Performance Evaluation of a Prioritized, Limited Multi-Server Processor-Sharing System That Includes Servers with Various Capacities
We present a prioritized, limited multi-server processor sharing (PS) system where each server has various capacities, and N (≥2) priority classes are allowed in each PS server. In each prioritized, limited server, different service ratio is assigned to each class request, and the number of requests to be processed is limited to less than a certain number. Routing strategies of such prioritized, limited multi-server PS systems that take into account the capacity of each server are also presented, and a performance evaluation procedure for these strategies is discussed. Practical performance measures of these strategies, such as loss probability, mean waiting time, and mean sojourn time, are evaluated via simulation. In the PS server, at the arrival (or departure) of a request, the extension (shortening) of the remaining sojourn time of each request receiving service can be calculated by using the number of requests of each class and the priority ratio. Utilising a simulation program which executes these events and calculations, the performance of the proposed prioritized, limited multi-server PS rule can be analyzed. From the evaluation results, most suitable routing strategy for the loss or waiting system is clarified.
 L. Kleinrock, "Time-Shared Systems: A Theoretical Treatment", J.A.C.M Vol.1, No.14, 242-261 (1967).
 G.Fayolle and I.Mitrani, “Sharing a Processor Among many Job Classes”, J.A.C.M Vol.27, No.3, July 1980. Pp519-532
 E. Altman, K. Avrachenkov and U. Ayesta, “A survey on processor sharing”, Queueing Syst (2006) 53:53-63
 M. Haviv and J. Val, “Mean sojourn times for phase-type discriminatory processor sharing system”, European Journal of Operational Research, 189(2008), 375-386
 G. Yamazaki and H. Sakasegawa, “An optimal design problem for limited sharing systems, Management Science”, vol.33(8), pp.1010--1019 (1987).
 Y. Shikata, W. Katagiri, and Y. Takahashi, “Prioritized Limited Processor-Sharing System with its Performance Analysis”, International Conference on Operations Research, August 30 - 1, 2011 Zurich.
 H.L. Chen, J. Marden, and A. Wierman, “The effect of local scheduling in load balancing designs”, In Proceedings of IEEE INFOCOM, 2009.
 V. Gupta, M. Harchol-Balter, K. Sigman, and W. Whitt, “Analysis of join-the-shortest-queue routing for web server farms”, In Proceedings of Performance, page 180, 2007.
 E. Altman1, U. Ayesta, and B.J. Prabhu, “Load Balancing in Processor Sharing Systems”, Telecommunication Systems, June 2011, Volume 47, Issue 1-2, pp 35-48.
 M. Haviv and T. Roughgarden. “The price of anarchy in an exponential multi-server”, Operations Research Letters, 35:421–426, 2007.
 H. Kameda, E. Altman, O. Pourtallier, J. Li, and Y. Hosokawa. “Paradoxes in performance optimization of distributed systems”, In Proceedings of SSGRR 2000 Computer and ebusiness conference, 2000.
 D. Starobinski and T. Wu. “Performance of server selection algorithms for content replication networks”, In IFIP Networking, 2005.