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This special issue includes research papers related to a workshop held at the Royal Society on 21st of September 2010, honouring Erol Gelenbe on his 65th birthday. The workshop brought together some 40 participants including some of Erol's former and current PhD students, colleagues and friends with whom he has interacted over the years, both in Europe and the USA. The papers focus on probability models in computer science, at the core of the field of computer performance engineering, which Erol pioneered. [ABSTRACT FROM AUTHOR]