Transient Queueing Analysis

The exact distribution of the nth customer's sojourn time in an M/M/s queue with k customers initially present is derived. Algorithms for computing the covariance between sojourn times for an M/M/1 queue with k customers present at time 0 are also developed. Maple computer code is developed for practical application of transient queue analysis for many system measures of performance without regard to traffic intensity (i.e., the system may be unstable with traffic intensity greater than 1).

[1]  S. Wittevrongel,et al.  Queueing Systems , 2019, Introduction to Stochastic Processes and Simulation.

[2]  Winfried K. Grassmann.  Transient solutions in markovian queueing systems , 1977, Comput. Oper. Res..

[3]  Matthew Rosenshine,et al.  Some New Results for the M/M/1 Queue , 1982 .

[4]  W. David Kelton,et al.  Transient exponential-Erlang queues and steady-state simulation , 1985, CACM.

[5]  Frank Ruskey,et al.  Generating Balanced Parentheses and Binary Trees by Prefix Shifts , 2008, CATS.

[6]  Eric R. Zieyel.  Operations research : applications and algorithms , 1988 .

[7]  Tsuneo Morisaku.  Techniques for data-truncation in digital computer simulation. , 1976 .

[8]  P. R. Parthasarathy.  A transient solution to an M/M/1 queue: a simple approach , 1987, Advances in Applied Probability.

[9]  Gerardo Rubino,et al.  Transient analysis of the M/M/1 queue , 1993, Advances in Applied Probability.

[10]  Averill M. Law,et al.  The Transient Behavior of the M/M/s Queue, with Implications for Steady-State Simulation , 1985, Oper. Res..

[11]  R. Faure,et al.  Introduction to operations research , 1968 .

[12]  R. Stanley.  Enumerative Combinatorics: Volume 1 , 2011 .

[13]  DAVID G. KENDALL,et al.  Introduction to Mathematical Statistics , 1947, Nature.

[14]  R. Stanley,et al.  Enumerative Combinatorics: Index , 1999 .

[15]  Edmundo de Souza e Silva,et al.  Calculating transient distributions of cumulative reward , 1995, SIGMETRICS '95/PERFORMANCE '95.

[16]  Winfried K. Grassmann.  WARM-UP PERIODS IN SIMULATION CAN BE DETRIMENTAL , 2008, Probability in the Engineering and Informational Sciences.

[17]  C. J. Ancker,et al.  The problem of the initial transient in digital computer simulation , 1976, WSC '76.

[18]  W. Whitt,et al.  Transient behavior of the M/M/1 queue via Laplace transforms , 1988, Advances in Applied Probability.

[19]  Charles Hagwood,et al.  An Application of the Residue Calculus: The Distribution of the Sum of Nonhomogeneous Gamma Variates , 2009 .

[20]  Amedeo R. Odoni,et al.  An Empirical Investigation of the Transient Behavior of Stationary Queueing Systems , 1983, Oper. Res..

[21]  Andrew G. Glen,et al.  APPL: A Probability Programming Language , 2001 .