Wide-area traffic: the failure of Poisson modeling
SIGCOMM '94 Proceedings of the conference on Communications architectures, protocols and applications
Queueing Systems: Theory and Applications
Traffic Modeling of IP Networks Using the Batch Markovian Arrival Process
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
Dynamics of TCP traffic over ATM networks
IEEE Journal on Selected Areas in Communications
Efficient management of idleness in storage systems
ACM Transactions on Storage (TOS)
The MAP + MAP/PH/1/N queuing system with single and batch arrivals of customers
Automation and Remote Control
Restrained utilization of idleness for transparent scheduling of background tasks
Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems
Computers & Mathematics with Applications
Operations Research Letters
The virtual waiting time in a finite-buffer queue with a single vacation policy
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Analysis of a versatile batch-service queueing model with correlation in the arrival process
Performance Evaluation
Computers and Industrial Engineering
Computers and Industrial Engineering
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We consider a finite-capacity single-server vacation queue with close-down/setup times and batch Markovian arrival process (BMAP), where both the service time, the vacation time, the setup time, and the close-down time are generally distributed. The queueing model has potential applications in SVC (switched virtual connection)-based IP-over-ATM networks and multiple protocol label switched (MPLS) networks. By applying the supplementary variable technique, we develop a unified solution to both the single-vacation and multiple-vacation models and for either the PBAS (partial batch acceptance strategy) or the WBAS (whole batch acceptance strategy) service disciplines. For both models, we obtain the queue length distribution at batch arrival epochs and that at an arbitrary time instant, the loss probability of a whole batch or an arbitrary customer in a batch, server setup rate, server utilization ratio, and the LST of the waiting time distribution. Through the numerical examples, we find that: (1) there is a trade-off between the user's quality-of-service (e.g., loss probabilities, wanting times) and the system performance (e.g., server setup rate, server utilization ratio); (2) the system performance is closely related not only to the first and second order moments of the arrival process but also the pattern (distribution) of the customer arrivals; (3) mean batch size is a much more critical factor to influence the queueing system's performance than the type of batch size distribution. These conclusions are of instructive meanings in the design of IP-over-ATM or more generally MPLS-based networks.