Introduction to queueing networks
Introduction to queueing networks
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Tail asymptotics for M/G/1 type queueing processes with subexponential increments
Queueing Systems: Theory and Applications
A new approach to an N/G/1 queue
Queueing Systems: Theory and Applications
Analysis of Markov Multiserver Retrial Queues with Negative Arrivals
Queueing Systems: Theory and Applications
The BMAP/G/1 QUEUE: A Tutorial
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
A queueing network model with catastrophes and product form solution
Operations Research Letters
Performance of two-stage tandem queues with blocking: the impact of several flows of signals
Performance Evaluation
Heavy-tailed asymptotics for a fluid model driven by an M/G/1 queue
Performance Evaluation
The M/G/1 processor-sharing queue with disasters
Computers & Mathematics with Applications
An initiative for a classified bibliography on G-networks
Performance Evaluation
Proceedings of the 6th International Conference on Queueing Theory and Network Applications
Stability analysis of single server retrial queueing system with Erlang service
Proceedings of the 6th International Conference on Queueing Theory and Network Applications
Bibliography on G-networks, negative customers and applications
Mathematical and Computer Modelling: An International Journal
LU-Factorization Versus Wiener-Hopf Factorization for Markov Chains
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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In this paper, we consider a MAP/G/1 queue with MAP arrivals of negative customers, where there are two types of service times and two classes of removal rules: the RCA and RCH, as introduced in section 2. We provide an approach for analyzing the system. This approach is based on the classical supplementary variable method, combined with the matrix-analytic method and the censoring technique. By using this approach, we are able to relate the boundary conditions of the system of differential equations to a Markov chain of GI/G/1 type or a Markov renewal process of GI/G/1 type. This leads to a solution of the boundary equations, which is crucial for solving the system of differential equations. We also provide expressions for the distributions of stationary queue length and virtual sojourn time, and the Laplace transform of the busy period. Moreover, we provide an analysis for the asymptotics of the stationary queue length of the MAP/G/1 queues with and without negative customers.