Using the Transform Approximation Method to Analyze Queues with Heavy-Tailed Service

A method for preparing a stable vinyl chloride based resin emulsion which comprises a copolymer colloidally dispersed in an aqueous medium, the copolymer having a Tg from 0 DEG to 50 DEG C., about 65 to 90 wt% vinyl chloride, about 5 to 35 wt% ethylene, 0 to 10 wt% olefinically unsaturated copolymerizable monomer and prepared by emulsion polymerization of vinyl chloride, ethylene and, optionally, an olefinically unsaturated comonomer in the presence of about 3 to 15 wt% polyvinyl alcohol as the dispersing agent, the polymerization method comprising (a) forming an aqueous emulsion reaction mixture containing substantially all the polyvinyl alcohol and a portion, preferably at least 5%, of the total vinyl chloride monomer, (b) pressurizing the reaction mixture with an ethylene pressure sufficient to provide the copolymer with a 5 to 35 wt% ethylene content, (c) initiating the reaction mixture by the addition of a free radical generating source and continuing polymerization until the rate of polymerization begins to decrease to provide a prepolymer emulsion, and (d) adding the remaining vinyl chloride at a substantially uniform rate and continuing polymerization until the polymerization reaction is no longer self-sustaining, ethylene being neither withdrawn nor added during the polymerization in one embodiment.

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

[2]  A. Pakes.  ON THE TAILS OF WAITING-TIME DISTRIBUTIONS , 1975 .

[3]  Ward Whitt,et al.  The Fourier-series method for inverting transforms of probability distributions , 1992, Queueing Syst. Theory Appl..

[4]  Walter Willinger,et al.  On the self-similar nature of Ethernet traffic , 1993, SIGCOMM '93.

[5]  W. Whitt,et al.  The transient BMAP/G/l queue , 1994 .

[6]  Ward Whitt,et al.  Waiting-time tail probabilities in queues with long-tail service-time distributions , 1994, Queueing Syst. Theory Appl..

[7]  Ward Whitt,et al.  Numerical Inversion of Laplace Transforms of Probability Distributions , 1995, INFORMS J. Comput..

[8]  C. Klüppelberg,et al.  Subexponential distributions , 1998 .

[9]  Anja Feldmann,et al.  Fitting Mixtures of Exponentials to Long-Tail Distributions to Analyze Network , 1998, Perform. Evaluation.

[10]  M. Crovella,et al.  Heavy-tailed probability distributions in the World Wide Web , 1998 .

[11]  Walter Willinger,et al.  Self-similarity and heavy tails: structural modeling of network traffic , 1998 .

[12]  William G. Marchal,et al.  Distribution Estimation Using Laplace Transforms , 1998, INFORMS J. Comput..

[13]  M. Naldi,et al.  Measurement-based modelling of Internet dial-up access connections , 1999, Comput. Networks.

[14]  Karl Sigman,et al.  Appendix: A primer on heavy-tailed distributions , 1999, Queueing Syst. Theory Appl..

[15]  Lester Lipsky,et al.  The Importance of Power-Tail Distributions for Modeling Queueing Systems , 1999, Oper. Res..

[16]  Søren Asmussen,et al.  Tail asymptotics for M/G/1 type queueing processes with subexponential increments , 1999, Queueing Syst. Theory Appl..

[17]  Carl M. Harris,et al.  Internet-Type Queues with Power-Tailed Interarrival Times and Computational Methods for Their Analysis , 2000, INFORMS J. Comput..

[18]  Ward Whitt,et al.  The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution , 2000, Queueing Syst. Theory Appl..

[19]  A. P. Zwart,et al.  Tail Asymptotics for the Busy Period in the GI/G/1 Queue , 2001, Math. Oper. Res..

[20]  Geert Jan Franx,et al.  A simple solution for the M/D/c waiting time distribution , 2001, Oper. Res. Lett..

[21]  J. Corcoran.  Modelling Extremal Events for Insurance and Finance , 2002 .

[22]  Martin J. Fischer,et al.  An Algorithm to Compute the Waiting Time Distribution for the M/G/1 Queue , 2004, INFORMS J. Comput..