Sample-Path Analysis of Queues

In this paper we provide a survey of sample-path methods in queueing theory, particularly in connection with “distribution-free” analysis such as (i) relations between customer averages and time averages, such as L = λW (Little’s formula); (ii) relations between the stationary distribution of a process and an imbedded process; and (iii) the phenomenon of insensitivity.

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

[2]  J D Littler,et al.  A PROOF OF THE QUEUING FORMULA , 1961 .

[3]  R. M. Loynes,et al.  The stability of a queue with non-independent inter-arrival and service times , 1962, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  Klaus Matthes,et al.  Verallgemeinerungen der Erlangschen Formeln. I , 1963 .

[5]  Dénes König,et al.  Verallgemeinerungen der Erlangschen und Engsetschen Formeln : Eine Methode in der Bedienungstheorie , 1967 .

[6]  William S. Jewell,et al.  A Simple Proof of: L = λW , 1967, Oper. Res..

[7]  Samuel Eilon,et al.  Letter to the Editor - A Simpler Proof of L = λW , 1969, Oper. Res..

[8]  R. Wolff.  Work-conserving priorities , 1970 .

[9]  Shaler Stidham,et al.  On the Optimality of Single-Server Queuing Systems , 1970, Oper. Res..

[10]  William L. Maxwell,et al.  Letter to the Editor - On the Generality of the Equation L = λW , 1970, Oper. Res..

[11]  Gordon F. Newell,et al.  Applications of queueing theory , 1971 .

[12]  S. Brumelle.  On the relation between customer and time averages in queues , 1971 .

[13]  W. Whitt.  Embedded renewal processes in the GI/G/s queue , 1972, Journal of Applied Probability.

[14]  S. Stidham.  Regenerative processes in the theory of queues, with applications to the alternating-priority queue , 1972, Advances in Applied Probability.

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

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

[17]  Carl M. Harris,et al.  Fundamentals of queueing theory , 1975 .

[18]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[19]  F. Kelly,et al.  Networks of queues , 1976, Advances in Applied Probability.

[20]  Austin J. Lemoine.  State-of-the-Art---Networks of Queues---A Survey of Equilibrium Analysis , 1977 .

[21]  Donald F. Towsley,et al.  Product Form and Local Balance in Queueing Networks , 1977, JACM.

[22]  R. Schassberger.  Insensitivity of steady-state distributions of generalized semi-Markov processes by speeds , 1978, Advances in Applied Probability.

[23]  R. Schassberger.  The insensitivity of stationary probabilities in networks of queues , 1978, Advances in Applied Probability.

[24]  Peter J. Denning,et al.  The Operational Analysis of Queueing Network Models , 1978, CSUR.

[25]  M. Miyazawa.  A formal approach to queueing processes in the steady state and their applications , 1979 .

[26]  M. Reiser,et al.  A Queueing Network Analysis of Computer Communication Networks with Window Flow Control , 1979, IEEE Trans. Commun..

[27]  Frank Kelly,et al.  Reversibility and Stochastic Networks , 1979 .

[28]  Stephen S. Lavenberg,et al.  Stationary state probabilities at arrival instants for closed queueing networks with multiple types of customers , 1980, Journal of Applied Probability.

[29]  Peter J. Denning,et al.  Measuring and Calculating Queue Length Distributions , 1980, Computer.

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

[31]  Stephen S. Lavenberg,et al.  Mean-Value Analysis of Closed Multichain Queuing Networks , 1980, JACM.

[32]  Raymond A. Marie,et al.  Calculating equilibrium probabilities for λ(n)/Ck/1/N queues , 1980, Performance.

[33]  Uwe Jansen,et al.  Insensitivity and Steady-state Probabilities in Product Form for Queueing Networks , 1980, J. Inf. Process. Cybern..

[34]  Richard Weber,et al.  Note-On the Marginal Benefit of Adding Servers to G/GI/m Queues , 1980 .

[35]  Tomasz Rolski,et al.  Stationary Random Processes Associated with Point Processes , 1981 .

[36]  Raymond M. Bryant,et al.  On Homogeneity and On Line=Off-Line Behavior in M/G/1 Queueing Systems , 1981, IEEE Transactions on Software Engineering.

[37]  Benjamin Weiss,et al.  A SIMPLE PROOF OF , 1982 .

[38]  Paul J. Schweitzer.  Bottleneck Determination in Networks of Queues , 1982 .

[39]  Ronald W. Wolff,et al.  Poisson Arrivals See Time Averages , 1982, Oper. Res..

[40]  Matthew J. Sobel,et al.  The Optimality of Full Service Policies , 1982, Oper. Res..

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