Analysis of the parallel service model of multiple service requests operating in unsteady mode.

Parallelism of information processing is one of the main principles in the network design. The aim of this paper is to analyze the mathematical models with parallel operating service blocks and common incoming flows.The queuing system with two (three) service blocks with unlimited number of devices is comsidered.. Binary (triplex) flow of service requests comes into every system. We assume that two or three service requests come simultaneously into the system at the arrival time.The first service request comes into the first block, the second service request comes into the second block and the third service request comes into the third one. Every service request takes any of the vacant devices. The service times are exponentially distributed with parameters µ₁ µ_2, µ₃ This defines the dispatching rule.The systems states are defined by the number of devices occupied in every service block.The generating functions for this queuing system under unsteady operating is found. The main probabilistic characteristics of bi- and third-dimensional Markov chains characterizing the number of service requests in every block (subsystem) can be found for every instant.

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