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The N ‐seasons S ‐servers loss system
Author(s) -
Svoronos Antony,
Green Linda
Publication year - 1987
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198708)34:4<579::aid-nav3220340410>3.0.co;2-k
Subject(s) - poisson distribution , mathematical proof , exponential function , steady state (chemistry) , transient (computer programming) , poisson process , simple (philosophy) , computer science , server , class (philosophy) , state (computer science) , exponential distribution , mathematics , mathematical optimization , statistics , algorithm , computer network , mathematical analysis , artificial intelligence , philosophy , chemistry , geometry , epistemology , operating system
We consider a class of loss systems with exponential service times and a Poisson arrival process with a rate that varies periodically among N levels called seasons. For two special cases, we derive transient and steady‐state solutions and provide simple proofs that losses are minimized when the arrival rates for all seasons are equal. In the general case, we describe a straightforward procedure to derive the steady‐state probabilities. We also prove that when S =1, the server is generally busier during the high arrival rate seasons.