The M/G/1 queue with processor sharing and its relation to a feedback queue
Queueing Systems: Theory and Applications
Sojourn time approximations in queueing networks with feedback
Performance Evaluation
The BMAP/G/1--·/PH/1/M tandem queue with feedback and losses
Performance Evaluation
Performance modelling of asynchronous replica distribution technique on distributed database systems
International Journal of Computer Mathematics - Distributed Algorithms in Science and Engineering
Response time in a tandem queue with blocking, Markovian arrivals and phase-type services
Operations Research Letters
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The study presented in this paper is motivated by the performance analysis of response times in distributed information systems, where transactions are handled by iterative server and database actions. We model system response times as sojourn times in a two-node open queueing network with a processor sharing (PS) node and a first-come-first-served (FCFS) node. External customers arrive at the PS node according to a Poisson process. After departing from the PS node a customer proceeds to the FCFS node with probability p, and with probability 1 - p the customer departs from the system. After a visit to the FCFS node, customers are fed back to the PS node. The service requirements at both nodes are exponentially distributed. The model is a Jackson network, admitting a product-from solution for the joint number of customers at the nodes, immediately leading to a closed-form expression for the mean sojourn times in steady-state. The variance of the sojourn times, however, does not admit an exact expression-the complexity is caused by the possibility of overtaking. In this paper we propose a methodology for deriving simple, explicit and fast-to-evaluate approximations for the variance of the sojourn times. Numerical results demonstrate that the approximations are very accurate in most model instances.