A matrix-algebraic solution to two Km servers in a loop
Journal of the ACM (JACM) - The MIT Press scientific computation series
Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Stochastic modelling and analysis: a computational approach
Stochastic modelling and analysis: a computational approach
Survey of closed queueing networks with blocking
ACM Computing Surveys (CSUR)
Performance analysis of teletraffic models with renewal distributions
Performance analysis of teletraffic models with renewal distributions
Connection-wise end-to-end performance analysis of queuing networks with MMPP inputs
Performance Evaluation
Decomposition of general tandem queueing networks with MMPP input
Performance Evaluation
Switching and Traffic Theory for Integrated Broadband Networks
Switching and Traffic Theory for Integrated Broadband Networks
IEEE Transactions on Computers
INFORMS Journal on Computing
Explicit solutions of generalized m/g/c//n systems including an analysis of the transient behavior (queueing loops)
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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.