This book is devoted entirely to the development of the least quadratic problems and their applications. The textbook is an outgrowth of the lecture notes that the author has used in a graduate course for several years in the Department of Mathematics at the University of Wisconsin, Madison. This book has also been complemented by the author's association with the control system group at Honeywell Inc., Minneapolis, MN. This cooperation has yielded a unique and extremely informative textbook that contains a rich body of analysis, design, and/or numerical algorithms that have immediate useful applications in the real control-engineering world. In the preface the author says that his aim in this textbook is to expose a body of materials to an audience, “scientifically literate, but without the extensive preparation in engineering and innocent of most mathematics beyond elementary analysis and linear algebra.” Bridging this gap is one of the unique and excellent features of this textbook.

A virtual circuit (or path) is a full-duplex logical connection between two processes. Two varieties of idealized virtual circuits that differ in their reliability characteristics can be distinguished: simple virtual circuits and reliable virtual circuits. Simple virtual circuits have the basic characteristic that data are transmitted across the circuit with no errors as long as the circuit is operational; however, the circuit may fail at any time. Reliable virtual circuits transmit data reliably at all times, in spite of link or processor failures: any recovery and/or reconfiguration that takes place to reconstruct a failed circuit is totally invisible to the two endpoints; any recovery and/or reconfiguration of a failed endpoint (process or processor) is invisible to the nonfailed end. A simple uniform mechanism for managing simple and reliable virtual circuits and for coping with failures of virtual circuits in a local area computer network is described. The mechanism supports the movement of Virtual circuit endpoints to different machines (as part of reconfiguration following failure, for example), and is robust with respect to the failure of any of the software components involved in the establishment and management of simple virtual circuits.

In systems of asynchronous processes using messagelists with SEND–RECEIVE primitives for interprocess communication recovery primitives are defined to perform state restoration: MARK saves a particular point in the execution of the program; RESTORE resets the system state to an earlier point (saved by MARK); and PURGE discards redundant information when it is no longer needed for possible state restoration.

System state restoration after detection of an error is discussed for producer-consumer systems, with emphasis on the control of the domino effect. Recovery primitives MARK, RESTORE, and PURGE are proposed that, in conjunction with the use of SEND-RECEIVE interprocess communication primitives, allow bounds to be placed on the amount of unnecessary restoration that can occur as a result of system state restoration.

A general class of buddy systems is defined and the overallocation of memory due to internal fragmentation is examined. It is shown that, for a uniform distribution of requests, the overallocation varies between $2x_{1}/(x_{1}+1)$ and $\frac{1}{2}(x_{1}+1)$, where $x_{1}>1$ is the largest real root of the characteristic equation of the particular buddy system. Bounds are found for the overallocation for request distributions characterized by a parameterization of Zipf’s law. The expected value of the overallocation is independent of the request distribution within wide values of the parameter, and is given by $(x_{1}-1)/\ln x_{1}$. For the binary buddy system $x_{1}= 2$; the overallocation varies between 1.33 and 1.50 and the expected value is $\approx 1.44$.

This paper is concerned with error processing for parallel producer-consumer interactions such as encountered in the desing of multi-process operating systems. Solutions to resynchronization problems that occur when a consumer process detects errors in information received from a producer process are presented. Fundamental properties of this error processing are discussed. It is shown that explicit error processing results in an increase in program complexity and a decrease in the ease of understanding a program.