Nikolaos Limnios - Queueing Theory 1

Figure 8.9.Mean waiting time versus intensity of incoming customers. For a colo... Figure 8.10.Steady-state distributions of gamma distributed interarrival times.... Figure 8.11.Mean waiting time versus shape parameter. For a color version of th... Figure 8.12.Mean interrupted service time versus shape parameter. For a color v... Figure 8.13.Steady-state distributions of gamma distributed retrial times. For ... Figure 8.14.Comparison of steady-state distributions for mode 2. For a color ve... Figure 8.15. Mean waiting time versus intensity of incoming customers of Case 1.... Figure 8.16. Mean waiting time versus intensity of incoming customers of Case 2.... Figure 8.17. Mean waiting time versus intensity of incoming customers of Case 3.... Figure 8.18.Mean successful service time versus intensity of incoming customers... Figure 8.19.Mean successful service time versus intensity of incoming customers... Figure 8.20.Mean successful service time versus intensity of incoming customers... Figure 8.21.Mean waiting time versus intensity of failure rate. For a color ver... Figure 8.22.Steady-state distributions of scenario B. For a color version of th... Figure 8.23. Mean waiting time versus shape parameter, α = β = 0.5. For a color ... Figure 8.24.Mean waiting time versus shape parameter, α = β = 1. For a color ve... Figure 8.25. Mean waiting time versus shape parameter, α = β = 2. For a color ve... Figure 8.26. Mean successful service time versus shape parameter, α = β = 0.5. F... Figure 8.27. Mean successful service time versus shape parameter, α = β = 1. For... Figure 8.28. Mean successful service time versus shape parameter , α = β = 2. For...

6 Chapter 10 Figure 10.1. Function H ( y ) = H ( y , t )

1 Chapter 1 Table 1.1. Mean number in system for the three cases Table 1.2. Complementary Cumulative distributions of interarrival times

2 Chapter 6 Table 6.1. n = 50, k = 2, q = 2 5, ε = 1% Table 6.2. n = 50, ω = 2, q = 2 5, ε = 1% Table 6.3. n = 50, k = 10, q = 2 5, ε = 1% Table 6.4.Estimates of the number of “good” permutations by the fast simulation... Table 6.5. E stimates for the p arameters α ( s ) and β ( s ) Table 6.6. Comparison of exact values with statistical estimates

3 Chapter 8 Table 8.1. Mean sojourn time E ( TS ) of the customer under service at various valu... Table 8.2. Mean number of retrials for various values of λ and α = β Table 8.3. Numerical values of model parameters Table 8.4. Kolmogorov distance between prelimit distribution P ( i ) and the asympt... Table 8.5.Kolmogorov distance between prelimit distribution P(i) and the asympt... Table 8.6.Kolmogorov distance between distribution Ps(i) and approximation of t... Table 8.7.Mean number of retrials in prelimiting and limiting situations for va... Table 8.8. Numerical values of model parameters Table 8.9. Simulation results Table 8.10.Numerical values of parameters of gamma distributed interarrival tim... Table 8.11. Simulation results Table 8.12. Numerical values of parameters of gamma distributed retrial times Table 8.13. Simulation results Table 8.14. Numerical values of model parameters Table 8.15. Numerical results of scenario A Table 8.16. Numerical values of parameters of scenario B Table 8.17. Numerical results of scenario B

1 Cover

2 Table of Contents

3 Title Page SCIENCES Mathematics , Field Director – Nikolaos Limnios Queuing Theory and Applications , Subject Head – Vladimir Anisimov

4 Copyright First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK www.iste.co.uk John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.wiley.com © ISTE Ltd 2020 The rights of Vladimir Anisimov and Nikolaos Limnios to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2019955378 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78945-001-9 ERC code: PE1 Mathematics PE1_21 Application of mathematics in industry and society

5 Preface

6 Begin Reading

7 List of Authors

8 Index

9 End User License Agreement

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