On Bounds for Bulk Arrival Queues

Article Abstract:

A basic and useful method for deriving bounds for bulk arrival queues is given based on the bounds of single arrival queues. Upper bounds of actual and virtual waiting times and mean queue length at random times are found. Lower bounds can be found in a similar fashion. Single server and multiserver systems are considered. Interarrival times, size and service times are individually and severally independent. Service discipline is first come-first serve. Tables of related data are included. Upper bounds for customers in arriving groups are given, first in terms of the random customer and then as to group rates, and tables of system evaluation data for this are given. Single arrival queues can be enlarged for bulk queues without the sacrifice of generality or tightness.

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Product form stationary distributions for the M/G/k group-arrival group-departure loss system under a general acceptance policy

Article Abstract:

A study was conducted to derive a closed-product form of stationary distribution for the numbers of groups of varying sizes in the M/G/k group- arrival group-departure loss system under a general acceptance policy. It is assumed that the accepted customers of each group have equal service times with probability 1 and therefore leave the system together. An algorithm was also developed for calculating the stationary distribution of the number of customers in the system.

Models, Distributions, Theory of (Functional analysis), Theory of distributions, Evaluation, Mathematical models, Stochastic processes, Numerical calculations, Stationary processes

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Parametric nonlinear programming approach to fuzzy queues with bulk service

Article Abstract:

A method of changing a fuzzy queue with bulk services into a bunch of crisp queues with bulk services, by using a parametric nonlinear programming is suggested.

Taiwan, Methods, Usage, Queuing theory, Nonlinear programming

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