DOMAIN EXTENSIONS OF THE ERLANG LOSS FUNCTION: THEIR SCALABILITY AND ITS APPLICATIONS TO COOPERATIVE GAMES. Issue 4 (5th September 2014)

• Record Type: Journal Article
• Authors: Karsten, Frank; Slikker, Marco; van Houtum, Geert-Jan
• Is Part Of: Probability in the engineering and informational sciences. Volume 28:Issue 4(2014)
• Page Start: 473
• Page End: 488
• Publication Date: 2014-09-05
• Subjects: Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964814000102
• Languages: English
• ISSNs: 0269-9648

Abstract

<abstract abstract-type="normal"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>We prove that several extensions of the classic Erlang loss function to non-integral numbers of servers are scalable: the blocking probability as described by the extension decreases when the offered load and the number of servers <italic>s</italic> are increased with the same relative amount, even when scaling up from integral <italic>s</italic> to non-integral <italic>s</italic>. We use this to prove that when several Erlang loss systems pool their resources for efficiency, various corresponding cooperative games have a non-empty core.</p> </abstract>