This introductory textbook is designed for a one-semester course on queueing theory that does not require a course in stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, this book provides a foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students. Containing exercises and examples, this volume may be used as a textbook by first-year graduate and upper-level undergraduate students. The work may also be useful as a self-study reference for applications and further research.
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From the reviews: "This is a new addition to the literature in Queueing Theory, which has been a subject area of intense interest because of its theoretical [richness] and wide applicability. This book has brought a freshness and novelty as it deals mainly with modeling and analysis in applications as well as with statistical inference for queueing problems. The book includes basics of stochastic processes and some mathematical topics, in addition to a chapter written by two computer scientists on modeling and analysis using computational tools, with useful simulation programs...With his 40 years of valuable experience in teaching and high level research in this subject area, Professor Bhat has been able to achieve what he aimed: to make [the work] somewhat different in content and approach from other books."—Assam Statistical Review “The huge range of applications makes queueing theory an interesting object of study for students of mathematics, computer science, operations research and engineering. This book is an introduction to queueing theory. … The book also contains 3 appendices about Poisson and Markov processes and other background material … . the extensive bibliography of the queueing literature (202 references) which is given at the end of the book … help readers to further their research.” (Slobodanka S. Mitrović, Mathematical Reviews, Issue 2010 a)
From the Back Cover
This introductory textbook is designed for a one-semester course on queueing theory that does not require a course in stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, the work provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students in mathematics, statistics, and applied disciplines such as computer science, operations research, and engineering. Key features: * An introductory chapter including a historical account of the growth of queueing theory in the last 100 years. * A modeling-based approach with emphasis on identification of models using topics such as collection of data and tests for stationarity and independence of observations. * Rigorous treatment of the foundations of basic models commonly used in applications with appropriate references for advanced topics. * A chapter on modeling and analysis using computational tools. * A comprehensive treatment of statistical inference for queueing systems. * A discussion of operational and decision problems. * Modeling exercises as a motivational tool, and review exercises covering background material on statistical distributions. An Introduction to Queueing Theory may be used as a textbook by first-year graduate students in fields such as computer science, operations research, industrial and systems engineering, as well as related fields such as manufacturing and communications engineering. Upper-level undergraduate students in mathematics, statistics, and engineering may also use the book in an elective introductory course on queueing theory. With its rigorous coverage of basic material and extensive bibliography of the queueing literature, the work may also be useful to applied scientists and practitioners as a self-study reference for applications and further research.
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Format:Hardcover
This book purports to be a simplified version of a queueing theory textbook WITHOUT much needed probabilistic background. That is missing no doubt, for example Markov Chains theory is nowhere to be found in the book except for few skimpy pages in the appendix. This makes the whole text rather poor mathematically and it could be only considered a textbook for industrial engineering. This intention of making it more "intuitive" can hold on some more elementary level but unfortunately the author himself, when faced with needed deductions, peppers the book with numerous references to more sofisticated treatises and papers, in some cases quite obscure, turning it into a research work for the reader. It looks like the author himself is confused about whom he is writing for. Just take a look at the bibliography.
A total of 17 times the reference for a missing proof or deduction is "Fundamentals of Queueing Theory" by Gross and Harris, which is certainly a vastly superior text leaving the reader with a clear cut question - then why am I reading this book and not Gross/Harris? There is not good answer to that else than to say that the book is shorter! Unfortunately, that means defficient in every way. The best illustration of this defficiency of rigor is the 8th chapter where the author presents "renewal theory," or should we better say his idea of digest of Renewal Theory. Without building up proper rigor, this chapter is a completely unreadable survey, inaccessible to a student who has not learned that elsewhere. Thank god there are other textbooks on stochastic processes where one can find Key Renewal Theorem, Blackwell Theorem and few other things which was "presented" in this short Chapter.
The book is also littered with numerous misprints all over the place. For example on page 115 author introduces d_k group distribution but in definition of probabilities he uses p_k which stands for stationary probabilities. In the first equation (6.1.1) that follows, the index of summation k is written without bounds (should be from 1 to n), then in the next equation (6.1.2) the bounds for k are from 1 to infinity, obviously wrong again making it hard to deduce summation switch. Or on the top of page 111 there are four lines of equations with three misprints (wrong index on the fourth line and two missing powers of -1 in the second and third line), or on page 104 the equation (5.3.26) is missing a power of z^n in the second term on the right side and so on, and on, and on ...
