OR FORUM - Little's Law as Viewed on Its 50th Anniversary

Fifty years ago, the author published a paper in Operations Research with the title, “A proof for the queuing formula: L D aW ” [Little, J. D. C. 1961. A proof for the queuing formula: L D aW . Oper. Res. 9(3) 383‐387]. Over the years, L D aW has become widely known as “Little’s Law.” Basically, it is a theorem in queuing theory. It has become well known because of its theoretical and practical importance. We report key developments in both areas with the emphasis on practice. In the latter, we collect new material and search for insights on the use of Little’s Law within the fields of operations management and computer architecture. Subject classifications: Little’s Law; queuing theory; operations management; computer engineering; computer

[1]  Neil J. Gunther.  Analyzing computer system performance with Perl::PDQ , 2005 .

[2]  Shaler Stidham,et al.  L = λW: A Discounted Analogue and a New Proof , 1972, Oper. Res..

[3]  R. Escarpit.  Perspectives on Publishing , 1976 .

[4]  Timothy J. Lowe,et al.  Building intuition insights from basic operations management models and principles , 2008 .

[5]  J. Little.  A Proof for the Queuing Formula: L = λW , 1961 .

[6]  K. Sigman.  A Note on a Sample-Path Rate Conservation Law and its Relationship with H = λG , 1991, Advances in Applied Probability.

[7]  Shaler Stidham,et al.  The Relation between Customer and Time Averages in Queues , 1980, Oper. Res..

[8]  Ward Whitt,et al.  A review ofL=λW and extensions , 1991, Queueing Syst. Theory Appl..

[9]  Ronald W. Wolff,et al.  Stochastic Modeling and the Theory of Queues , 1989 .

[10]  Tom W. Berrie,et al.  Queues and Point Processes , 1983 .

[11]  Philip M. Morse,et al.  Queues, Inventories, And Maintenance , 1958 .

[12]  Ronald W. Wolff,et al.  Little's Law and Related Results , 2011 .

[13]  Edward D. Lazowska,et al.  Quantitative system performance - computer system analysis using queueing network models , 1983, Int. CMG Conference.

[14]  A. Chang,et al.  Relationship between cocaine use and coronary artery disease in patients with symptoms consistent with an acute coronary syndrome. , 2011, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[15]  W. Lovejoy,et al.  Little's law flow analysis of observation unit impact and sizing. , 2011, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[16]  D C LittleJohn.  A Proof for the Queuing Formula , 1961 .

[17]  Stanley F. Bullington.  FACTORY PHYSICS: FOUNDATIONS OF MANUFACTURING MANAGEMENT, 2ND EDITION, WALLACE J. HOPP AND MARK L. SPEARMAN, IRWIN MCGRAW-HILL, 2001, 720 PP., ISBN 0-256-24795-1, LIST: $96 , 2001 .

[18]  Ward Whitt,et al.  Extensions of the Queueing Relations L = λW and H = λG , 1989, Oper. Res..

[19]  Masakiyo Miyazawa,et al.  Rate conservation laws: A survey , 1994, Queueing Syst. Theory Appl..

[20]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[21]  S. Stidham,et al.  Sample-Path Analysis of Queueing Systems , 1998 .

[22]  V. Schmidt,et al.  Queues and Point Processes , 1983 .

[23]  Dimitris Bertsimas,et al.  The Distributional Little's Law and Its Applications , 1995, Oper. Res..

[24]  Michael L. George,et al.  Lean Six Sigma : combining Six Sigma quality with lean speed , 2002 .

[25]  G. F. Newell,et al.  A relation between stationary queue and waiting time distributions , 1971, Journal of Applied Probability.

[26]  Wallace J. Hopp,et al.  Factory physics : foundations of manufacturing management , 1996 .

[27]  Shaler Stidham,et al.  Technical Note - A Last Word on L = λW , 1974, Oper. Res..

[28]  John L. Gustafson,et al.  Little's Law , 2011, Encyclopedia of Parallel Computing.

[29]  Shaler Stidham,et al.  Analysis, Design, and Control of Queueing Systems , 2002, Oper. Res..