Introduction to queueing theory (2nd ed)
Introduction to queueing theory (2nd ed)
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Self-similarity in World Wide Web traffic: evidence and possible causes
IEEE/ACM Transactions on Networking (TON)
The Importance of Power-Tail Distributions for Modeling Queueing Systems
Operations Research
A Markovian approach for modeling packet traffic with long-range dependence
IEEE Journal on Selected Areas in Communications
Transient Properties of Many-Server Queues and Related QBDs
Queueing Systems: Theory and Applications
Buffer overflow calculations in a batch arrival queue
ACM SIGMETRICS Performance Evaluation Review
Time to buffer overflow in an MMPP queue
NETWORKING'07 Proceedings of the 6th international IFIP-TC6 conference on Ad Hoc and sensor networks, wireless networks, next generation internet
Buffer overflow period in a constant service rate queue
TELE-INFO'06 Proceedings of the 5th WSEAS international conference on Telecommunications and informatics
The total overflow during a busy cycle in a markov-additive finite buffer system
MMB&DFT'10 Proceedings of the 15th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
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Let τn be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean Eτn and the Laplace transform Ee−sτn is derived in closed form using a martingale introduced in Kella and Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen and Kella (2000) to derive sets of linear equations determining the same quantities. Numerical illustrations are presented in the framework of M/M/1 and MMPP/M/1 with an application to performance evaluation of telecommunication systems with long-range dependent properties in the packet arrival process. Different approximations that are obtained from asymptotic theory are compared with exact numerical results.