The notation is given without much thought as well, using the same symbol for different things, making it really hard to read. Take a look at the pages 98 and 99. On page 98 the symbol Z_n stands for n-th interarrival, on page 99, right before equation (5.3.5), that is for the number of "potential" services. Or, try to figure out what the superscript (j) in formula (6.7.46) on page 138 stands for ... apparently nothing else than some residue copied from author's notes meaning "single" service time, how bizarre. For the same purpose on the second half of page 137 the author uses superscript (i). The difference is probably due to a misprint. Or the notation F(a,b;c,d) used in one meaning on page 25 and another on page 178, accompanied with misprints as well. In the first 5 chapters the author also uses bizarre notation for piecewise defined functions writing them as a double equality which is fairly confusing until one gets used to it. It looks like the author could not figure out how to make a standard multi-line one-sided bracket for the first five chapters but then he rediscovered this in the sixth chapter! This itself shows how little editing preparation went into publishing of this text. The book contains a number of spelling errors, sentences with math symbols instead of words (for example "=" instead of the word equal) and similar anomalies giving indication there was not even a minor editing available before printing.
It is also interesting to note that when a precision of math language is needed, author resort to meaningless expressions. For example, on the bottom of page 146 it is said that a system of equations (7.3.2) "can be broken up into" another system of equations (7.3.6). What does that mean? This is supposedly explained on the next page where it is said that by "back substitution" we can establish "validity" of this new system. In other words we are suppose to decipher this as "the solutions of the new system satisfy the old system" or ... ? This unmathematical gibberish is occuring typically throughout the text. Lack of precision is always supplemented with reference to some paper or book. For a good laugh check pages 174-176, this is author's idea to explain Little's Law intuitively. The truth is that Little's Law in fractional form L/W=\lambda is very easy to comprehend as it basically shows the rate of leaving the system as (number of customers)/(time each spends) and the rate of leaving the system is equal to the rate of arrival in a stable system. Sure, this is far away from any proof but it is a lot better intuitive idea than silly "example" for which the author wasted two pages while "providing" reference at the end of section. I wonder whether he actually used to teach this to students as it is obvious he does not know to explain simple intuitive idea behind Little's Law. After such a waste of space he embarks on explaining the usage of diffusions in Queueing Theory, in section 9.4. Of course with references to obscure papers. I think it is safe to say he himself has serious problem understanding major concepts of advanced stochastic processes, given the pittance of what has been exhibited elsewhere in this textbook. Another example how author makes a total mess out of fairly trivial algebra is the section 9.5. It is hard to believe this is something an educated mathematician would allow into his publication, I can honestly assume that the author simply did not even read this part of the draft for the text beyond first writing as I am sure he would have noticed how incomprehensible this subsection is. I devoted some effort to it and I can say the deductions are correct but the explanations by the author are lacking. At the end of Chapter 9, in closing remarks the author yet again excuses himself for not being able to provide more sensible treatment and guides the reader to (unidentified) research journals. Rather funny, unfortunately.
Graphics in the book are almost non-existent which is very weird for Queueing Theory text since graphics can help to gain intuition and understanding. Apparently there was no support or effort to do that. Few if any graphics are available and even those are poorly done. For example, on page 170, in general analysis of G/G/1 a figure illustrating concepts is available but with arrow for W(t) pointing to a skew segment when it is obviously the notion of the length of vertical segment. Notion X_4 is attached to a point instead to a vertical segment. Obviously the author and those helping him did not know how to do these graphics correctly. So instead of helping it only creates a confusion.
While the text has a number of examples, still insufficient in my view, there are no solutions to the problems provided. If this is elementary text as assumed then that would be certainly needed. This is a fatal flaw of the book for use as a textbook.
