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Mathematical theory of connecting networks and telephone traffic networks and telephone traffic
Book Reviews The following nine chapters contain a wealth of information carefully collected from recent literature including most of 1964; even some results from work still unpublished at that time have been included. The presentation is not intended to be critical, and the literature coverage is not intended to be complete; nevertheless the selection of material appears well balanced. The objections which may be against certain points (e.g., the lack of mention of the fact, very pertinent to the discussion of halo-substituted kete-steroids, that on theoretical grounds substituted fluorine should be expected to have the opposite effect of that of the other halogens because of the difference in polarizability; and the author's declination on p. 249 to classify skewed dienes as inherently dissymmetric chromophores simply on the grounds that "at least one asymmetric center is present in the molecule") appear to be of minor importance in comparison to the value of the book as a whole. Of a particular interest is an appendix (contributed by G. J. Elman and J. I. Brauman) dealing with "Automatic Processing of Circular Dichroism Data". The time invested by the author in his formidable task of organizing and representing most of the contents of upwards of six hundred references will undoubtedly pay good dividends in time-saving for workers in the field of ORD and CD, and it is to be hoped that many of these will benefit from the assistance offered by Pierre Crabbd.
V. E. Benes does not dwell on a detailed description of the literature. Rather he proceeds to initiate a systematic study of telephone traffic with emphasis on structural features of such systems that affect performance. A communication system is simply taken to consist of: a set of terminals; a control unit to process requests for connections; and a connecting network through which the connections are made. The text is mainly concerned with three categories of problems: combinatorial as related to network design; probabalistic for traffic analysis; and variational as related to traffic routing. The emphasis is on basic concepts rather than form~as. The reader of this book should have a working knowledge of modern algebra, basic concepts of probability theory and statistics as well as some acquaintance with combinatorial mathematics, including the use of linear graphs. Chapter 1 provides some general background into the mathematical nature of the problems of modeling connecting networks in essentially nontechnical terms and sketches out the plan of attack for the rest of the book. Chapter 2 is concerned with the structure and combinatorial properties of the connection network as defined and represented in algebraic and topological terms. Use is made of labeled graphs and state diagrams. Chapter 3 discusses new, as well as lmown results, on rearrangeable uetworlm made up of square crossbar switches. This ia dons with FLEMMING WOLDBYE the aid of systematic notation and several theorems. Subsequently the study of netKemisk Labaratorium Denmark Tekniske H~jskole works with the same number of inputs and Copenhagen, Denmark outputs is based on the theory of permutation groups. Finally, attention is fooumd on MATHEMATICAL THEORY OF CONNECTING the synthesis problem for a rearraupable NETWORKS AND TELEPHONE TRAFFIC~ by network with a minimum number of V. E. Benes. Vol. 17: Mathematics in points. Shannon's earlier work on memory Science and Engineering. 313 pages, requirements in a telephone ¢ ~ c l ~ z ~ is diagrams, 6 X 9 in. New York, Academic taken as a point of departure. Press, Inc., 1965. Price $12.00. Chapter 4, unlike all the othea~ is based This research monograph is based largely primarily on the unique work of C. Clos of on the author's extensive work in this area rather than that of the author. The ~ in the past decade. Beginning with a very strictly nonblocking m u l e brief historical sketch of traffic theory since made up of rectangular detailed. Chapter 5 is the turn of the century the author then follows with a critique suggesting the factors theoretical problems an, on responsible for the present state of the theory, urements for obtaining s u f l i c i ~ t . ! aliaparticularly since Erlang's classic work. simple system models. This j Vol. 28I. No. 4, April I ~
Book Reviews cussion of various models and aspects of model selection. Certain parameters of the model are shown to serve as estimators based on four specified statistics. The latter are further taken as random variables with distributions deduced from the model structure. A generating function is found which yields the ioint distribution of the sufficient statistics. Chapter 6 includes a study of the covariance function of a simple stochastic model of a group of telephone trunks. Exact and approximate formulas are deduced for sampling error in traffic measurement. In Chapter 7 a thermodynamic model of random traffic is developed by analogy with the methods of statistical mechanics. This is examined in detail since it is applicable, to any connecting network without regard to its structure. I n spite of its shortcomings, it provides useful concepts and results for more realistic approaches to the problem. The final chapter considers a more realistic model of random traffic with its inherently more complex results. This model takes into account the structure of the network and the method used for routing calls. Theoretical calculations are shewn for establishing the grade of service provided. Each chapter contains an adequate list of references with a general reading list at the end of the book. As may be expected from a research monograph, it is concise, clear and critical throughout. From time to time the author points out problems that remain to be solved. This reviewer found the book remarkably free of typographical and other errors. Minor exceptions include the use of the term "salva" in pages 77-78 with no apparent definition; also, from pages 198-212 one finds "ctnh" used instead of "coth." Although there is a minimum of numerical calculation, an adequate number of tabular and graphical results are included. There is also suitable tie in with existing telephone system practice. On the whole this volume should be of interest to the serious workers in communication system as well as to applied mathematicians. S. D. BEDROSIAN
Moore ~chool of Eledrical Engineering Unizer~ity of Pvnn~yl~ania Philadelphia, Pennsylvania
360
ORGANO-METALLIC SYNTHESIS, edited by John J. Eisch and R. Bruce King. Vol. I: Transition-Metal Compounds, by R. Bruce King. 185 pages, diagrams, 6 X 9 in, New York and London, Academic Press, Inc., 1965. Price, $6.50.
