Optimal design and performance modelling of M/G/1/K queueing systems

Approximating the performance measures of M/G/1/K systems is a difficult, challenging, and important problem for applications in science and engineering. An approach based on a two-moment approximation of the process is presented and is contrasted with an embedded Markov chain approach, Gelenbe's approach, simulation, and finally, the statistics of M/M/1/K systems. The closed form expressions for the different performance measures should be very handy. The use of the approximation in the performance modelling and design of M/G/1/K systems is also explored in order to demonstrate the practical usefulness of the concepts contained within the paper.

[1]  J. A. Buzacott,et al.  Queueing models for a flexible machining station Part I: The diffusion approximation , 1985 .

[2]  Mark C. Springer,et al.  Queueing models for performance analysis: Selection of single station models , 1992 .

[3]  Paul J. Schweitzer,et al.  Buffer overflow calculations using an infinite-capacity model , 1978 .

[4]  Carl M. Harris,et al.  Fundamentals of queueing theory (2nd ed.). , 1985 .

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

[6]  Henk Tijms,et al.  Tables for multi-server queues , 1985 .

[7]  Toshikazu Kimura,et al.  A Transform-Free Approximation for the Finite Capacity M/G/s Queue , 1996, Oper. Res..

[8]  Toshikazu Kimura.  Optimal buffer design of an m/g/s queue with finite capacity ∗ , 1996 .

[9]  Toshikazu Kimura.  Equivalence relations in the approximations for the M/G /s/s + r queue , 2000 .

[10]  Henk C. Tijms,et al.  A Two-Moment Approximation for a Buffer Design Problem Requiring a Small Rejection Probability , 1985, Perform. Evaluation.

[11]  Donald P. Gaver,et al.  Processor Utilization in Multiprogramming Systems via Diffusion Approximations , 1973, Oper. Res..

[12]  W. D. Ray,et al.  Stochastic Models: An Algorithmic Approach , 1995 .

[13]  Randall P. Sadowski,et al.  Simulation with Arena , 1998 .

[14]  Erol Gelenbe,et al.  On Approximate Computer System Models , 1975, JACM.

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

[16]  Henk Tijms,et al.  Heuristics for Finite-Buffer Queues , 1992, Probability in the Engineering and Informational Sciences.

[17]  Genji Yamazaki,et al.  Evaluating the Overflow Probability Using the Infinite Queue , 1993 .

[18]  Donald P. Gaver,et al.  Approximate Models for Processor Utilization in Multiprogrammed Computer Systems , 1973, SIAM J. Comput..