THE DEPLETION TIME FOR M/IG/1 SYSTEMS AND A

Waiting-time distributions for M/G/1 systems with priority dependent on class, order of arrival, service length, etc., are difficult to obtain. For singleserver multipurpose processors the difficulties are compounded. A certain ergodic post-arrival depletion time is shown to be a true maximum for all delay times of interest. Explicit numerical evaluation of the distribution of this time is available. A heavy-traffic distribution for this time is shown to provide a simple and useful engineering tool with good results and insensitivity to service-time distribution even at modest traffic intensity levels. The relationship to the diffusion approximation for heavy traffic is described.

[1]  J. Keilson,et al.  The bilateral Laguerre transform , 1981 .

[2]  J. Keilson,et al.  Laguerre transformation as a tool for the numerical solution of integral equations of convolution type , 1979 .

[3]  J. Keilson.  Markov Chain Models--Rarity And Exponentiality , 1979 .

[4]  J. Keilson,et al.  Exponential spectra as a tool for the study of server-systems with several classes of customers , 1978, Journal of Applied Probability.

[5]  J. Keilson,et al.  Monotone matrices and monotone Markov processes , 1977 .

[6]  J. Keilson,et al.  Sojourn times, exit times and jitter in multivariate Markov processes , 1974, Advances in Applied Probability.

[7]  J. Keilson,et al.  MIXTURES OF DISTRIBUTIONS, MOMENT INEQUALITIES AND MEASURES OF EXPONENTIALITY AND NORMALITY' , 1974 .

[8]  Joseph Tomko,et al.  The rate of convergence in limit theorems for service systems with finite queue capacity , 1972, Journal of Applied Probability.

[9]  D. Daley.  Stochastically monotone Markov Chains , 1968 .

[10]  Lajos Takács,et al.  Combinatorial Methods in the Theory of Stochastic Processes , 1967 .

[11]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[12]  J. Keilson.  The First Passage Time Density for Homogeneous Skip-free Walks on the Continuum , 1963 .

[13]  G. F. Newell,et al.  Introduction to the Theory of Queues. , 1963 .

[14]  J. Keilson.  Queues Subject to Service Interruption , 1962 .

[15]  D. Gaver.  A Waiting Line with Interrupted Service, Including Priorities , 1962 .

[16]  J. Keilson,et al.  On Time Dependent Queuing Processes , 1960 .

[17]  L. Takács.  On certain sojourn time problems in the theory of stochastic processes , 1957 .

[18]  J. Conway,et al.  Functions of a Complex Variable , 1964 .

[19]  E. T. Copson,et al.  An introduction to the theory of functions of a complex variable , 1950 .