Performability Modelling Techniques and Tools

by Haverkort, Boudewijn R.; Marie, Raymond; Rubino, Gerardo; Trivedi, Kishor S.

• ISBN13: 9780471491958
• ISBN10: 0471491950
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-06-08
• Publisher: WILEY

Summary

Computer scientists and engineers will find this excellent overview compulsive reading as will postgraduates and researchers in computer science and related fields.

Author Biography

Boudewijn R. Haverkort is the editor of Performability Modelling : Techniques and Tools, published by Wiley. Raymond Marie is the editor of Performability Modelling : Techniques and Tools, published by Wiley.

Table of Contents

Contributing authors	v
Foreword	xiii
Preface	xvii
Introduction	1	(10)
The performability concept	1	(2)
Mathematical framework	3	(4)
Overview of the book	7	(4)
Queues with Breakdowns	11	(20)
Introduction	11	(1)
The multiprocessor queue with independent interruptions	12	(9)
Generating functions	14	(1)
Matrix-geometric solution	15	(1)
Spectral expansion	16	(1)
Comparison	17	(2)
Asymptotics	19	(2)
Generalizations	21	(4)
Several queues coupled by breakdowns	25	(5)
Conclusion	30	(1)
The Uniformization Method in Performability Analysis	31	(28)
Introduction	31	(2)
The uniformization technique	33	(9)
The basic approach	33	(4)
Extensions to the basic approach	37	(5)
Expected values	42	(5)
Basic results	43	(2)
Additional results	45	(2)
Probability distributions	47	(10)
Conclusions	57	(2)
Closed-Form Solutions for Performability	59	(24)
Introduction	59	(3)
Reward models	62	(1)
Properties of reward model solutions	63	(4)
Definition and genesis of closed-form solutions	67	(7)
Analytical-probabilistic approaches	68	(3)
Direct probabilistic approaches	71	(2)
Computational complexity	73	(1)
Alternative solution of reward models	74	(3)
Conclusions	77	(1)
Appendices	78	(5)
Proof of equation (4.3)	78	(3)
Proof of theorem 4.1	81	(1)
Proof of equation (4.13)	82	(1)
Markov-Reward Models and Hyperbolic Systems	83	(24)
Introduction	84	(4)
Motivation	84	(1)
Markov-reward process	85	(1)
Scope and organization	86	(2)
Duality in Markov-reward models	88	(5)
Dual systems of hyperbolic PDEs	88	(2)
Duality in the transform domain	90	(1)
Dual systems of moment recursions	91	(2)
Method of characteristics and uniformization	93	(9)
Uniformized renewal equation and the MOC	93	(2)
Uniformization as the analytic solution of an infinite set of scalar PDEs	95	(3)
Successive approximation (Picard's method)	98	(2)
Asymptotic properties	100	(2)
Conclusions and future directions	102	(2)
Appendix: Distribution of cumulative operational time	104	(3)
Monotonicity and Error Bound Results	107	(32)
Introduction	107	(3)
Preliminaries and a motivating example	110	(8)
Marginal expectations	111	(1)
Cumulative measures	112	(1)
A performability example	113	(5)
Monotonicity in time	118	(6)
A performability model	119	(1)
Time monotonicity results	119	(4)
A performability application	123	(1)
Comparison results	124	(8)
Introduction	124	(1)
General comparison lemma	125	(2)
A special performability application	127	(5)
Error bound results	132	(6)
General error bound theorem	132	(2)
Two special performability applications	134	(4)
Summary	138	(1)
The Task Completion Time in Degradable Systems	139	(24)
Introduction	139	(2)
The barrier hitting problem	141	(4)
The distribution of the completion time	145	(4)
Applications and extensions	149	(2)
Completion time and Petri nets	151	(9)
Generally Distributed Transitions SPN	152	(2)
Deterministic SPN	154	(1)
Markov Regenerative SPN	155	(1)
Modelling completion time	156	(1)
Petri nets
Numerical examples	157	(3)
Conclusion	160	(3)
Rare Event Simulation	163	(16)
Introduction	164	(2)
Problem statement	166	(1)
Rare event simulation	167	(1)
Importance sampling	167	(3)
Applications of importance sampling	170	(6)
Reliability models	170	(3)
Queueing models	173	(3)
Other models	176	(1)
The splitting method	176	(2)
Acknowledgements	178	(1)
Specification and Construction of Performability Models	179	(44)
Introduction	180	(4)
Performability model specification	184	(17)
Measure specification	186	(4)
Base model specification	190	(8)
Reward structure specification	198	(3)
Performability model construction	201	(20)
Marking-transition algorithms	202	(3)
Detailed base model construction	205	(6)
Reduced base model construction	211	(10)
Summary	221	(2)
A Survey of Performability Modelling Tools	223	(40)
Introduction	223	(2)
A general modelling tool framework	225	(5)
Classifying performability measures	230	(1)
Performability modelling tool survey	231	(28)
DSPN Express	232	(2)
DyQNtool+	234	(2)
Metaphor	236	(1)
Metasan	237	(1)
Metfac	238	(2)
Numas	240	(1)
Panda	241	(1)
Penelope and COSTPN	242	(2)
Penpet	244	(2)
Save	246	(1)
Sharpe and GISharpe	247	(2)
SPNP	249	(2)
Surf-2	251	(1)
Tangram-II	251	(2)
TimeNET	253	(2)
TIPPtool	255	(2)
UltraSAN	257	(2)
Summary and outlook	259	(4)
Bibliography	263	(50)
Concise glossary	313	(2)
Index	315