Transient Solution to an infinite Server Queue with Varying Arrival and Departure Rate
A. A. El-Sherbiny
DOI : 10.3844/jmssp.2010.1.3
Journal of Mathematics and Statistics
Volume 6, 2010
Problem statement: In many potential application of queueing theory, the transient solution of queueing system is important. Approach: This study presented the transient solution for infinite server queues with Poisson arrivals and exponential service times when the parameters of both distributions are allowed to vary with time. Based on generating functions technique which results in a simple differential equation. Using the properties of Bessel functions in the solution of this differential equation, the solution of an infinite server queues can be given in simple form. Results: The researcher obtained the transient solution an infinite server queues with Poisson arrivals and exponential service times when the parameters of both distributions are allowed to vary with time and prove that some past results are special case from his results. Conclusion: These results indicated that the probabilities can be extracted in a direct way.
© 2010 A. A. El-Sherbiny. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.