I t is perhaps appropriate that this first volume of a series concerned with the synthetic methods and instrumentation used in organo-metallic synthesis be written by Bruce King who has been one of the foremost investigators in the area of transition metal organometallic compounds. The book is divided into two parts: general techniques; and the preparation of specific transition metal organometallic compounds, the latter section occupying about two-thirds of the text. Much of the first section should be common knowledge to anyone acquainted with synthetic chemistry, and particularly the initial few pages are of a too elementary standard for anyone concerned with the preparations included in the second section. The discussion of the use of infrared, n.m.r., ultraviolet, and visible spectroscopic techniques is, in general, very brief and the utility of the account at this level, other than to accentuate the necessity for considering such approaches in a discussion of structures of organometallie compounds, is not apparent in a book of this type. The second section, however, is an extremely good account and collection of the preparative details and "know-how" involved in this area of chemistry, and illnstrates well the author's command of his discipline. Little doubt remains that this is an excellent addition to the preparative literature, much needed and well-timed, and the reviewer feels there are few inorganic chemists who will not obtain and use this book. J. L~.wIs
Department of Chemistry University of Manch~ter Manchester, England FOUNDATIONS OF SOLID MECHANICS, edited by Y. C. Fung. 525 pages, diagrams, 6 X 9 in. Englewood Cliffs, N. J., PrenticeHall, Inc., 1965. Price, $18.00.
The intention of introducing general methodology into a traditional course in
JoUrnalof The FranklinInititute
V. E. Benes does not dwell on a detailed description of the literature. Rather he proceeds to initiate a systematic study of telephone traffic with emphasis on structural features of such systems that affect performance. A communication system is simply taken to consist of: a set of terminals; a control unit to process requests for connections; and a connecting network through which the connections are made. The text is mainly concerned with three categories of problems: combinatorial as related to network design; probabalistic for traffic analysis; and variational as related to traffic routing. The emphasis is on basic concepts rather than form~as. The reader of this book should have a working knowledge of modern algebra, basic concepts of probability theory and statistics as well as some acquaintance with combinatorial mathematics, including the use of linear graphs. Chapter 1 provides some general background into the mathematical nature of the problems of modeling connecting networks in essentially nontechnical terms and sketches out the plan of attack for the rest of the book. Chapter 2 is concerned with the structure and combinatorial properties of the connection network as defined and represented in algebraic and topological terms. Use is made of labeled graphs and state diagrams. Chapter 3 discusses new, as well as lmown results, on rearrangeable uetworlm made up of square crossbar switches. This ia dons with FLEMMING WOLDBYE the aid of systematic notation and several theorems. Subsequently the study of netKemisk Labaratorium Denmark Tekniske H~jskole works with the same number of inputs and Copenhagen, Denmark outputs is based on the theory of permutation groups. Finally, attention is fooumd on MATHEMATICAL THEORY OF CONNECTING the synthesis problem for a rearraupable NETWORKS AND TELEPHONE TRAFFIC~ by network with a minimum number of V. E. Benes. Vol. 17: Mathematics in points. Shannon's earlier work on memory Science and Engineering. 313 pages, requirements in a telephone ¢ ~ c l ~ z ~ is diagrams, 6 X 9 in. New York, Academic taken as a point of departure. Press, Inc., 1965. Price $12.00. Chapter 4, unlike all the othea~ is based This research monograph is based largely primarily on the unique work of C. Clos of on the author's extensive work in this area rather than that of the author. The ~ in the past decade. Beginning with a very strictly nonblocking m u l e brief historical sketch of traffic theory since made up of rectangular detailed. Chapter 5 is the turn of the century the author then follows with a critique suggesting the factors theoretical problems an, on responsible for the present state of the theory, urements for obtaining s u f l i c i ~ t . ! aliaparticularly since Erlang's classic work. simple system models. This j Vol. 28I. No. 4, April I ~
