A note on the GI/GI/infinity system with identical service and interarrival-time distributions
We study the stationary distribution of the number of busy servers in a GI/GI/infinity 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.
gamma distribution infinite-server system busy-server distribution mellin transform