Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Use of Polya distributions in approximate solutions to nonstationary M/M/s queues
Communications of the ACM - Special issue on simulation modeling and statistical computing
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
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Continuous simulations of queueing networks avoid the statistical sampling problems caused by Monte Carlo operations. Also, one may want to simulate a queueing network as part of a larger continuous simulation. The network considered in this paper is nonstationary, has time-dependent exponential service time, and finite queues which block upstream service if they are at capacity. One approach to simulating the network is to define the entire set of Kolmogorov equations and numerically integrate them. This is impractical because the number of equations is quite large even for modest networks. This paper presents two continuous simulation approximations to the exact solution that reduce the number of equations to be integrated to a manageable number. The independence approximation assumes that the probability of a particular system state is approximated by the product of the probabilities each queueing station assumes a particular state. The partition approximation groups states for each queueing station into subsets and uses a weighting factor applied to joint probabilities calculated under the independence assumption. Results from an illustrative example show that partition approximation is more accurate than the independence assumption; however, the independence approximation does very well.