The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Automation and Remote Control
Modeling IP traffic using the batch Markovian arrival process
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
A vacation queue with setup and close-down times and batch Markovian arrival processes
Performance Evaluation
Modeling multiple IP traffic streams with rate limits
IEEE/ACM Transactions on Networking (TON)
Lack of Invariant Property of the Erlang Loss Model in Case of MAP Input
Queueing Systems: Theory and Applications
Queueing model with time-phased batch arrivals
ITC20'07 Proceedings of the 20th international teletraffic conference on Managing traffic performance in converged networks
The MAP/M/N retrial queueing system with time-phased batch arrivals
Problems of Information Transmission
A queueing system with batch arrival of customers in sessions
Computers and Industrial Engineering
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A single-server queueing model with finite buffer and flows of customers is considered. Flow means a group of customers which should be sequentially processed in the system. In contrast to the standard batch arrival when a whole group of customers arrives into the system at one epoch, we assume that the customers of an accepted flow arrive one by one in exponentially distributed times. Service time has Phase type (PH) distribution. Generation of flows is described by the Markov Arrival Process (MAP). A flow consists of a random number of customers. This number is geometrically distributed and is not known at a flow arrival epoch. The number of flows, which can be admitted into the system simultaneously, is subject to control. Accepted flow can be lost, with a given probability, in the case of any customer from this flow rejection. Analysis of the joint distribution of the number of flows and customers in the system, flow loss probability and sojourn time distribution is implemented by means of the matrix technique and method of catastrophes. The effect of control on the main performance measures of the system is demonstrated numerically. The influence of correlation in the arrival process of flows, variation of service time and probability of a flow loss in case of any customer from this flow rejection is illustrated.