(Batch Markovian Arrival Process). After receiving service at the first stage a customer proceeds to the second stage. The service at the second stage requires a random number of servers. If a customer does not see the required number of free servers it leaves the system forever or waits the releasing of servers.
The waiting period is accompanied by blocking of the first stage server operating. We derive the condition for the stable operation of the system and determine the stationary distribution of the system states at embedded epochs and at arbitrary time.
The main performance measures are calculated. Numerical results are presented. Keywords: queueing system, distribution, Marcov chain, model, queue. Queuing networks are widely used in capacity planning and performance evaluation of computer and communication systems, service centers, manufacturing systems, etc.
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Tandem queues can be used for modeling real-life two-node networks as well as for validation of general networks decomposition algorithms. In particular, the arrival process should be able to capture correlation and burstness since real traffic of modern communication networks exhibits these characteristics.
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We deal with a tandem queue under the assumption that customers arrive according to the.