There are also a plenty of errors beyond misprints, both in formulas and in calculations, ambiguous definitions, all that escaped superficial editing. All in all, this book looks like a bare draft for a textbook that was somehow let go into printing, unfortunately. I would strongly suggest to avoid it as a textbook until the author, undoubtedly a capable queueing theorist, proofreads the text, makes corrections, decreases a number of references to obscure papers when faced with the needed deductions and presents a little more deductions instead, changes silly notation, and adds at least a few solutions to the problems. A decent list of symbols would be welcome as well, if nothing else but to make the author himself more accountable for consistency.
As it is now, this is only a potential textbook, perhaps in the second edition. At this point I do not see any value of this text else than as a collection of references to other works. As a textbook, which is what it has been designed for, this book fails. Other than that it is just another proof that lately Springer will publish unedited toilet paper just to make a profit of selling it to libraries. I believe the author is capable of writing a better text on Queueing Theory but he will need to exert a lot more serious effort to be taken seriously, ambitious bibliography cannot replace everything else that is so sorely missing.
A total of 17 times the reference for a missing proof or deduction is "Fundamentals of Queueing Theory" by Gross and Harris, which is certainly a vastly superior text leaving the reader with a clear cut question - then why am I reading this book and not Gross/Harris? There is not good answer to that else than to say that the book is shorter! Unfortunately, that means defficient in every way. The best illustration of this defficiency of rigor is the 8th chapter where the author presents "renewal theory," or should we better say his idea of digest of Renewal Theory. Without building up proper rigor, this chapter is a completely unreadable survey, inaccessible to a student who has not learned that elsewhere. Thank god there are other textbooks on stochastic processes where one can find Key Renewal Theorem, Blackwell Theorem and few other things which was "presented" in this short Chapter.
The book is also littered with numerous misprints all over the place. For example on page 115 author introduces d_k group distribution but in definition of probabilities he uses p_k which stands for stationary probabilities. In the first equation (6.1.1) that follows, the index of summation k is written without bounds (should be from 1 to n), then in the next equation (6.1.2) the bounds for k are from 1 to infinity, obviously wrong again making it hard to deduce summation switch. Or on the top of page 111 there are four lines of equations with three misprints (wrong index on the fourth line and two missing powers of -1 in the second and third line), or on page 104 the equation (5.3.26) is missing a power of z^n in the second term on the right side and so on, and on, and on ...
The notation is given without much thought as well, using the same symbol for different things, making it really hard to read. Take a look at the pages 98 and 99. On page 98 the symbol Z_n stands for n-th interarrival, on page 99, right before equation (5.3.5), that is for the number of "potential" services. Or, try to figure out what the superscript (j) in formula (6.7.46) on page 138 stands for ... apparently nothing else than some residue copied from author's notes meaning "single" service time, how bizarre. For the same purpose on the second half of page 137 the author uses superscript (i). The difference is probably due to a misprint. Or the notation F(a,b;c,d) used in one meaning on page 25 and another on page 178, accompanied with misprints as well. In the first 5 chapters the author also uses bizarre notation for piecewise defined functions writing them as a double equality which is fairly confusing until one gets used to it. It looks like the author could not figure out how to make a standard multi-line one-sided bracket for the first five chapters but then he rediscovered this in the sixth chapter! This itself shows how little editing preparation went into publishing of this text. The book contains a number of spelling errors, sentences with math symbols instead of words (for example "=" instead of the word equal) and similar anomalies giving indication there was not even a minor editing available before printing.
