Öncelikli Olmayan ve Sınırlı Olmayan Öncelikli Kuyrukların Performans Ölçülerinin Karşılaştırılması

Year 2021, Volume: 6 Issue: 2, 86 - 90, 25.05.2021

Abdullah Çelik , Vedat Sağlam

https://doi.org/10.23834/isrjournal.886183

Abstract

Bir kuyruk sisteminde farklı müşteri sınıfları olduğunda, j-inci sınıf müşteriler hizmetlerini j+1,j=1,2,… sınıfı müşterilerden önce alırlar. Bu tür kuyruklar, öncelikli kuyruklar olarak adlandırılır. Bu çalışmada, iki müşteri sınıfına sahip bir Markov öncelikli kuyruk sistemi hem sınırlı olmayan hem de önceliksiz planlama kapsamında analiz edilmiş ve performans ölçümleri (sistemdeki beklenen müşteri sayısı, sistemdeki ortalama bekleme süresi) Little yasası kullanılarak elde edilmiştir. Performans kriterleri öncelik durumuna göre karşılaştırılmıştır. Ayrıca gerçek parametre tahminleri simülasyon sonuçlarıyla karşılaştırılmıştır. Simülasyon, R programı kullanılarak yapılmıştır.

Keywords

Kuyruk Sistemleri, Öncelikli Planlama, Performans Ölçüleri, Little Yasası

Comparison of Efficiency Measures of Non-Priority and Non-Pre-Emptive Priority Queues

Abstract

When there are different customer classes in a queue system, the j-th class customers have their services before the j+1,j=1,2,… class customers. Such queues are named as queues with priority scheduling. In this study a Markov priority queue system with two customer classes is analyzed both under non-pre-emptive and nonpriority scheduling and the efficiency measures (the expected number of customer in system, the average waiting time in system) are obtained using Little’s Law. The efficiency criteria are compared according to the priority situation. In addition, parameter estimates were compared with simulation results. The simulation was performed using the R program.

Keywords

Queuing Systems, Priority Scheduling, Performance Measures, Little's Law

References

• Alfa, A. S. 1998. Matrix-Geometric solution of discrete time MAP/PH/1 priority queue, John Wiley & Sons, Inc. Naval Research Logistics, 45, pp. 23-50.
• Atencia, I. 2017. A Geo/G/1 retrial queuing system with priority services, European Journal of Operational Research 256, pp. 178-186.
• Barberis, G. 1980. A Useful Tool in the Theory of Priority Queueing, IEEE Transactions on Communications, 28, pp. 1757-1762.
• Bitran, G. and Caldentey, R. 2002. Two-Class Priority Queueing System with State-Dependent Arrivals, Queueing Systems, 40, pp. 355-382.
• Brodal, G. S., Träff, J. L. and Zaroliagis, C. D. (1998). A parallel priority queue with constant time operations. Journal of Parallel and Distributed Computing, 49 (1), pp. 4-21.
• Burruni, R., Cuany, B., Valerio, M., Jichlinski, P. and Kulik, G. 2019. Reduction and follow-up of hospital discharge letter delay using Little’s law. International Journal for Quality in Health Care, 31 (10), pp. 787-792.
• Chaudhry, M. L., Goswami, V. and Mansur, A. Analytically closed-form solutions for the distribution of a number of customers served during a busy period for special cases of the GEO/G/1 queue. Probability in the Engineering and Informational Sciences, pp. 1-30.
• Çelik, A. 2017. Priority queuing systems with two customer classes and a numerical example, Master thesis, Ondokuz Mayıs University, Samsun, Turkey.
• Hayati, F. 2017. Some perspectives on the application of Little's law: L= λW. International Journal of Modelling in Operations Management, 6 (3), pp. 141-152.
• Jolai, F., Asadzadeh, S. M., Ghodsi, R. and Bagheri-Marani, S. 2016. A multi-objective fuzzy queuing priority assignment model. Applied Mathematical Modelling, 40 (21-22), pp. 9500-9513.
• Kim, C., Klimenok, V. I. and Dudin, A. N. 2016. Priority tandem queueing system with retials and reservation of channels as a model of call center, Computers & Industrial Engineering, 96, pp. 61-71.
• Leavens, K. and Bruneel, H. 1998. Discrete-time multiserver queues with priorities, Performance Evaluation, 33, pp. 249-275.
• Mehmet Ali, M. and Song, X. 2004. A performance analysis of a discrete-time priority queuing system with correlated arrivals”. Performance Evaluation, 57, pp. 307-339.
• Nazarov, A. and Paul, S. A. 2016. Cyclic Queuing System with Priority Customers and TStrategy of Service, Distributed Computer and Communication Networks, pp. 182-193.
• Perel, N. and Yechiali, U. (2010). Queues with slow servers and impatient customers. European Journal of Operational Research, 201(1), 247-258.
• Sanders, P. 1998. Randomized Priority Queues for Fast Parallel Access, Journal of Parallel and Distributed Computing 49, pp. 86-97.
• Stewart, W. J. 2009. Probability, Markov Chains, Queues, and Simulation, Princeton University Press, United Kingdom.