The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Optimal flow control schemes that regulate the burstiness of traffic
IEEE/ACM Transactions on Networking (TON)
INFOCOM'96 Proceedings of the Fifteenth annual joint conference of the IEEE computer and communications societies conference on The conference on computer communications - Volume 3
Stability and performance analysis of rate-based feedback flow controlled ATM networks
Queueing Systems: Theory and Applications
PERFORMANCE ANALYSIS OF THE RANDOM EARLY DETECTION ALGORITHM
Probability in the Engineering and Informational Sciences
Stability and Analysis of TCP Connections with RED Control and Exogenous Traffic
Queueing Systems: Theory and Applications
Performance analysis of a fluid queue with random service rate in discrete time
ITC20'07 Proceedings of the 20th international teletraffic conference on Managing traffic performance in converged networks
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We consider a single server queue with the interarrival times and the service times forming a regenerative sequence. This traffic class includes the standard models: \mathit{iid}, periodic, Markov modulated (e.g., BMAP model of Lucantoni [18]) and their superpositions. This class also includes the recently proposed traffic models in high speed networks, exhibiting long range dependence. Under minimal conditions we obtain the rates of convergence to stationary distributions, finiteness of stationary moments, various functional limit theorems and the continuity of stationary distributions and moments. We use the continuity results to obtain approximations for stationary distributions and moments of an MMPP/GI/1 queue where the modulating chain has a countable state space. We extend all our results to feed-forward networks where the external arrivals to each queue can be regenerative. In the end we show that the output process of a leaky bucket is regenerative if the input process is and hence our results extend to a queue with arrivals controlled by a leaky bucket.