It is also interesting to note that when a precision of math language is needed, author resort to meaningless expressions. For example, on the bottom of page 146 it is said that a system of equations (7.3.2) "can be broken up into" another system of equations (7.3.6). What does that mean? This is supposedly explained on the next page where it is said that by "back substitution" we can establish "validity" of this new system. In other words we are suppose to decipher this as "the solutions of the new system satisfy the old system" or ... ? This unmathematical gibberish is occuring typically throughout the text. Lack of precision is always supplemented with reference to some paper or book. For a good laugh check pages 174-176, this is author's idea to explain Little's Law intuitively. The truth is that Little's Law in fractional form L/W=\lambda is very easy to comprehend as it basically shows the rate of leaving the system as (number of customers)/(time each spends) and the rate of leaving the system is equal to the rate of arrival in a stable system. Sure, this is far away from any proof but it is a lot better intuitive idea than silly "example" for which the author wasted two pages while "providing" reference at the end of section. I wonder whether he actually used to teach this to students as it is obvious he does not know to explain simple intuitive idea behind Little's Law. After such a waste of space he embarks on explaining the usage of diffusions in Queueing Theory, in section 9.4. Of course with references to obscure papers. I think it is safe to say he himself has serious problem understanding major concepts of advanced stochastic processes, given the pittance of what has been exhibited elsewhere in this textbook. Another example how author makes a total mess out of fairly trivial algebra is the section 9.5. It is hard to believe this is something an educated mathematician would allow into his publication, I can honestly assume that the author simply did not even read this part of the draft for the text beyond first writing as I am sure he would have noticed how incomprehensible this subsection is. I devoted some effort to it and I can say the deductions are correct but the explanations by the author are lacking. At the end of Chapter 9, in closing remarks the author yet again excuses himself for not being able to provide more sensible treatment and guides the reader to (unidentified) research journals. Rather funny, unfortunately.
Graphics in the book are almost non-existent which is very weird for Queueing Theory text since graphics can help to gain intuition and understanding. Apparently there was no support or effort to do that. Few if any graphics are available and even those are poorly done. For example, on page 170, in general analysis of G/G/1 a figure illustrating concepts is available but with arrow for W(t) pointing to a skew segment when it is obviously the notion of the length of vertical segment. Notion X_4 is attached to a point instead to a vertical segment. Obviously the author and those helping him did not know how to do these graphics correctly. So instead of helping it only creates a confusion.
While the text has a number of examples, still insufficient in my view, there are no solutions to the problems provided. If this is elementary text as assumed then that would be certainly needed. This is a fatal flaw of the book for use as a textbook.
There are also a plenty of errors beyond misprints, both in formulas and in calculations, ambiguous definitions, all that escaped superficial editing. All in all, this book looks like a bare draft for a textbook that was somehow let go into printing, unfortunately. I would strongly suggest to avoid it as a textbook until the author, undoubtedly a capable queueing theorist, proofreads the text, makes corrections, decreases a number of references to obscure papers when faced with the needed deductions and presents a little more deductions instead, changes silly notation, and adds at least a few solutions to the problems. A decent list of symbols would be welcome as well, if nothing else but to make the author himself more accountable for consistency.
As it is now, this is only a potential textbook, perhaps in the second edition. At this point I do not see any value of this text else than as a collection of references to other works. As a textbook, which is what it has been designed for, this book fails. Other than that it is just another proof that lately Springer will publish unedited toilet paper just to make a profit of selling it to libraries. I believe the author is capable of writing a better text on Queueing Theory but he will need to exert a lot more serious effort to be taken seriously, ambitious bibliography cannot replace everything else that is so sorely missing.
Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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renewal process models, state balance equations, machine interference problem, infinitesimal transition rates, remaining service time, busy cycle, imbedded chain, queue length process, general queue, least positive root, departure epochs, service time distribution, queueing systems, total service time, interarrival period, arrival epochs, mean waiting time, queue discipline, local balance equations, limiting distribution, queueing networks, finite queue, mean value analysis, arriving customer, queueing theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
Simple Markovian Queueing Systems, Springer Science, Business Media, Imbedded Markov Chain Models, The General Queue, Extended Markov Models, The Finite Queue, The Bulk Queue, Decision Problems, System Element Models, Basic Concepts, Other Models, Priority Disciplines Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
renewal process models, state balance equations, machine interference problem, infinitesimal transition rates, remaining service time, busy cycle, imbedded chain, queue length process, general queue, least positive root, departure epochs, service time distribution, queueing systems, total service time, interarrival period, arrival epochs, mean waiting time, queue discipline, local balance equations, limiting distribution, queueing networks, finite queue, mean value analysis, arriving customer, queueing theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
Simple Markovian Queueing Systems, Springer Science, Business Media, Imbedded Markov Chain Models, The General Queue, Extended Markov Models, The Finite Queue, The Bulk Queue, Decision Problems, System Element Models, Basic Concepts, Other Models, Priority Disciplines Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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