Analytical observations for a multiservice node

Motivated by a desire to understand a GI/∞ node in a closed queueing network environment, we study in this paper a finite population multiserver model, where the number of processes is equal to the population in the network. We study its steady-state behavior under various scenarios, e.g., the first three moments of the arrival and service distributions. We show that when the arrivals are bursty, an increase in service time variation can actually decrease congestion. Furthermore, such a decrease is also observed for an increase in the skewness in the arrivals. Additionally, several insensitivity properties in limiting behaviors are observed. In particular, the finite population GI/GI///s-loop is insensitive to the service time distribution when the arrival distribution either has an infinite variance (a form of heavy tail), or is highly skewed. In the latter case, the congestion approaches that of the all Markovian system M/M///s-loop. We conclude that the influence of the third moment can be very significant, indicating that the first two moments do not suffice to characterize the performance measures under consideration.