with another service time resampled from the same service time distribution.
참고문헌 (25)
- Adiri, I., "A Single Server Queueing System Working under Mixed Priority Disciplines", Operations Research, 30(1), pp.97~115 (1982)
- Adiri, I., "Mixing of Non-Preemptive and Preemptive Repeat Priority Disciplines", Journal of Operational Research, 18(1), pp.86~97 (1984)
- Avi-Itzhak, B., "On Discretionary Priority Queueing", ZAMM-Journal of Applied Mathematics and Mechanics, 44(6), pp.235~242 (1964)
- Cho, Y.Z., "Analysis of the M", G, Nonpreemptive Priority Discipline, pp.IEEE Transactions on Communications, 1993[DOI]
- Conway, R. W., "Theory of scheduling" (1967), Addison-Wesley
- Drekic, S., "Reducing Delay in Preemptive Repeat Priority Queues", Operations Research, 49(1), pp.145~156 (2001)
- Drekic, S., "Threshold-Based Interventions to Optimize Performance in Preemptive Priority Queues", Queueing Systems, 35(1), pp.289~315 (2000)
- Drekic, S., "A Preemptive Resume Queue with an Expiry Time for Retained Service", Performance Evaluation, 54(1), pp.59~74 (2003)
- Dudin, A., "Analysis of Priority Retrial Queue with Many Types of Customers and Servers Reservation as a Model of Cognitive Radio System", IEEE Transactions on Communications, 65(1), pp.186~199 (2017)
- Gao, S., "A Preemptive Priority Retrial Queue with Two Classes of Customers and General Retrial Times", Operational Research, 15(2), pp.233~251 (2015)
- Gay, T.W., "Composite Priority Queue", IBM Journal of Research and Development, 19(1), pp.78~81 (1975)
- Jouini, O., "On Multiple Priority Multi-Server Queues with Impatience", Journal of the Operational Research Society, 65(5), pp.616~632 (2014)
- Kim, K., "Discrete-Time Queues with Discretionary Priorities", European Journal of Operational Research, 200(2), pp.473~485 (2010)
- Kim, K., "(N, n)-Preemptive Priority Queues", Performance Evaluation, 68(7), pp.575~585 (2011)
- 김길환, "엄격한 T‐축출 우선순위 대기행렬을 이용한 기회 주파수 접근 방식의 성능 분석", 산업경영시스템학회지, 35(4), pp.162~170 (2012), 한국산업경영시스템학회[DOI]
- Kim, K., "T-Preemptive Priority Queue and Its Application to the Analysis of an Opportunistic Spectrum Access in Cognitive Radio Networks", Computers & Operations Research, 39(7), pp.1394~1401 (2012)
- Lee, Y., "Discrete-Time Queue with Preemptive Repeat Different Priority", Queueing Systems, 44(4), pp.399~411 (2003)
- Ma, Z., "Analysis of the Geom", Geom, Journal of Information & Computational Science, pp.2015, 12(3)[DOI]
- Ma, Z., "Performance Analysis and Optimization of the (N, n)-Preemptive Priority Queue with Multiple Working Vacation", ICIC Express Letters, 10(11), pp.2735~2741 (2016)
- Paterok, M., "Sojourn Time and Waiting Time Distributions for M", GI, Operations Research, pp.1994, 42(6)[DOI]
- Sharif, A. B., "A Multi-Class Multi-Server Accumulating Priority Queue with Application to Health Care", Operations Research for Health Care, 3(2), pp.73~79 (2014)
- Stanford, D. A., "Waiting Time Distributions in the Accumulating Priority Queue", Queueing Systems, 77(3), pp.297~330 (2014)
- Takagi, H., "Queueing Analysis, Volume 1 : Vacation and Priority Systems, Part 1" (1991), North-Holland
- Walraevens, J., "A Semi-Preemptive Priority Scheduling Discipline : Performance Analysis", European Journal of Operational Research, 224(2), pp.324~332 (2013)
- Walraevens, J., "A Preemptive Repeat Priority Queue with Resampling : Performance Analysis", Annals of Operations Research, 146(1), pp.189~202 (2006)