Queueing networks: rare events and fast simulations

Acknowledgements From the very beginning I would like to thank my supervisor Werner Scheinhardt. I am deeply grateful for the time we spent in the discussions, for his faithful suggestions , his great patience and certainly for the great work atmosphere we had for the last four years. Above all I would like to thank Werner for his help outside the university. I am sure that this thesis could not have its current form without the help and supervision of my promoter Michel Mandjes. I would like to express my gratitude for his irreplaceable ideas, motivation and for steering me in the right direction. Finally, I would like to thank my other promoter and chair of the Stochastic Operations Research group Richard Boucherie for giving me the opportunity to complete my Ph.D. research in The Netherlands. I am also grateful to him for introducing new horizons of precision and accuracy to me. Ridder for their valuable inputs and efforts in reviewing this thesis. I would like to thank all of my SOR colleagues for a pleasant and efficient job climate. My special gratitude goes to my constant officemate Tom Coenen, who was not only an excellent companion, but one of my main guides into Dutch culture. I would like to acknowledge all members of the SOR group: Kamphuis-Kuijpers and Yana Volkovich. My distinct recognition goes to Yana, who was not only a co-worker but a friend, for all great times we had in the past years. I would like to express my gratitude to my former supervisors Victor Goryainov and Alexander Gnedin for arising and maintaining an interest for stochastics in me. and Sabrina for being such great guys. My special appreciation goes to Jon my roommate, friend and a great person to watch ice hockey with. Thanks to Domi for lots of 'Goulash' events, and to Paul for keeping me updated about important changes in Enschede's life. I would like to mention my friends in Russia, 5 6 Anya, Dima and Anton. And of course I am very thankful to my mom, dad and all my family for their support and belief! Last but not least I am infinitely thankful to my girlfriend Katya. It is difficult or even impossible to underestimate her input to my life and to this work in particular. Katya, thank you for your love, understanding, support and everything else you have been doing for …