On a synchronization queue with two finite buffers

On a synchronization queue with two finite buffers

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Article ID: iaor2004805
Country: Netherlands
Volume: 36
Issue: 1/3
Start Page Number: 107
End Page Number: 123
Publication Date: Nov 2000
Journal: Queueing Systems
Authors: , ,
Keywords: markov processes
Abstract:

In this paper, we consider a synchronization queue (or synchronization node) consisting of two buffers with finite capacities. One stream of tokens arriving at the system forms a Poisson process and the other forms a PH-renewal process. The tokens are held in the buffers until one is available from each flow, and then a group-token is instantaneously released as a synchronized departure. We show that the output stream of a synchronization queue is a Markov renewal process, and that the time between consecutive departures has a phase type distribution. Thus, we obtain the throughput of this synchronization queue and the loss probabilities of each type of tokens. Moreover, we consider an extended synchronization model with two Poisson streams where a departing group-token consists of several tokens in each buffer.

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