An approximate analysis of asynchronous, packet-switched buffered banyan networks with blocking
Performance Evaluation - Special issue: performance modeling of parallel processing systems
G-networks with multiple classes of negative and positive customers
Theoretical Computer Science
Probabilistic modelling
Performance Modelling of Communication Networks and Computer Architectures (International Computer S
Performance Modelling of Communication Networks and Computer Architectures (International Computer S
An initiative for a classified bibliography on G-networks
Performance Evaluation
Bibliography on G-networks, negative customers and applications
Mathematical and Computer Modelling: An International Journal
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We obtain the sojourn time probability distribution function at equilibrium for a Markov modulated, multi-server, single queue with generalised exponential (GE) service time distribution and compound Poisson arrivals of both positive and negative customers. Such arrival processes can model both burstiness and correlated traffic and are well suited to models of ATM and other telecommunication networks. Negative customers remove (ordinary) customers in the queue and are similarly correlated and bursty. We consider both the cases where negative customers remove positive customers from the front and the end of the queue and, in the latter case, where a customer currently being served can and cannot be killed by a negative customer. These cases can model an unreliable server or load balancing respectively. The results are obtained as Laplace transforms and can be inverted numerically. The MM CPP/GE/c G-Queue therefore holds the promise of being a viable building block for the analysis of queues and queueing networks with bursty, correlated traffic, incorporating load balancing and node-failures, since the equilibrium behaviour of both queue lengths and response times can be determined in a tractable way.