A note on the GI/GI/&infin system with identical service and interarrival-time distributions

Authors: E.A. van Doorn and A.A. Jagers

Abstract: We study the stationary distribution of the number of busy servers in a GI/GI/&infin system in which the service-time distribution is identical to the interarrival-time distribution, and obtain several representations for the variance. As a result we can verify an expression for the variance, conjectured by Rajaratnam and Takawira (IEEE Trans. Vehicular Technol. 50 (2001) 954-970), when the common distribution of interarrival and service times is a gamma distribution.

Keywords: infinite-server system, busy-server distribution, gamma distribution, Mellin transform

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