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5 Jun 2020: Specifically, we give an elementaryand fairly short proof of the following asymptotic result,. ... Department of Informatics, Athens University of Economics and Business, Patission 76, Athens 10434, Greece.Email: yiannis@aueb.gr.

5 Jun 2020: D. Cheliotis, I. Kontoyiannis†, M. Loulakis$, S. Toumpis† Department of Mathematics, University of Athens, Panepistimiopolis, 157 84, Athens, Greece. † ... Department of Informatics, Athens University of Economics and Business, Patission 76, 104 34,

5 Jun 2020: Emails: mr622@cam.ac.uk, ta417@cam.ac.uk, sjg30@cam.ac.uk†Department of Electrical Engineering, Linköping University, Linköping, SE-581 83, Sweden. ... Email:tohid.ardeshiri@liu.se‡Department of Informatics, Athens University of Economics and

5 Jun 2020: 2000 AMS Subject Classification: 60J05, 60J10, 37A30, 37A25. Department of Informatics, Athens University of Economics and Business, Patission 76, Athens 10434,Greece. ... Email: yiannis@aueb.gr.I.K. was supported in part by a Sloan Foundation Research

5 Jun 2020: Department of Informatics, Athens University of Economics and Business, Patission 76, Athens 10434,Greece. ... Department of Electrical and Computer Engineering, University of Florida, Gainesville, USA.

5 Jun 2020: Keywords. k-server; probabilistic analysis; on-line algorithms. Department of Informatics and System Sciences, Sapienza University of Rome, Via Ariosto 25, 00185 Rome,Italy. ... Email:nadine.guillotin@univ-lyon1.fr. Department of Informatics, Athens

5 Jun 2020: Department of Informatics, Athens University of Economics and Business, Patission 76, Athens 10434, Greece. ... Email: yiannis@aueb.gr.†I.K. was supported, in part, by a Marie Curie International Outgoing Fellowship, PIOF-GA-2009-235837.‡Department

5 Jun 2020: O. Johnson is with the Department of Mathematics, University of Bristol,Bristol, BS8 1TW, United Kingdom (e-mail: O.Johnson@bristol.ac.uk). ... I. Kontoyiannis is with the Department of Informatics, Athens University ofEconomics and Business, Athens 10434

5 Jun 2020: Email:O.Johnson@bristol.ac.uk. Department of Informatics, Athens University of Economics & Business, Patission 76, Athens 10434,Greece. ... Department of Statistics, Yale University, 24 Hillhouse Avenue, New Haven CT 06511, USA.

5 Jun 2020: C. Gioran and I. Kontoyiannis are with Department of Informatics, Athens University of Economics andBusiness, Patission 76, Athens 10434, Greece. ... 1]. The rest of of the proof is identical, except for thefact that we do not need to invoke the law of