Book Reviews cussion of various models and aspects of model selection. Certain parameters of the model are shown to serve as estimators based on four specified statistics. The latter are further taken as random variables with distributions deduced from the model structure. A generating function is found which yields the ioint distribution of the sufficient statistics. Chapter 6 includes a study of the covariance function of a simple stochastic model of a group of telephone trunks. Exact and approximate formulas are deduced for sampling error in traffic measurement. In Chapter 7 a thermodynamic model of random traffic is developed by analogy with the methods of statistical mechanics. This is examined in detail since it is applicable, to any connecting network without regard to its structure. I n spite of its shortcomings, it provides useful concepts and results for more realistic approaches to the problem. The final chapter considers a more realistic model of random traffic with its inherently more complex results. This model takes into account the structure of the network and the method used for routing calls. Theoretical calculations are shewn for establishing the grade of service provided. Each chapter contains an adequate list of references with a general reading list at the end of the book. As may be expected from a research monograph, it is concise, clear and critical throughout. From time to time the author points out problems that remain to be solved. This reviewer found the book remarkably free of typographical and other errors. Minor exceptions include the use of the term "salva" in pages 77-78 with no apparent definition; also, from pages 198-212 one finds "ctnh" used instead of "coth." Although there is a minimum of numerical calculation, an adequate number of tabular and graphical results are included. There is also suitable tie in with existing telephone system practice. On the whole this volume should be of interest to the serious workers in communication system as well as to applied mathematicians. S. D. BEDROSIAN
Moore ~chool of Eledrical Engineering Unizer~ity of Pvnn~yl~ania Philadelphia, Pennsylvania
360
ORGANO-METALLIC SYNTHESIS, edited by John J. Eisch and R. Bruce King. Vol. I: Transition-Metal Compounds, by R. Bruce King. 185 pages, diagrams, 6 X 9 in, New York and London, Academic Press, Inc., 1965. Price, $6.50.
I t is perhaps appropriate that this first volume of a series concerned with the synthetic methods and instrumentation used in organo-metallic synthesis be written by Bruce King who has been one of the foremost investigators in the area of transition metal organometallic compounds. The book is divided into two parts: general techniques; and the preparation of specific transition metal organometallic compounds, the latter section occupying about two-thirds of the text. Much of the first section should be common knowledge to anyone acquainted with synthetic chemistry, and particularly the initial few pages are of a too elementary standard for anyone concerned with the preparations included in the second section. The discussion of the use of infrared, n.m.r., ultraviolet, and visible spectroscopic techniques is, in general, very brief and the utility of the account at this level, other than to accentuate the necessity for considering such approaches in a discussion of structures of organometallie compounds, is not apparent in a book of this type. The second section, however, is an extremely good account and collection of the preparative details and "know-how" involved in this area of chemistry, and illnstrates well the author's command of his discipline. Little doubt remains that this is an excellent addition to the preparative literature, much needed and well-timed, and the reviewer feels there are few inorganic chemists who will not obtain and use this book. J. L~.wIs
Department of Chemistry University of Manch~ter Manchester, England FOUNDATIONS OF SOLID MECHANICS, edited by Y. C. Fung. 525 pages, diagrams, 6 X 9 in. Englewood Cliffs, N. J., PrenticeHall, Inc., 1965. Price, $18.00.
The intention of introducing general methodology into a traditional course in
JoUrnalof The FranklinInititute