Abstract:We develop an analytical model of multiprocessor with private caches and shared memory and obtain the following results: the instantaneous state probabilities and the steady-state probabilities of the system. Both transient behaviour and equilibrium can be studied and analyzed. We showed that results can be applied to determine the output parameters for both blocking and non-blocking caches.

The present article explores a queuing system with multiple inputs, single server, different service rates, and limited size of the buffer. The system parameters are crucial for the performance of numerous applications. We develop an analytical model of such a system and obtain the following results: steady-state probabilities of the system and system throughput.

We consider a queueing network consisting of multiservers in parallel and connected to a merger queue. All servers have an infinite capacity buffers. The configuration is decomposed into two subsystems: merging multiservers and merger server and then analyzed in isolation. All times are assumed to be exponentially distributed. First we set and solve the equations for the aggregated merger queue, then express the occupancy probabilities of the original queue through the probabilities of the aggregated one, which reduces significantly the number of equations describing the behavior of the network. Using the fore-mentioned result, we derive expressions for the occupancy probabilities and other parameters of the merging queue.

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